Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel

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Salih Al-Khafajy" } ], "publisher": { "@type": "Organization", "name": "F1000Research", "logo": { "@type": "ImageObject", "url": "https://f1000research.com/img/AMP/F1000Research_image.png", "height": 480, "width": 60 } }, "image": { "@type": "ImageObject", "url": "https://f1000research.com/img/AMP/F1000Research_image.png", "height": 1200, "width": 150 }, "description": " Background Peristaltic or undulating flow plays a significant role in various biomedical and industrial processes, where it provides an efficient mechanism for transporting fluids through flexible conduits such as catheters and endoscopic channels. Understanding such flow behavior is essential for improving medical devices and industrial applications involving non-Newtonian fluids. Methods This study investigates the peristaltic motion of a Carreau fluid whose viscosity varies with both temperature and concentration within a flexible, axisymmetric channel composed of two overlapping cylindrical tubes. The outer wall of the channel exhibits a sinusoidal wave pattern, simulating a realistic endoscopic configuration. The governing nonlinear, nonhomogeneous partial differential equations were formulated in cylindrical coordinates under the assumption of a long wavelength and low Reynolds number. The equations were transformed into a dimensionless form and solved using the uniform perturbation method. Graphical analyses were performed using Mathematica software. Results The results illustrate the combined effects of temperature-dependent and concentration-dependent viscosity on the velocity distribution and pressure gradient within the channel. Increasing temperature and solute concentration were found to enhance fluid velocity and reduce flow resistance. Conclusions The study provides a comprehensive understanding of peristaltic transport in variable-viscosity Carreau fluids under realistic physiological conditions. These findings may contribute to optimizing the design and performance of endoscopic and biomedical fluid transport systems. " } { "@context": "http://schema.org", "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": "1", "item": { "@id": "https://f1000research.com/", "name": "Home" } }, { "@type": "ListItem", "position": "2", "item": { "@id": "https://f1000research.com/browse/articles", "name": "Browse" } }, { "@type": "ListItem", "position": "3", "item": { "@id": "https://f1000research.com/articles/15-18/v1", "name": "Analysis of the peristaltic flow of a variable viscosity Carreau fluid..." } } ] } Home Browse Analysis of the peristaltic flow of a variable viscosity Carreau fluid... ALL Metrics - Views Downloads Get PDF Get XML Cite How to cite this article Al-Tamimi Skk and Al-Khafajy DGS. Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.12688/f1000research.172584.1 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. Close Copy Citation Details Export Export Citation Sciwheel EndNote Ref. Manager Bibtex ProCite Sente EXPORT Select a format first Track Share ▬ ✚ Research Article Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] Salwa k. kazem Al-Tamimi https://orcid.org/0009-0007-3841-1795 1 , Dheia G. Salih Al-Khafajy 2 Salwa k. kazem Al-Tamimi https://orcid.org/0009-0007-3841-1795 1 , Dheia G. Salih Al-Khafajy 2 PUBLISHED 07 Jan 2026 Author details Author details 1 Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, AL-Qadisiya, 58001, Iraq 2 Department of Fluid Mechanics, University of Al-Qadisiya, Al-Qadisiya, Al-Qadisiya, 58001, Iraq Salwa k. kazem Al-Tamimi Roles: Conceptualization, Formal Analysis, Investigation, Methodology, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing Dheia G. Salih Al-Khafajy Roles: Conceptualization, Methodology, Supervision, Validation, Writing – Review & Editing OPEN PEER REVIEW DETAILS REVIEWER STATUS This article is included in the Fallujah Multidisciplinary Science and Innovation gateway. Abstract Background Peristaltic or undulating flow plays a significant role in various biomedical and industrial processes, where it provides an efficient mechanism for transporting fluids through flexible conduits such as catheters and endoscopic channels. Understanding such flow behavior is essential for improving medical devices and industrial applications involving non-Newtonian fluids. Methods This study investigates the peristaltic motion of a Carreau fluid whose viscosity varies with both temperature and concentration within a flexible, axisymmetric channel composed of two overlapping cylindrical tubes. The outer wall of the channel exhibits a sinusoidal wave pattern, simulating a realistic endoscopic configuration. The governing nonlinear, nonhomogeneous partial differential equations were formulated in cylindrical coordinates under the assumption of a long wavelength and low Reynolds number. The equations were transformed into a dimensionless form and solved using the uniform perturbation method. Graphical analyses were performed using Mathematica software. Results The results illustrate the combined effects of temperature-dependent and concentration-dependent viscosity on the velocity distribution and pressure gradient within the channel. Increasing temperature and solute concentration were found to enhance fluid velocity and reduce flow resistance. Conclusions The study provides a comprehensive understanding of peristaltic transport in variable-viscosity Carreau fluids under realistic physiological conditions. These findings may contribute to optimizing the design and performance of endoscopic and biomedical fluid transport systems. READ ALL READ LESS Keywords Viscous Carreau fluid, peristaltic flow, endoscopic hollow flexible channel. Corresponding Author(s) Salwa k. kazem Al-Tamimi ( [email protected] ) Dheia G. Salih Al-Khafajy ( [email protected] ) Close Corresponding authors: Salwa k. kazem Al-Tamimi, Dheia G. Salih Al-Khafajy Competing interests: No competing interests were disclosed. Grant information: The author(s) declared that no grants were involved in supporting this work. Copyright: © 2026 Al-Tamimi Skk and Al-Khafajy DGS. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. How to cite: Al-Tamimi Skk and Al-Khafajy DGS. Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.12688/f1000research.172584.1 ) First published: 07 Jan 2026, 15 :18 ( https://doi.org/10.12688/f1000research.172584.1 ) Latest published: 02 Mar 2026, 15 :18 ( https://doi.org/10.12688/f1000research.172584.2 )  There is a newer version of this article available. Suppress this message for one day. 1. Introduction An unique and crucial mechanism for carrying fluids via flexible tubes, undulating flow has several medicinal and industrial uses. The non-Newtonian fluid model that describes the behavior of increasing viscosity, the Carreau model, is the main focus of this work. Ali and Hayat compared the results for Newtonian and Carreau fluids, and they looked at the pumping characteristics, axial pressure gradient, and trapping mechanisms. 7 Using the long wavelength and low Reynolds number assumption, Nadeem and colleagues studied the propagation of peristaltic waves in Carreau fluid down the horizontal side walls of a rectangular duct. 10 Ullah et al. 12 investigated Carreau fluid peristaltic flow in an elastic tube. Peristaltic flow of Jeffrey fluid inside a flexible tube was studied by Al-Khalidi and Al-Khafajy. 6 The most important and consequential property of fluid motion is viscosity. The medical and food industries rely heavily on viscosity, and a number of mathematical models explain how temperature and fluid concentration affect its flow via different channels. Although fluid velocity shows minimal modification with changes in concentration and position within the channel, most research agrees that raising the temperature boosts it. 1 , 11 , 5 , 9 Nadeem et al. 8 investigated the peristaltic flow of a reactive viscous fluid with viscosity that depends on temperature, while Akram and Akbar 2 performed a biological study of Careau nanofluid within an endoscope with changing viscosity. The impact of concentration and temperature on oscillatory flow in an inclined porous channel was investigated by Al-Khafajy and Labban, 4 while the impact of concentration and temperature on the peristaltic flow of a Williamson fluid through an endoscopic hollow flexible channel was studied by Al-Delfi and Al-Khafajy. 3 Previous studies inspired us to study a mathematical model of the flow of a non-Newtonian, incompressible, and variable-viscosity fluid, which is the Carreau fluid (similar to human blood), through a flexible wave channel with a catheter tube in the middle. This fluid is influenced by changes in temperature and concentration at the channel wall. 2. Mathematical formulation We study the peristaltic flow of an incompressible Carreau fluid between two cylinders that are in a central location, with an endoscope in the middle of the main channel that has a flexible wall structured like a sine wave. A cylinder's coordinates are specified by the radius of the channel (R) and the tube's axis (Z). The geometry wall of the flow channel form is r ¯ = r 1 ¯ ( z ¯ , t ¯ ) = a 1 r ¯ = r 2 ¯ ( z ¯ , t ¯ ) = a 2 + b sin ( 2 π γ ( z ¯ − c t ¯ ) ) Here “the unobstructed radius of the pipe” is represented by a 1 , the radius of the disturbed tube is represented by a 2 , b is “amplitude of the peristaltic wave”, γ is “a wave length”, c is “a wave propagation speed”, and t ¯ is “a time”. The basic governing equations of the problem system (1) ∇ . U ¯ = 0 ( continuity equation ) (2) ρ ( U . ¯ ∇ ) U ¯ = ∇ σ ´ + ρg β 1 ( T − T 0 ) + ρg β 2 ( ∁ − ∁ 0 ) ( momentum equation ) (3) T p . ρ ( U . ¯ ∇ ) T = K . ∇ 2 T − ∇ . Q r − Q ( T − T 0 ) ( temperature equation ) (4) ( U . ¯ ∇ ¯ ) ∁ = D n ∇ 2 ∁ + D n K T T n ∇ 2 T ( concentration equation ) Where ∇ 2 = 1 r ∂ ∂ r ( r ∂ ∂ r ) “Laplace operator”, U ¯ = ( U ¯ 1 , 0 , U ¯ 3 ) is “the velocity field”, ρ is a “density”, σ ´ is “the Cauchy stress tensor”, T is “the temperature”, ∁ is a concentration of the fluid, T p is “the specific heat capacity at constant pressure”, Q r is “the radiation heat flux”, D n is “the coefficient of mass diffusivity”, T n is “the mean fluid temperature”, K T is “the thermal diffusion ratio”. The equation of incompressible Carreau fluid with variable viscosity as the distance travelled is given by 7 (5) σ ´ = − P ¯ I ¯ + S ¯ (6) S ¯ = − μ ( T ) [ 1 + ( n − 1 2 ) Γ 2 α ̇ ¯ 2 ] α ̇ ¯ Where S ¯ is “extra stress tensor”, P ¯ "pressure", I ¯ “identity tensor”, μ “dynamic viscosity”, Γ “time constant”, n “dimensionless power law index” and α ̇ is defined as; (7) α ̇ = 1 2 ∑ i = 1 3 ∑ j = 1 3 α ̇ ij α ̇ ji The model can be reduced to a Newtonian model n = 1 or Γ = 0 , so we investigate the case for Γ ≠ 0 . To understand how an elastic wall behaves, the equation L ∗ ∗ = P ¯ − p ¯ 0 , where L ∗ ∗ is “an operator”, which is used to represent the motion of stretched membrane with viscosity damping forces such that, see 3 L ∗ ∗ = B ∂ 4 ∂ Z ¯ 4 − ℂ ∂ 2 ∂ Z ¯ 2 + m ∂ 2 ∂ t ¯ 2 + D ∂ ∂ t ¯ + A L Wall flexural rigidity is denoted by B, longitudinal tension per unit width by ℂ , mass per unit area by m, coefficient of viscous damping by D, and spring stiffness by A L . This is the equation that controls the properties of a flexible wall canal at r ¯ = r 2 ¯ , is obtained as; (8) ∂ P ¯ ∂ Z ¯ = ∂ ∂ Z ¯ ( B ∂ 4 ∂ Z ¯ 4 − ℂ ∂ 2 ∂ Z ¯ 2 + m ∂ 2 ∂ t ¯ 2 + D ∂ ∂ t ¯ + A L ) ( r 2 ¯ ) 3. Solution method For the sake of accuracy in writing the continuity equation and the momentum equations, in addition to the temperature and concentration equations, we use the velocity components U 1 ¯ ( R ¯ , Z ¯ , t ¯ ) and U 3 ¯ ( R ¯ , Z ¯ , t ¯ ) , which represent the radial and axial velocity components, respectively, in an unsteady two-dimensional flow. The fluid temperature and concentration functions are expressed in terms of T = T ( R ¯ , Z ¯ , t ¯ ) and ∁ = ∁ ( R ¯ , Z ¯ , t ¯ ) , respectively. Now, by substituting the governing equations for the problem (1) - (4), we obtain the following system of nonlinear, nonhomogeneous partial differential equations; (9) ∂ U 1 ¯ ∂ R ¯ + U 1 ¯ R ¯ + ∂ U 3 ¯ ∂ Z ¯ = 0 (10) ρ ( ∂ U 1 ¯ ∂ t ¯ + U 1 ¯ ∂ U 1 ¯ ∂ R ¯ + U 3 ¯ ∂ U 1 ¯ ∂ Z ¯ ) = − ∂ p ¯ ∂ R ¯ + 1 R ¯ ∂ ∂ R ¯ ( R ¯ S ¯ R ¯ R ¯ ) + ∂ S ¯ R ¯ Z ¯ ∂ Z ¯ (11) ρ ( ∂ U 3 ¯ ∂ t ¯ + U 1 ¯ ∂ U 3 ¯ ∂ R ¯ + U 3 ¯ ∂ U 3 ¯ ∂ Z ¯ ) = − ∂ p ¯ ∂ Z ¯ + 1 R ¯ ∂ ∂ R ¯ ( R ¯ S ¯ Z ¯ R ¯ ) + ∂ S ¯ Z ¯ Z ¯ ∂ Z ¯ + ρg β 1 ( T − T 0 ) + ρg β 2 ( ∁ − ∁ 0 ) (12) ∂ T ∂ t ¯ + U 1 ¯ ∂ T ∂ R ¯ + U 3 ¯ ∂ T ∂ Z ¯ = T n T p ρ ( 1 R ¯ ∂ T ∂ R ¯ + ∂ 2 T ∂ R ¯ 2 + ∂ 2 T ∂ Z ¯ 2 ) + 16 σ 0 T 2 E 3 k 0 T p ρ ( 1 R ¯ ∂ T ∂ R ¯ + ∂ 2 T ∂ R ¯ 2 ) − q T p ρ ( T − T 0 ) (13) ∂ ∁ ∂ t ¯ + U 1 ¯ ∂ ∁ ∂ R ¯ + U 3 ¯ ∂ ∁ ∂ Z ¯ = D n ( 1 R ¯ ∂ ∁ ∂ R ¯ + ∂ 2 ∁ ∂ R ¯ 2 + ∂ 2 ∁ ∂ Z ¯ 2 ) + D n K T T n ( 1 R ¯ ∂ T ∂ R ¯ + ∂ 2 T ∂ R ¯ 2 + ∂ 2 T ∂ Z ¯ 2 ) The component S ¯ R ¯ Z ¯ of the shear stress is S ¯ R ¯ Z ¯ = μ ( T ) { 1 + ( n − 1 2 ) Γ 2 ( 2 [ ( ∂ U 1 ¯ ∂ R ¯ ) 2 + ( U 1 ¯ R ¯ ) 2 + ( ∂ U 3 ¯ ∂ Z ¯ ) 2 ] + [ ( ∂ U 1 ¯ ∂ Z ¯ + ∂ U 3 ¯ ∂ R ¯ ) 2 ] ) } ( ∂ U 1 ¯ ∂ Z ¯ + ∂ U 3 ¯ ∂ R ¯ ) We use generic and specific frame coordinate transformations as shown below. U 1 ¯ = u 1 ¯ , U 3 ¯ = u 3 ¯ + c , R ¯ = r ¯ , and Z ¯ = z ¯ . Substituting these transformations into a system (9) - (13), we get: (14) ∂ u 1 ¯ ∂ r ¯ + u 1 ¯ r ¯ + ∂ ( u 3 ¯ + c ) ∂ z ¯ = 0 (15) ρ ( ∂ u 1 ¯ ∂ t ¯ + u 1 ¯ ∂ u 1 ¯ ∂ r ¯ + ( u 3 ¯ + c ) ∂ u 1 ¯ ∂ z ¯ ) = − ∂ p ¯ ∂ r ¯ + 1 r ¯ ∂ ∂ r ¯ ( r ¯ S ¯ r ¯ r ¯ ) + ∂ S ¯ r ¯ z ¯ ∂ z ¯ (16) ρ ( ∂ ( u 3 ¯ + c ) ∂ t ¯ + u 1 ¯ ∂ ( u 3 ¯ + c ) ∂ r ¯ + ( u 3 ¯ + c ) ∂ ( u 3 ¯ + c ) ∂ z ¯ ) = − ∂ p ¯ ∂ z ¯ + 1 r ¯ ∂ ∂ r ¯ ( r ¯ S ¯ r ¯ z ¯ ) + ∂ S ¯ z ¯ z ¯ ∂ z ¯ + ρg β 1 ( T − T 0 ) + ρg β 2 ( ∁ − ∁ 0 ) (17) ∂ T ∂ t ¯ + u 1 ¯ ∂ T ∂ r ¯ + ( u 3 ¯ + c ) ∂ T ∂ z ¯ = T n T p ρ ( 1 r ¯ ∂ T ∂ r ¯ + ∂ 2 T ∂ r ¯ 2 + ∂ 2 T ∂ z ¯ 2 ) + 16 σ 0 T 2 E 3 k 0 T p ρ ( 1 r ¯ ∂ T ∂ r ¯ + ∂ 2 T ∂ r ¯ 2 ) − q T p ρ ( T − T 0 ) (18) ∂ ∁ ∂ t ¯ + u 1 ¯ ∂ ∁ ∂ r ¯ + ( u 3 ¯ + c ) ∂ ∁ ∂ z ¯ = D n ( 1 r ¯ ∂ ∁ ∂ r ¯ + ∂ 2 ∁ ∂ r ¯ 2 + ∂ 2 ∁ ∂ z ¯ 2 ) + D n K T T n ( 1 r ¯ ∂ T ∂ r ¯ + ∂ 2 T ∂ r ¯ 2 + ∂ 2 T ∂ z ¯ 2 ) The corresponding boundary conditions of the problem are: (19) u 1 ¯ = 0 , u 3 ¯ + c = 0 , T = T 0 , ∁ = ∁ 1 at r ¯ = r 1 ¯ = a 1 u 1 ¯ = 0 , u 3 ¯ + c = 0 , T = T 1 , ∁ = ∁ 0 at r ¯ = r 2 ¯ = a 2 + b sin ( 2 π γ ( z ¯ − c t ¯ ) ) } Where the motion equation with condition of the elastic wall as follows: (20) ∂ ∂ z ¯ ( B ∂ 4 ∂ Z ¯ 4 − C ∂ 2 ∂ Z ¯ 2 + m ∂ 2 ∂ t ¯ 2 + D ∂ ∂ t ¯ + A L ) ( r 2 ¯ ) = ∂ p ¯ ∂ z ¯ = − ρ ( ∂ ( u 3 ¯ + c ) ∂ t ¯ + u 1 ¯ ∂ ( u 3 ¯ + c ) ∂ r ¯ + ( u 3 ¯ + c ) ∂ ( u 3 ¯ + c ) ∂ z ¯ ) + 1 r ¯ ∂ ∂ r ¯ ( r ¯ S ¯ r ¯ z ¯ ) + ∂ S ¯ z ¯ z ¯ ∂ z ¯ + ρg β 1 ( T − T 0 ) + ρg β 2 ( ∁ − ∁ 0 ) To simplify the governing equations of the problem and to show the important parameters that affect the fluid flow, we introduce the following dimensionless transformations: (21) u 1 = u 1 ¯ γ a 2 c , u 3 = u 3 ¯ c , r = r ¯ a 2 , z = z ¯ γ , S = a 2 S ¯ μ v c , p = a 2 2 p ¯ μ v cγ , φ = b a 2 , t = c t ¯ γ , r 2 = r 2 ¯ a 2 , r 1 = r 1 ¯ a 2 , a 1 a 2 = ε < 1 , Ω = q a 2 2 μ v T p , δ = a 2 γ , Re = ρc a 2 μ v , P r = μ v T p T n , M ( H ) = μ ( T ) μ v , W e = Γc a 2 , α ̇ = a 2 α ̇ ¯ c , R n = K 0 μ T p 4 T 2 E σ 0 , H = T − T 0 T 1 − T 0 , ξ = ∁ − ∁ 0 ∁ 1 − ∁ 0 , G 1 = ρg β 1 a 2 2 ( T 0 − T 1 ) μ v s , G 2 = ρg β 2 a 2 2 ( C 1 − C 0 ) μ v s , S 1 = ρ D n K T ( T 1 − T 0 ) μ v T n ( C 1 − C 0 ) , S 2 = μ v ρ D n } where φ “amplitude ratio”, Re “Reynolds number”, P r “Prandtl number”, R n “thermal radiation parameter”, S 2 “Schmidt number”, S 1 “Soret number”, G 1 “thermal Grashof number”, G 2 “Solutal Grashof number”, δ “dimensionless wave number”, Ω “heat source/sink parameter”, and W e is the Weissenberg number, μ v “viscosity constant”. Substituting Equations (21) into Eqs. (14) - (20) , we reformulate the governing equations and accompanying boundary conditions as follows: (22) ( c γ ) ( ∂ u 1 ∂ r + u 1 r + ∂ u 3 ∂ z ) = 0 (23) Re δ 3 ( ∂ u 1 ∂ t + u 1 ∂ u 1 ∂ r + ( u 3 + 1 ) ∂ u 1 ∂ z ) = − ∂ p ∂ r + δ 1 r ∂ ∂ r ( r S rr ) + δ 2 ∂ S rz ∂ z (24) Re δ ( ∂ u 3 ∂ t + u 1 ∂ u 3 ∂ r + ( u 3 + 1 ) ∂ u 3 ∂ z ) = − ∂ p ∂ z + 1 r ∂ ∂ r ( r S rr ) + δ ∂ S zz ∂ z + G 2 ξ + G 1 H (25) Re δ ( ∂ H ∂ t + u 1 ∂ H ∂ r + ( u 3 + 1 ) ∂ H ∂ z ) = 1 P r ( 1 r ∂ H ∂ r + ∂ 2 H ∂ r 2 + δ 2 ∂ 2 H ∂ z 2 ) + 4 3 Rn ( 1 r ∂ H ∂ r + ∂ 2 H ∂ r 2 ) − ΩH (26) Re δ ( ∂ ξ ∂ t + u 1 ∂ ξ ∂ r + ( u 3 + 1 ) ∂ ξ ∂ z ) = 1 S 2 ( 1 r ∂ ξ ∂ r + ∂ 2 ξ ∂ r 2 + δ 2 ∂ 2 ξ ∂ z 2 ) + S 1 ( 1 r ∂ H ∂ r + ∂ 2 H ∂ r 2 + δ 2 ∂ 2 H ∂ z 2 ) The component S rz of the shear stress in dimensionless transformation form is (27) S rz = M ( H ) { 1 + ( n − 1 2 ) We 2 ( 2 δ 2 [ ( ∂ u 1 ∂ r ) 2 + ( u 1 r ) 2 + ( ∂ u 3 ∂ z ) 2 ] + [ ( δ 2 ∂ u 1 ∂ z + ∂ u 3 ∂ r ) 2 ] ) } ( δ 2 a 2 ∂ u 1 ∂ z + ∂ u 3 ∂ r ) The corresponding dimensionless boundary conditions of the problem are (28) u 1 = 0 , u 3 = − 1 , H = 0 , ξ = 1 at r = r 1 = ε u 1 = 0 , u 3 = − 1 , H = 1 , ξ = 0 at r = r 2 = 1 + φ sin ( 2 π ( z − t ) ) } (29) ( e 1 ∂ 5 ∂ z 5 − e 2 ∂ 3 ∂ z 3 + e 3 ∂ 3 ∂z ∂t 2 + e 4 ∂ 2 ∂z∂t + e 5 ∂ ∂z ) r 2 = 1 r ∂ ∂ r ( r S rz ) + δ ∂ S zz ∂ z − Re δ ( ∂ u 3 ∂ t + u 1 ∂ u 3 ∂ r + ( u 3 + 1 ) ∂ u 3 ∂ z ) + G 2 ξ + G 1 H where e 1 = B a 2 3 μ v c γ 5 is the flexural stiffness of the wall, e 2 = C a 2 3 μ v c γ 3 is the longitudinal tension per unit width, e 3 = mc a 2 3 μ v γ 3 is the mass per unit area, e 4 = D a 2 3 μ v γ 2 is the coefficient of viscid damping, and e 4 = A L a 2 3 μ v cγ is spring stiffness, respectively. It is very difficult to solve the system of Equations (22) - (27) and (29) , so we assume a very small wave number ( δ ≪ 1) concerning the width of the channel to its length. Thus, the system becomes in the following form after abbreviating its writing, taking into account the condition of the flexibility of the outer wall of the flow channel: (30) ( e 1 ∂ 5 ∂ z 5 − e 2 ∂ 3 ∂ z 3 + e 3 ∂ 3 ∂z ∂t 2 + e 4 ∂ 2 ∂z∂t + e 5 ∂ ∂z ) r 2 = 1 r ∂ ∂ r ( r S rz ) + G 2 ξ + G 1 H (31) ( 1 Pr + 4 3 Rn ) ( ∂ 2 H ∂ r 2 + 1 r ∂ H ∂ r ) − ΩH = 0 (32) 1 S 2 ( ∂ 2 ξ ∂ r 2 + 1 r ∂ ξ ∂ r ) + S 1 ( ∂ 2 H ∂ r 2 + 1 r ∂ H ∂ r ) = 0 with (33) S rz = M ( μ ) { 1 + ( n − 1 2 ) We 2 ( ∂ u 3 ∂ r ) 2 } ( ∂ u 3 ∂ r ) 4. Solve the problem This section involves solving the heat and concentration equations, then substituting the result into the velocity equation to solve it. 4.1 Temperature and concentration function The solution to the equations for heat fluid (31) and concentration fluid (32) based on the boundary condition Equation (28) are respectively: H = J [ 0 , i A r ] B 1 + Y [ 0 , − i A r ] B 2 , ξ = B 4 + B 3 log [ r ] + Σ ( − 1 + I [ 0 , A r 2 ] B 1 ) A + Σ ( Y [ 0 , − i A r ] ) B 2 A . where = Ω ( 1 Pr + 4 3 Rn ) , Σ = − S 1 S 2 A , and B 1 = Y [ 0 , − i A ε ] / ( − J [ 0 , i A ε ] Y [ 0 , − i A h ] + J [ 0 , i A h ] Y [ 0 , − i A ε ] ) , B 2 = J [ 0 , i A ε ] / ( J [ 0 , i A ε ] Y [ 0 , − i A h ] − J [ 0 , i A h ] Y [ 0 , − i A ε ] ) . B 3 = − 1 A ( ( Log [ h ] − Log [ ε ] ) ( A + Σ I [ 0 , A h 2 ] B 1 − Σ I [ 0 , A ε 2 ] B 1 + Σ Y [ 0 , − i A h ] B 2 − Σ Y [ 0 , − i A ε ] B 2 ) , B 4 = − 1 A ( Log [ h ] − Log [ ε ] ) ( − A Log [ h ] − Σ Log [ h ] B 1 + Σ I [ 0 , A ε 2 ] Log [ h ] B 1 + Σ Log [ ε ] B 1 − Σ I [ 0 , A h 2 ] Log [ ε ] B 1 + Σ Y [ 0 , − i A ε ] Log [ h ] B 2 − Σ Y [ 0 , − i A h ] Log [ ε ] B 2 ) . 4.3 Velocity function The formula for the velocity equation under the influence of the elasticity of the outer wall of the flow channel, after substituting the shear stress equation in Equation (30) , is (34) ( e 1 ∂ 5 ∂ z 5 − e 2 ∂ 3 ∂ z 3 + e 3 ∂ 3 ∂z ∂t 2 + e 4 ∂ 2 ∂z∂t + e 5 ∂ ∂z ) r 2 = G 2 ξ + G 1 H + 1 r ∂ ∂ r ( r M ( H ) { 1 + ( n − 1 2 ) W e 2 ( ∂ u 3 ∂ r ) 2 } ( ∂ u 3 ∂ r ) ) For the variable viscosity M ( H ) , we use Reynolds’ model of viscosity M ( H ) = e − αH . By using the Maclaurin series, we have M ( H ) = 1 − αH when α ≪ 1 , where α is the coefficient of variable viscosity, the viscosity is fixed at α = 0 . Thus, the final form of the velocity equation will be (35) ( e 1 ∂ 5 ∂ z 5 − e 2 ∂ 3 ∂ z 3 + e 3 ∂ 3 ∂z ∂t 2 + e 4 ∂ 2 ∂z∂t + e 5 ∂ ∂z ) r 2 = G 2 ξ + G 1 H + 1 r ∂ ∂ r ( r ( 1 − αH ) { 1 + ( n − 1 2 ) W e 2 ( ∂ u 3 ∂ r ) 2 } ( ∂ u 3 ∂ r ) ) Equation (35) is a non-linear and non-homogeneous partial differential equation, which is difficult to find an exact solution for it, so the perturbation method (twice in terms of W e parameter first, then in terms of the α parameter) will be used to find the solution to the problem, as follows: First let u 3 = u 30 + W e 2 u 32 + O ( W e 4 ) , and second u 3 i = u 3 i 0 + α u 3 i 1 + O ( α 2 ) , for i = 0 , 2 . Therefore, the final form of the velocity function will be u 3 = ( u 300 + α u 301 ) + W e 2 ( u 320 + α u 321 ) . We will simplify the order of the equations by equating the similar powers of W e and α , respectively. 4.3.1 Zero order system ( W e 0 ) ( e 1 ∂ 5 ∂ z 5 − e 2 ∂ 3 ∂ z 3 + e 3 ∂ 3 ∂ z ∂ t 2 + e 4 ∂ 2 ∂ z ∂ t + e 5 ∂ ∂ z ) r 2 − G 2 ξ − G 1 H = 1 r ∂ u 30 ∂ r − 1 r αH ∂ u 30 ∂ r + ∂ 2 u 30 ∂ r 2 − αH ∂ 2 u 30 ∂ r 2 − α ∂ H ∂ r ( ∂ u 30 ∂ r ) (i) Zero order system ( α 0 ) ( e 1 ∂ 5 ∂ z 5 − e 2 ∂ 3 ∂ z 3 + e 3 ∂ 3 ∂ z ∂ t 2 + e 4 ∂ 2 ∂ z ∂ t + e 5 ∂ ∂ z ) r 2 − G 2 ξ − G 1 H = 1 r ∂ u 300 ∂ r + ∂ 2 u 300 ∂ r 2 The associated boundary conditions u 300 ( r 1 ) = u 300 ( r 2 ) = − 1 . (ii) First order system ( α ) ∂ 2 u 301 ∂ r 2 + 1 r ∂ u 301 ∂ r = H ( 1 r ∂ u 300 ∂ r + ∂ 2 u 300 ∂ r 2 ) − ∂ H ∂ r ( ∂ u 300 ∂ r ) The associated boundary conditions u 301 ( r 1 ) = u 301 ( r 2 ) = 0 . 4.3.2 Second order system ( W e 2 ) Ο = 1 r ∂ u 31 ∂ r + 1 r ( n − 1 2 ) ( ∂ u 30 ∂ r ) 3 − 1 r αH ( n − 1 2 ) ( ∂ u 30 ∂ r ) 3 − 1 r αH ∂ u 31 ∂ r + ∂ 2 u 31 ∂ r 2 + 3 ( n − 1 2 ) ( ∂ u 30 ∂ r ) 2 ( ∂ 2 u 30 ∂ r 2 ) − αH ∂ 2 u 31 ∂ r 2 − 3 αH ( n − 1 2 ) ( ∂ u 30 ∂ r ) 2 ( ∂ 2 u 30 ∂ r 2 ) − α ∂ H ∂ r ( ∂ u 31 ∂ r ) − α ∂ H ∂ r ( n − 1 2 ) ( ∂ u 30 ∂ r ) 3 (i) Zero order system ( α 0 ) ∂ 2 u 310 ∂ r 2 + 1 r ∂ u 310 ∂ r = − 1 r ( n − 1 2 ) ( ∂ u 300 ∂ r ) 3 − 3 ( n − 1 2 ) ( ∂ u 300 ∂ r ) 2 ( ∂ 2 u 300 ∂ r 2 ) The associated boundary conditions u 320 ( r 1 ) = u 320 ( r 2 ) = 0 . (ii) First order system ( α ) ∂ 2 u 311 ∂ r 2 + 1 r ∂ u 311 ∂ r = H ( ∂ 2 u 310 ∂ r 2 + 1 r ∂ u 310 ∂ r ) + 3 ( 1 − n 2 ) ( 1 r ( ∂ u 301 ∂ r ) + ( ∂ 2 u 301 ∂ r 2 ) ) ( ∂ u 300 ∂ r ) 2 − 3 ( n − 1 ) ( ∂ u 300 ∂ r ) ( ∂ u 301 ∂ r ) ( ∂ 2 u 300 ∂ r 2 ) + ( n − 1 2 ) H ( 3 ( ∂ 2 u 300 ∂ r 2 ) ( ∂ u 300 ∂ r ) 2 + 1 r ( ∂ u 300 ∂ r ) 3 ) − ∂ H ∂ r [ ( n − 1 2 ) ( ∂ u 300 ∂ r ) 3 + ( ∂ u 301 ∂ r ) ] The associated boundary conditions u 321 ( r 1 ) = u 321 ( r 2 ) = 0 . We obtain very long solutions for the velocity and stream function, known as u 3 = 1 r ∂ ψ ∂ r , that mean ψ = ∫ r ( ( u 300 + α u 301 ) + W e 2 ( u 320 + α u 321 ) ) dr . The associated constants can be determined using the associated boundary conditions. Therefore, we will discuss these solutions graphically in the next section. 5. Solution analysis Through the graphs of the fluid velocity function, we discussed and analysed the effect of changing temperature on the viscosity of a Carreau fluid and thus on its velocity through a hollow flexible channel. The program “MATHEMATICA 14” was used in this analysis. The following values were adopted to plot the fluid velocity function: e 1 = 0.3 , e 2 = 0.7 , e 3 = 0.5 , e 4 = 0.5 , e 5 = 0.2 , Ω = 0.5 , G 1 = 2 , G 2 = 1 , S 1 = 0.7 , S 2 = 0.3 , R n = 0.5 , P r = 1.7 , ε = 0.2 , φ = 0.15 , W e = 0.2 , α = 0.1 , n = 0.3 . The general shape of the fluid velocity function is a downward-concave curve where the maximum value of the curve is close to the catheter tube around the value of r = 0.3 , also the ends of the curve are close to zero at the walls of the channel (the rigid inner and the flexible outer), which matches the boundary condition of the problem. Through Figures 2 - 9 , we discussed the effect of the important parameters affecting the fluid velocity. We began by examining the elasticity parameters of the outer wall of the flow channel, it was observed when increasing the parameters e 1 , e 2 , and e 5 the velocity fluid increases, as indicated by Figure 2 and Figure 4 . In contrast, the parameters e 3 and e 4 harmed the velocity fluid, as shown in Figure 3 . The temperature and concentration parameters had a mixed effect on the fluid velocity, with increase in the parameters G 1 , G 2 , S 1 , and S 2 the fluid velocity increases, as shown in Figure 5 and Figure 6 . In contrast, increasing parameters Ω , R n , and P r the fluid velocity decreases, as shown in Figure 4 and Figure 7 . We also noticed that the effect of the outer wall wave parameter φ is positive on the fluid velocity, while the catheter tube radius ε hurts the fluid velocity, Figure 8 . As for the two perturbation parameters W e and α , their effect was clear and positive from Figure 9 . Figure 1. The problem ometry. Figure 2. For different values of e 1 and e 2 . Figure 3. For different values of e 3 and e 4 . Figure 4. For different values of Ω and e 5 . Figure 5. For different values of G 1 and G 2 . Figure 6. For different values of S 1 and S 2 . Figure 7. For different values of R n and P r . Figure 8. For different values of φ and ε . Figure 9. For different values of W e and α . Through the Figures 10 - 15 , we discuss the temperature and concentration degree function consists of upward-curving lines that are nearly concave, starting from a value close to zero at the left end and gradually increasing until approaching one at the right end. We notice in the two Figures 10 and 11 that the temperature of the fluid decreases with increase of the variables ε , P r , Ω , and R n , respectively, while the opposite is true in Figure 12 , where the temperature of the fluid increases with increasing φ , t . In Figure 13 , the concentration of the fluid decreases with the increase of the variables φ , t , respectively, while the opposite is true in Figures 14 , and 15 where the concentration of the fluid with increasing, S 1 , S 2 , R n , and Ω . Figure 10. Temperature profile for different values of P r and ε . Figure 11. Temperature profile for different values of R n and Ω . Figure 12. Temperature profile for different values of φ and t . Figure 13. Concentration profile for different values of φ and t . Figure 14. Concentration profile for different values of S 1 and S 2 . Figure 15. Concentration profile for different values of R n and Ω . Through the Figures 16 - 23 , we discuss the trapped boluses that arise as a result of the movement of the fluid through the flow channel and thus take the form of bracelets that move in the direction of the fluid movement. We discussed the influence of some important parameters on the boluses and neglected the parameters that did not have a clear effect on them. We observed an increase in the bolus size by increasing the value of e 1 and e 2 , Figure 16 and Figure 17 , respectively. We observed the opposite effect of the parameter e 3 on the bolus size as they decreased in size, see Figure 18 . While the size of the bolus size expanded with increasing parameters G 2 , ε , φ , W e , and α , see Figure 19 - Figure 23 , respectively. Figure 16. Wave frame streamlines for different values of. Figure 17. Wave frame streamlines for different values of e 2 = 0.6,0.7,0.8 . Figure 18. Wave frame streamlines for different values of e 3 = 0.2,0.3,0.4 . Figure 19. Wave frame streamlines for different values of G 2 = 1 , 3 , 5 . Figure 20. Wave frame streamlines for different values of ε = 0.125,0.15,0.2 . Figure 21. Wave frame streamlines for different values of φ = 0.12,0.14,0.16 . Figure 22. Wave frame streamlines for different values of W e = 0.15,0.2,0.25 . Figure 23. Wave frame streamlines for different values of α = 0.125,0.15,0.2 . Conclusions and Summary Here we will go over the main points that affect the flow of an incompressible Carreau fluid via a flexible endoscopic hollow tube. Utilizing the perturbation method in conjunction with the MATHEMATICA-14 program, we ascertained the velocity function. We visually examined all the results that came from changing different relevant settings. The key points may be summarized as follows: 1- There is a positive correlation between the growth of e 1 , e 2 , W e , φ , e 5 , α , G 1 , G 2 , S 1 , and S 2 while decreases the velocity is due to the increase in parameter e 3 , e 4 , ε , P r , R n and Ω . 2- The trapped bolus expands with an increase e 1 , e 2 , W e , φ , and ε , the trapped bolus shrinks increasing the values of α , e 3 . 3- The following parameters S 1 , S 1 , P r , R n , Ω , G 1 , e 5 , and e 4 , have no effect on the stream function Data availability All data underlying the results presented in this study are contained within the article. The figures were generated directly from analytical mathematical expressions, and no external datasets or numerical data were produced or used. Therefore, no datasets requiring deposition in a public repository are associated with this work. References 1. Akbar NS: Endoscopy analysis for the peristaltic flow of nanofluids containing carbon nanotubes with heat transfer. 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Iraqi Journal of Science. 2022; 63 (12): 5476–5486. Publisher Full Text 7. Ali N, Hayat T: Peristaltic motion of a Carreau fluid in an asymmetric channel. Applied Mathematics and Computation. 2007; 193 (2): 535–552. Publisher Full Text 8. Nadeem S, Akbar NS, Hayat T: Peristaltic flow of reactive viscous fluid with temperature dependent viscosity. Mathematics. 2011; 18 (3): 198–210. 9. Nadeem S, Akbar NS, Hayat T: Numerical analysis for peristaltic transport of Carreau-Yasuda fluid with variable thermal conductivity and convective conditions. Frontiers in Mechanical Engineering. 2015; 10 (3): 300–311. 10. Nadeem S, Akram S, Hayat T, et al. : Peristaltic flow of a Carreau fluid in a rectangular duct. Journal of Fluid Engineering. 2012; 134 (4): 041201. Publisher Full Text 11. Sohail M, Hussain S, Thumma T: Heat and mass transfer analysis of Carreau couple stress nanofluid flow with Cattaneo-Christov heat flux model. Fluid Mechanics and Thermal Sciences. 2022; 8 (1): 19–31. 12. Ullah S, Khan AA, Riaz MB, et al. : The peristaltic flow for Carreau fluid through an elastic channel. Journal of Mechanics of Biological Materials. 2022; 17 (2): 123–135. Comments on this article Comments (0) Version 2 VERSION 2 PUBLISHED 07 Jan 2026 ADD YOUR COMMENT Comment Author details Author details 1 Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, AL-Qadisiya, 58001, Iraq 2 Department of Fluid Mechanics, University of Al-Qadisiya, Al-Qadisiya, Al-Qadisiya, 58001, Iraq Salwa k. kazem Al-Tamimi Roles: Conceptualization, Formal Analysis, Investigation, Methodology, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing Dheia G. Salih Al-Khafajy Roles: Conceptualization, Methodology, Supervision, Validation, Writing – Review & Editing Competing interests No competing interests were disclosed. Grant information The author(s) declared that no grants were involved in supporting this work. Article Versions (2) version 2 Revised Published: 02 Mar 2026, 15:18 https://doi.org/10.12688/f1000research.172584.2 version 1 Published: 07 Jan 2026, 15:18 https://doi.org/10.12688/f1000research.172584.1 Copyright © 2026 Al-Tamimi Skk and Al-Khafajy DGS. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Download Export To Sciwheel Bibtex EndNote ProCite Ref. Manager (RIS) Sente metrics Views Downloads F1000Research - - PubMed Central info_outline Data from PMC are received and updated monthly. - - Citations open_in_new 0 open_in_new 0 open_in_new SEE MORE DETAILS CITE how to cite this article Al-Tamimi Skk and Al-Khafajy DGS. Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.12688/f1000research.172584.1 ) NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS track receive updates on this article Track an article to receive email alerts on any updates to this article. TRACK THIS ARTICLE Share Open Peer Review Current Reviewer Status: ? Key to Reviewer Statuses VIEW HIDE Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Version 1 VERSION 1 PUBLISHED 07 Jan 2026 Views 0 Cite How to cite this report: Marudappa S. Reviewer Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448707 ) The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448707 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 23 Jan 2026 Shekar Marudappa , B. M. S. College of Engineering, Bengaluru, Karnataka, India Not Approved VIEWS 0 https://doi.org/10.5256/f1000research.190322.r448707 The research article titled "Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel”. In its current form the paper is "not recommended for indexing" . ... Continue reading READ ALL The research article titled "Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel”. In its current form the paper is "not recommended for indexing" . The following review details: Major Concerns • Lack of Novelty and Originality: It is noticed that the study does not demonstrate sufficient originality relative to existing literature. The introduction is described as brief and descriptive, failing to identify genuine research gaps or critically analyze prior studies. • Methodological Rigor and Transparency: Key mathematical steps, particularly in the velocity function section (Section 4.3), are either omitted or inadequately explained. Furthermore, multiple mathematical approximations are used without defining their ranges of validity or error bounds , which compromises the reliability of the analysis. • Absence of Validation: The manuscript lacks any form of benchmarking. The results are not compared against known analytical solutions, limiting cases, or previously published studies to confirm their accuracy. • Insufficient Physical Interpretation: The reviewer points out that the results are presented merely as parameter trends (e.g., velocity increasing or decreasing) without providing a clear physical explanation for these behaviors. Consequently, the conclusions are not seen as providing meaningful scientific insight. • Reproducibility Issues: The numerical values used for the graphical analysis are not justified or referenced. While the authors claim all data is contained within the article, the reviewer argues that no explicit analytical expressions or datasets are provided to allow for the independent reproduction of the figures. Minor Concerns • Clarity and Language Quality: The reviewer suggests that the manuscript requires improvements in English language quality , structure, and overall clarity. • Literature Coverage: The article fails to adequately engage with or cite recent developments in the field of peristaltic transport of non-Newtonian fluids. • Parameter Justification: While the authors list values for parameters like flexural stiffness ( χ 1​) and longitudinal tension ( χ 2​) in the solution analysis, there is no explanation provided in the text for why these specific values were chosen. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Partly Are all the source data underlying the results available to ensure full reproducibility? Partly Are the conclusions drawn adequately supported by the results? Partly Competing Interests: No competing interests were disclosed. Reviewer Expertise: Convective flow through porous medium. Biological fluid flow. I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Marudappa S. Reviewer Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448707 ) The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448707 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 02 Mar 2026 Salwa Al-Tamimi , Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq 02 Mar 2026 Author Response We sincerely thank the reviewer for the detailed and constructive comments. We greatly appreciate the time and effort taken to provide feedback, which has significantly helped improve the clarity, scientific ... Continue reading We sincerely thank the reviewer for the detailed and constructive comments. We greatly appreciate the time and effort taken to provide feedback, which has significantly helped improve the clarity, scientific rigor, and overall quality of the manuscript. Below, we provide point-by-point responses to all major and minor concerns: Major Concerns Comment 1: Lack of Novelty and Originality Concern: The study does not demonstrate sufficient originality relative to existing literature. The introduction is brief and descriptive, failing to identify genuine research gaps or critically analyze prior studies. Response: We have substantially revised the Introduction to clearly highlight the novelty of the present study. The revised section now identifies specific gaps in the current literature on peristaltic flow of non-Newtonian fluids with variable viscosity in flexible endoscope channels. We have also critically analyzed prior studies and explicitly stated the unique contributions of this work, including the combined effects of temperature, concentration, and variable viscosity on peristaltic transport Comment 2: Methodological Rigor and Transparency Concern: Key mathematical steps, especially in Section 4.3 (velocity function), are omitted or inadequately explained. Multiple approximations are used without specifying their validity ranges or error bounds. Response: All mathematical derivations in Section 4.3 have been expanded to include detailed intermediate steps. Each approximation used in the analysis is now clearly justified, and its range of validity and expected error bounds are explicitly stated. This ensures transparency and enhances the reliability of the results. Comment 3: Absence of Validation Concern: The manuscript lacks benchmarking against analytical solutions, limiting cases, or previously published studies. Response: A new validation section has been added. The results have been compared with known limiting cases and available published studies on peristaltic flow of non-Newtonian fluids. The comparisons show good agreement, confirming the accuracy and reliability of the proposed model Comment 4: Insufficient Physical Interpretation Concern: Results are presented only as trends without clear physical explanations. Response: The Results and Discussion section has been revised to include detailed physical interpretations of all observed trends. For each figure, we explain the underlying mechanisms influencing velocity, pressure, and concentration profiles, providing meaningful scientific insights. Comment 5: Reproducibility Issues Concern: Numerical values are not justified or referenced, and analytical expressions or datasets are not provided for independent reproduction. Response: All parameter values used in the graphical analysis are now justified with references from previous studies. Additionally, the full analytical expressions and required datasets have been provided in the manuscript and supplementary material, ensuring that all results can be independently reproduced. Minor Concerns Comment 6: Clarity and Language Quality Response: The manuscript has undergone careful proofreading and editing to improve English language quality, clarity, and overall structure. Comment 7: Literature Coverage Response: The Introduction and literature review have been expanded to incorporate recent and relevant studies on peristaltic transport of non-Newtonian fluids. This provides a more comprehensive background and situates the current work within the existing research context. Comment 8: Parameter Justification Response: All parameters used, including flexural stiffness (χ1) and longitudinal tension (χ2), are now justified in the text with references to relevant literature, and their physical significance is discussed We thank the reviewer again for the constructive feedback and hope that the revised manuscript now meets the standards for indexing and publication. We sincerely thank the reviewer for the detailed and constructive comments. We greatly appreciate the time and effort taken to provide feedback, which has significantly helped improve the clarity, scientific rigor, and overall quality of the manuscript. Below, we provide point-by-point responses to all major and minor concerns: Major Concerns Comment 1: Lack of Novelty and Originality Concern: The study does not demonstrate sufficient originality relative to existing literature. The introduction is brief and descriptive, failing to identify genuine research gaps or critically analyze prior studies. Response: We have substantially revised the Introduction to clearly highlight the novelty of the present study. The revised section now identifies specific gaps in the current literature on peristaltic flow of non-Newtonian fluids with variable viscosity in flexible endoscope channels. We have also critically analyzed prior studies and explicitly stated the unique contributions of this work, including the combined effects of temperature, concentration, and variable viscosity on peristaltic transport Comment 2: Methodological Rigor and Transparency Concern: Key mathematical steps, especially in Section 4.3 (velocity function), are omitted or inadequately explained. Multiple approximations are used without specifying their validity ranges or error bounds. Response: All mathematical derivations in Section 4.3 have been expanded to include detailed intermediate steps. Each approximation used in the analysis is now clearly justified, and its range of validity and expected error bounds are explicitly stated. This ensures transparency and enhances the reliability of the results. Comment 3: Absence of Validation Concern: The manuscript lacks benchmarking against analytical solutions, limiting cases, or previously published studies. Response: A new validation section has been added. The results have been compared with known limiting cases and available published studies on peristaltic flow of non-Newtonian fluids. The comparisons show good agreement, confirming the accuracy and reliability of the proposed model Comment 4: Insufficient Physical Interpretation Concern: Results are presented only as trends without clear physical explanations. Response: The Results and Discussion section has been revised to include detailed physical interpretations of all observed trends. For each figure, we explain the underlying mechanisms influencing velocity, pressure, and concentration profiles, providing meaningful scientific insights. Comment 5: Reproducibility Issues Concern: Numerical values are not justified or referenced, and analytical expressions or datasets are not provided for independent reproduction. Response: All parameter values used in the graphical analysis are now justified with references from previous studies. Additionally, the full analytical expressions and required datasets have been provided in the manuscript and supplementary material, ensuring that all results can be independently reproduced. Minor Concerns Comment 6: Clarity and Language Quality Response: The manuscript has undergone careful proofreading and editing to improve English language quality, clarity, and overall structure. Comment 7: Literature Coverage Response: The Introduction and literature review have been expanded to incorporate recent and relevant studies on peristaltic transport of non-Newtonian fluids. This provides a more comprehensive background and situates the current work within the existing research context. Comment 8: Parameter Justification Response: All parameters used, including flexural stiffness (χ1) and longitudinal tension (χ2), are now justified in the text with references to relevant literature, and their physical significance is discussed We thank the reviewer again for the constructive feedback and hope that the revised manuscript now meets the standards for indexing and publication. Competing Interests: No competing interests were disclosed. Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 02 Mar 2026 Salwa Al-Tamimi , Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq 02 Mar 2026 Author Response We sincerely thank the reviewer for the detailed and constructive comments. We greatly appreciate the time and effort taken to provide feedback, which has significantly helped improve the clarity, scientific ... Continue reading We sincerely thank the reviewer for the detailed and constructive comments. We greatly appreciate the time and effort taken to provide feedback, which has significantly helped improve the clarity, scientific rigor, and overall quality of the manuscript. Below, we provide point-by-point responses to all major and minor concerns: Major Concerns Comment 1: Lack of Novelty and Originality Concern: The study does not demonstrate sufficient originality relative to existing literature. The introduction is brief and descriptive, failing to identify genuine research gaps or critically analyze prior studies. Response: We have substantially revised the Introduction to clearly highlight the novelty of the present study. The revised section now identifies specific gaps in the current literature on peristaltic flow of non-Newtonian fluids with variable viscosity in flexible endoscope channels. We have also critically analyzed prior studies and explicitly stated the unique contributions of this work, including the combined effects of temperature, concentration, and variable viscosity on peristaltic transport Comment 2: Methodological Rigor and Transparency Concern: Key mathematical steps, especially in Section 4.3 (velocity function), are omitted or inadequately explained. Multiple approximations are used without specifying their validity ranges or error bounds. Response: All mathematical derivations in Section 4.3 have been expanded to include detailed intermediate steps. Each approximation used in the analysis is now clearly justified, and its range of validity and expected error bounds are explicitly stated. This ensures transparency and enhances the reliability of the results. Comment 3: Absence of Validation Concern: The manuscript lacks benchmarking against analytical solutions, limiting cases, or previously published studies. Response: A new validation section has been added. The results have been compared with known limiting cases and available published studies on peristaltic flow of non-Newtonian fluids. The comparisons show good agreement, confirming the accuracy and reliability of the proposed model Comment 4: Insufficient Physical Interpretation Concern: Results are presented only as trends without clear physical explanations. Response: The Results and Discussion section has been revised to include detailed physical interpretations of all observed trends. For each figure, we explain the underlying mechanisms influencing velocity, pressure, and concentration profiles, providing meaningful scientific insights. Comment 5: Reproducibility Issues Concern: Numerical values are not justified or referenced, and analytical expressions or datasets are not provided for independent reproduction. Response: All parameter values used in the graphical analysis are now justified with references from previous studies. Additionally, the full analytical expressions and required datasets have been provided in the manuscript and supplementary material, ensuring that all results can be independently reproduced. Minor Concerns Comment 6: Clarity and Language Quality Response: The manuscript has undergone careful proofreading and editing to improve English language quality, clarity, and overall structure. Comment 7: Literature Coverage Response: The Introduction and literature review have been expanded to incorporate recent and relevant studies on peristaltic transport of non-Newtonian fluids. This provides a more comprehensive background and situates the current work within the existing research context. Comment 8: Parameter Justification Response: All parameters used, including flexural stiffness (χ1) and longitudinal tension (χ2), are now justified in the text with references to relevant literature, and their physical significance is discussed We thank the reviewer again for the constructive feedback and hope that the revised manuscript now meets the standards for indexing and publication. We sincerely thank the reviewer for the detailed and constructive comments. We greatly appreciate the time and effort taken to provide feedback, which has significantly helped improve the clarity, scientific rigor, and overall quality of the manuscript. Below, we provide point-by-point responses to all major and minor concerns: Major Concerns Comment 1: Lack of Novelty and Originality Concern: The study does not demonstrate sufficient originality relative to existing literature. The introduction is brief and descriptive, failing to identify genuine research gaps or critically analyze prior studies. Response: We have substantially revised the Introduction to clearly highlight the novelty of the present study. The revised section now identifies specific gaps in the current literature on peristaltic flow of non-Newtonian fluids with variable viscosity in flexible endoscope channels. We have also critically analyzed prior studies and explicitly stated the unique contributions of this work, including the combined effects of temperature, concentration, and variable viscosity on peristaltic transport Comment 2: Methodological Rigor and Transparency Concern: Key mathematical steps, especially in Section 4.3 (velocity function), are omitted or inadequately explained. Multiple approximations are used without specifying their validity ranges or error bounds. Response: All mathematical derivations in Section 4.3 have been expanded to include detailed intermediate steps. Each approximation used in the analysis is now clearly justified, and its range of validity and expected error bounds are explicitly stated. This ensures transparency and enhances the reliability of the results. Comment 3: Absence of Validation Concern: The manuscript lacks benchmarking against analytical solutions, limiting cases, or previously published studies. Response: A new validation section has been added. The results have been compared with known limiting cases and available published studies on peristaltic flow of non-Newtonian fluids. The comparisons show good agreement, confirming the accuracy and reliability of the proposed model Comment 4: Insufficient Physical Interpretation Concern: Results are presented only as trends without clear physical explanations. Response: The Results and Discussion section has been revised to include detailed physical interpretations of all observed trends. For each figure, we explain the underlying mechanisms influencing velocity, pressure, and concentration profiles, providing meaningful scientific insights. Comment 5: Reproducibility Issues Concern: Numerical values are not justified or referenced, and analytical expressions or datasets are not provided for independent reproduction. Response: All parameter values used in the graphical analysis are now justified with references from previous studies. Additionally, the full analytical expressions and required datasets have been provided in the manuscript and supplementary material, ensuring that all results can be independently reproduced. Minor Concerns Comment 6: Clarity and Language Quality Response: The manuscript has undergone careful proofreading and editing to improve English language quality, clarity, and overall structure. Comment 7: Literature Coverage Response: The Introduction and literature review have been expanded to incorporate recent and relevant studies on peristaltic transport of non-Newtonian fluids. This provides a more comprehensive background and situates the current work within the existing research context. Comment 8: Parameter Justification Response: All parameters used, including flexural stiffness (χ1) and longitudinal tension (χ2), are now justified in the text with references to relevant literature, and their physical significance is discussed We thank the reviewer again for the constructive feedback and hope that the revised manuscript now meets the standards for indexing and publication. Competing Interests: No competing interests were disclosed. Close Report a concern COMMENT ON THIS REPORT Views 0 Cite How to cite this report: Lakshminarayana PL. Reviewer Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448710 ) The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448710 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 23 Jan 2026 P. Lakshminarayana Lakshminarayana , Vellore Institute of Technology, Vellore, Tamil Nadu, India Approved with Reservations VIEWS 0 https://doi.org/10.5256/f1000research.190322.r448710 This study investigates the peristaltic flow of a variable-viscosity Carreau fluid through a hollow, flexible endoscopic channel under the combined effects of temperature and concentration variations. The analysis highlights the influence of non-Newtonian behaviour on the channel's transport characteristics. ... Continue reading READ ALL This study investigates the peristaltic flow of a variable-viscosity Carreau fluid through a hollow, flexible endoscopic channel under the combined effects of temperature and concentration variations. The analysis highlights the influence of non-Newtonian behaviour on the channel's transport characteristics. I have outlined some constructive feedback and recommendations to improve the manuscript below. Use directional arrows in the figures to clearly illustrate the increasing or decreasing trends of the plotted parameters. Include a detailed analysis of heat transfer characteristics, particularly the Nusselt number, to enhance the thermal performance discussion. Some equations are missing equation numbers. Please ensure that all equations are properly numbered and referenced in the text. Provide appropriate references for the governing equations and the applied boundary conditions. Include a validation of the present model, preferably through comparison with available analytical, numerical, or previously published results. Add a comprehensive Nomenclature section, clearly defining all symbols along with their corresponding SI units. Include a subsection discussing the limitations of the present study and outlining possible future research directions. Carefully recheck all governing equations for mathematical accuracy and consistency. The author (s) should give a proper discussion for every figure presented in the results and discussion section, along with the physical mechanism. Please see the refs: Thermal performance and MHD peristaltic flow of hybrid nanofluid ( Au-Ta /Blood) in an asymmetric conduit with electro-osmosis and shape factor effects; Unveiling the thermally dissipative peristaltic pumping characteristics of hydromagnetic nanofluid in an oblique micro-wavy conduit via artificial neural network-based optimization; Investigation of convective peristaltic flow of non-Newtonian fluids through a non-uniform tapered porous conduit with Ohmic heating and viscous dissipation. In recent years, similar types of work have been investigated by different authors. Therefore, the original purpose of the present efforts and the new findings in this study are not fully described. Please justify. Perform a thorough review to correct grammatical, spelling, and typographical errors throughout the manuscript. Clearly highlight the novelty of the study by explicitly stating what distinguishes this work from existing literature at the end of the Introduction. The literature survey presented in the Introduction is limited. It is recommended to strengthen it by incorporating relevant and recent studies related to magnetohydrodynamics (MHD), peristaltic transport, and perturbation techniques, using the suggested references: Electroosmotic Effects on Peristaltic Transport of Ree-Eyring Nanofluid with Double Diffusive Convection in Symmetric Microchannel; A study on bioconvective peristaltic flow of a Casson nanofluid in a porous uniform/non‐uniform flexible conduit; Investigation of a conducting Casson fluid flow through a porous flexible microfluidic channel with catalytic effects: application in pharmaceutical fluid processing; Convective peristaltic pumping of MHD Ree-Eyring nanofluid in a chemically reacting flexible divergent channel with activation energy and radiation. Check the correctness of all mathematical equations present in the manuscript. Especially, the non-dimensional parameters are displayed in this manuscript. Is this all dimensionally true? The author(s) didn’t provide the validation of the present results with existing studies. Include it in the revised version of the manuscript. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Yes Competing Interests: No competing interests were disclosed. Reviewer Expertise: Heat transfer, Fluid mechanics, Peristaltic Transport I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Lakshminarayana PL. Reviewer Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448710 ) The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448710 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 02 Mar 2026 Salwa Al-Tamimi , Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq 02 Mar 2026 Author Response We sincerely thank the reviewer for the detailed and constructive comments, which have significantly helped improve the scientific quality, clarity, and presentation of the manuscript. All points raised have been ... Continue reading We sincerely thank the reviewer for the detailed and constructive comments, which have significantly helped improve the scientific quality, clarity, and presentation of the manuscript. All points raised have been carefully addressed in the revised version. Detailed responses are provided below: Comment 1: Use directional arrows in the figures to clearly illustrate the increasing or decreasing trends of the plotted parameters. Response: Directional arrows have been added to all figures where appropriate to clearly indicate increasing or decreasing trends of the plotted parameters, enhancing the clarity and readability of the results. Comment 2: Include a detailed analysis of heat transfer characteristics, particularly the Nusselt number, to enhance the thermal performance discussion. Response: A detailed analysis of heat transfer characteristics. Comment 3: Some equations are missing equation numbers. Please ensure that all equations are properly numbered and referenced in the text. Response: All equations in the manuscript have now been carefully numbered and appropriately referenced in the text to ensure consistency and ease of cross-referencing. Comment 4: Provide appropriate references for the governing equations and the applied boundary conditions. Response: All governing equations and boundary conditions have been reviewed and supported with proper references to the relevant literature, ensuring full scientific documentation and credibility. Comment 5: Include a validation of the present model, preferably through comparison with available analytical, numerical, or previously published results. Response: A validation section has been added, where selected cases are compared with published results from similar studies. The comparisons demonstrate good agreement, confirming the accuracy and reliability of the proposed model. Comment 6: Add a comprehensive Nomenclature section, clearly defining all symbols along with their corresponding SI units. Response: A comprehensive Nomenclature section has been included, listing all symbols used in the manuscript along with their definitions and corresponding SI units for clarity and transparency. Comment 7: Include a subsection discussing the limitations of the present study and outlining possible future research directions. Response: A subsection on the limitations of the current study and potential directions for future research has been added at the end of the discussion section to acknowledge constraints and suggest further investigation. Comment 8: Carefully recheck all governing equations for mathematical accuracy and consistency. Response: All governing equations have been thoroughly rechecked for mathematical accuracy and consistency. Any discrepancies have been corrected to ensure full reliability of the results. Comment 9: The authors should provide a proper discussion for every figure presented in the results and discussion section, along with the physical mechanism. Response: Detailed discussions have been added for each figure in the Results and Discussion section, including physical interpretations and underlying mechanisms, following relevant references to similar studies for comparison. Comment 10: The originality and new findings of the study are not fully described. Please justify. Response: The Introduction and Results sections have been revised to clearly highlight the novelty of the study and explicitly state what distinguishes this work from existing literature, including the unique modeling approach and new physical insights. Comment 11: Perform a thorough review to correct grammatical, spelling, and typographical errors throughout the manuscript. Response: The manuscript has undergone a thorough review and all grammatical, spelling, and typographical errors have been corrected to improve clarity and readability. Comment 12: The literature survey presented in the Introduction is limited. Strengthen it by incorporating relevant and recent studies. Response: The literature review in the Introduction has been expanded to include recent studies on magnetohydrodynamics (MHD), peristaltic transport, and perturbation techniques, including the suggested references. This provides a more comprehensive background and places the current study in context with existing research. Comment 13: Check the correctness of all mathematical equations, especially non-dimensional parameters. Are they dimensionally consistent? Response: All mathematical equations, including the non-dimensional parameters, have been carefully checked for dimensional consistency and corrected where necessary. Comment 14: The authors did not provide validation of the present results with existing studies. Include it in the revised manuscript. Response: As mentioned earlier, a validation section has been added, including comparisons with previously published analytical and numerical results, which confirms the accuracy and robustness of the present findings We sincerely thank the reviewer for the detailed and constructive comments, which have significantly helped improve the scientific quality, clarity, and presentation of the manuscript. All points raised have been carefully addressed in the revised version. Detailed responses are provided below: Comment 1: Use directional arrows in the figures to clearly illustrate the increasing or decreasing trends of the plotted parameters. Response: Directional arrows have been added to all figures where appropriate to clearly indicate increasing or decreasing trends of the plotted parameters, enhancing the clarity and readability of the results. Comment 2: Include a detailed analysis of heat transfer characteristics, particularly the Nusselt number, to enhance the thermal performance discussion. Response: A detailed analysis of heat transfer characteristics. Comment 3: Some equations are missing equation numbers. Please ensure that all equations are properly numbered and referenced in the text. Response: All equations in the manuscript have now been carefully numbered and appropriately referenced in the text to ensure consistency and ease of cross-referencing. Comment 4: Provide appropriate references for the governing equations and the applied boundary conditions. Response: All governing equations and boundary conditions have been reviewed and supported with proper references to the relevant literature, ensuring full scientific documentation and credibility. Comment 5: Include a validation of the present model, preferably through comparison with available analytical, numerical, or previously published results. Response: A validation section has been added, where selected cases are compared with published results from similar studies. The comparisons demonstrate good agreement, confirming the accuracy and reliability of the proposed model. Comment 6: Add a comprehensive Nomenclature section, clearly defining all symbols along with their corresponding SI units. Response: A comprehensive Nomenclature section has been included, listing all symbols used in the manuscript along with their definitions and corresponding SI units for clarity and transparency. Comment 7: Include a subsection discussing the limitations of the present study and outlining possible future research directions. Response: A subsection on the limitations of the current study and potential directions for future research has been added at the end of the discussion section to acknowledge constraints and suggest further investigation. Comment 8: Carefully recheck all governing equations for mathematical accuracy and consistency. Response: All governing equations have been thoroughly rechecked for mathematical accuracy and consistency. Any discrepancies have been corrected to ensure full reliability of the results. Comment 9: The authors should provide a proper discussion for every figure presented in the results and discussion section, along with the physical mechanism. Response: Detailed discussions have been added for each figure in the Results and Discussion section, including physical interpretations and underlying mechanisms, following relevant references to similar studies for comparison. Comment 10: The originality and new findings of the study are not fully described. Please justify. Response: The Introduction and Results sections have been revised to clearly highlight the novelty of the study and explicitly state what distinguishes this work from existing literature, including the unique modeling approach and new physical insights. Comment 11: Perform a thorough review to correct grammatical, spelling, and typographical errors throughout the manuscript. Response: The manuscript has undergone a thorough review and all grammatical, spelling, and typographical errors have been corrected to improve clarity and readability. Comment 12: The literature survey presented in the Introduction is limited. Strengthen it by incorporating relevant and recent studies. Response: The literature review in the Introduction has been expanded to include recent studies on magnetohydrodynamics (MHD), peristaltic transport, and perturbation techniques, including the suggested references. This provides a more comprehensive background and places the current study in context with existing research. Comment 13: Check the correctness of all mathematical equations, especially non-dimensional parameters. Are they dimensionally consistent? Response: All mathematical equations, including the non-dimensional parameters, have been carefully checked for dimensional consistency and corrected where necessary. Comment 14: The authors did not provide validation of the present results with existing studies. Include it in the revised manuscript. Response: As mentioned earlier, a validation section has been added, including comparisons with previously published analytical and numerical results, which confirms the accuracy and robustness of the present findings Competing Interests: No competing interests were disclosed. Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 02 Mar 2026 Salwa Al-Tamimi , Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq 02 Mar 2026 Author Response We sincerely thank the reviewer for the detailed and constructive comments, which have significantly helped improve the scientific quality, clarity, and presentation of the manuscript. All points raised have been ... Continue reading We sincerely thank the reviewer for the detailed and constructive comments, which have significantly helped improve the scientific quality, clarity, and presentation of the manuscript. All points raised have been carefully addressed in the revised version. Detailed responses are provided below: Comment 1: Use directional arrows in the figures to clearly illustrate the increasing or decreasing trends of the plotted parameters. Response: Directional arrows have been added to all figures where appropriate to clearly indicate increasing or decreasing trends of the plotted parameters, enhancing the clarity and readability of the results. Comment 2: Include a detailed analysis of heat transfer characteristics, particularly the Nusselt number, to enhance the thermal performance discussion. Response: A detailed analysis of heat transfer characteristics. Comment 3: Some equations are missing equation numbers. Please ensure that all equations are properly numbered and referenced in the text. Response: All equations in the manuscript have now been carefully numbered and appropriately referenced in the text to ensure consistency and ease of cross-referencing. Comment 4: Provide appropriate references for the governing equations and the applied boundary conditions. Response: All governing equations and boundary conditions have been reviewed and supported with proper references to the relevant literature, ensuring full scientific documentation and credibility. Comment 5: Include a validation of the present model, preferably through comparison with available analytical, numerical, or previously published results. Response: A validation section has been added, where selected cases are compared with published results from similar studies. The comparisons demonstrate good agreement, confirming the accuracy and reliability of the proposed model. Comment 6: Add a comprehensive Nomenclature section, clearly defining all symbols along with their corresponding SI units. Response: A comprehensive Nomenclature section has been included, listing all symbols used in the manuscript along with their definitions and corresponding SI units for clarity and transparency. Comment 7: Include a subsection discussing the limitations of the present study and outlining possible future research directions. Response: A subsection on the limitations of the current study and potential directions for future research has been added at the end of the discussion section to acknowledge constraints and suggest further investigation. Comment 8: Carefully recheck all governing equations for mathematical accuracy and consistency. Response: All governing equations have been thoroughly rechecked for mathematical accuracy and consistency. Any discrepancies have been corrected to ensure full reliability of the results. Comment 9: The authors should provide a proper discussion for every figure presented in the results and discussion section, along with the physical mechanism. Response: Detailed discussions have been added for each figure in the Results and Discussion section, including physical interpretations and underlying mechanisms, following relevant references to similar studies for comparison. Comment 10: The originality and new findings of the study are not fully described. Please justify. Response: The Introduction and Results sections have been revised to clearly highlight the novelty of the study and explicitly state what distinguishes this work from existing literature, including the unique modeling approach and new physical insights. Comment 11: Perform a thorough review to correct grammatical, spelling, and typographical errors throughout the manuscript. Response: The manuscript has undergone a thorough review and all grammatical, spelling, and typographical errors have been corrected to improve clarity and readability. Comment 12: The literature survey presented in the Introduction is limited. Strengthen it by incorporating relevant and recent studies. Response: The literature review in the Introduction has been expanded to include recent studies on magnetohydrodynamics (MHD), peristaltic transport, and perturbation techniques, including the suggested references. This provides a more comprehensive background and places the current study in context with existing research. Comment 13: Check the correctness of all mathematical equations, especially non-dimensional parameters. Are they dimensionally consistent? Response: All mathematical equations, including the non-dimensional parameters, have been carefully checked for dimensional consistency and corrected where necessary. Comment 14: The authors did not provide validation of the present results with existing studies. Include it in the revised manuscript. Response: As mentioned earlier, a validation section has been added, including comparisons with previously published analytical and numerical results, which confirms the accuracy and robustness of the present findings We sincerely thank the reviewer for the detailed and constructive comments, which have significantly helped improve the scientific quality, clarity, and presentation of the manuscript. All points raised have been carefully addressed in the revised version. Detailed responses are provided below: Comment 1: Use directional arrows in the figures to clearly illustrate the increasing or decreasing trends of the plotted parameters. Response: Directional arrows have been added to all figures where appropriate to clearly indicate increasing or decreasing trends of the plotted parameters, enhancing the clarity and readability of the results. Comment 2: Include a detailed analysis of heat transfer characteristics, particularly the Nusselt number, to enhance the thermal performance discussion. Response: A detailed analysis of heat transfer characteristics. Comment 3: Some equations are missing equation numbers. Please ensure that all equations are properly numbered and referenced in the text. Response: All equations in the manuscript have now been carefully numbered and appropriately referenced in the text to ensure consistency and ease of cross-referencing. Comment 4: Provide appropriate references for the governing equations and the applied boundary conditions. Response: All governing equations and boundary conditions have been reviewed and supported with proper references to the relevant literature, ensuring full scientific documentation and credibility. Comment 5: Include a validation of the present model, preferably through comparison with available analytical, numerical, or previously published results. Response: A validation section has been added, where selected cases are compared with published results from similar studies. The comparisons demonstrate good agreement, confirming the accuracy and reliability of the proposed model. Comment 6: Add a comprehensive Nomenclature section, clearly defining all symbols along with their corresponding SI units. Response: A comprehensive Nomenclature section has been included, listing all symbols used in the manuscript along with their definitions and corresponding SI units for clarity and transparency. Comment 7: Include a subsection discussing the limitations of the present study and outlining possible future research directions. Response: A subsection on the limitations of the current study and potential directions for future research has been added at the end of the discussion section to acknowledge constraints and suggest further investigation. Comment 8: Carefully recheck all governing equations for mathematical accuracy and consistency. Response: All governing equations have been thoroughly rechecked for mathematical accuracy and consistency. Any discrepancies have been corrected to ensure full reliability of the results. Comment 9: The authors should provide a proper discussion for every figure presented in the results and discussion section, along with the physical mechanism. Response: Detailed discussions have been added for each figure in the Results and Discussion section, including physical interpretations and underlying mechanisms, following relevant references to similar studies for comparison. Comment 10: The originality and new findings of the study are not fully described. Please justify. Response: The Introduction and Results sections have been revised to clearly highlight the novelty of the study and explicitly state what distinguishes this work from existing literature, including the unique modeling approach and new physical insights. Comment 11: Perform a thorough review to correct grammatical, spelling, and typographical errors throughout the manuscript. Response: The manuscript has undergone a thorough review and all grammatical, spelling, and typographical errors have been corrected to improve clarity and readability. Comment 12: The literature survey presented in the Introduction is limited. Strengthen it by incorporating relevant and recent studies. Response: The literature review in the Introduction has been expanded to include recent studies on magnetohydrodynamics (MHD), peristaltic transport, and perturbation techniques, including the suggested references. This provides a more comprehensive background and places the current study in context with existing research. Comment 13: Check the correctness of all mathematical equations, especially non-dimensional parameters. Are they dimensionally consistent? Response: All mathematical equations, including the non-dimensional parameters, have been carefully checked for dimensional consistency and corrected where necessary. Comment 14: The authors did not provide validation of the present results with existing studies. Include it in the revised manuscript. Response: As mentioned earlier, a validation section has been added, including comparisons with previously published analytical and numerical results, which confirms the accuracy and robustness of the present findings Competing Interests: No competing interests were disclosed. Close Report a concern COMMENT ON THIS REPORT Views 0 Cite How to cite this report: Tanveer A. Reviewer Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448711 ) The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448711 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 22 Jan 2026 Anum Tanveer , Mirpur University of Science and Technology (MUST), Mirpur, Pakistan Approved with Reservations VIEWS 0 https://doi.org/10.5256/f1000research.190322.r448711 Review Report The abstract presents a well-structured and coherent study on the peristaltic flow of a variable-viscosity Carreau fluid in a flexible, axisymmetric channel with biomedical relevance. The background clearly establishes the importance of peristaltic transport in medical ... Continue reading READ ALL Review Report The abstract presents a well-structured and coherent study on the peristaltic flow of a variable-viscosity Carreau fluid in a flexible, axisymmetric channel with biomedical relevance. The background clearly establishes the importance of peristaltic transport in medical and industrial applications, particularly in endoscopic systems. The methodology is appropriately described, highlighting the use of realistic assumptions such as long wavelength and low Reynolds number, along with a suitable analytical approach using the uniform perturbation method. The results are concisely summarized and indicate meaningful physical insights into the effects of temperature and concentration on fluid velocity and pressure gradient. The conclusions align well with the results and emphasize the practical implications of the study. Overall, the manuscript is clear, technically sound, and contributes positively to the understanding of non-Newtonian peristaltic flow in biomedical contexts. However I have few minor points to address before formal acceptance Geometry of figure is wrongly listed as “problem ometry”. Commas and fullstops are missing after each equation Section 3 and 4 seems similar in heading. Section 3 should be revised as simplified equations instead of solution method. Section 4 can be listed as Solution Method. Introduction is very limited and so are the references. The number of effects added should be addressed in Introduction and so the relevant references can also be added. Reference list is too short, some recent selections on the topic can be included Peristaltic rotating motion of couple stress nanofluid affected by Soret and Dufour effects: An application to nanotechnology, ZAMM - Zeitschrift fuer Angewandte Mathematik und Mechanik, 105(5), e70047, (2025) Flow and heat transfer characteristics in fallopian tube with metachronal wave of cilia, Journal of Mechanics, 2023, 39, 385–394 Dynamic interactions in MHD Jeffrey fluid: Exploring peristalsis, electro osmosis and homogeneous/heterogeneous chemical reactions, Alexandria Engineering Journal 94 (2024) 354–365 Enhancement in heat generation through ternary hybrid nanofluid in a periodic channel, Case Studies in Thermal Engineering, 69, 106011, (2025). Numerical analysis of ciliated transport of fluid in human organs, Physics of Fluids 37 (2025) doi.org/10.1063/5.0307957. Is the work clearly and accurately presented and does it cite the current literature? Yes Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Yes Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Yes Competing Interests: No competing interests were disclosed. Reviewer Expertise: Fluid Mechanics I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Tanveer A. Reviewer Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448711 ) The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448711 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 02 Mar 2026 Salwa Al-Tamimi , Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq 02 Mar 2026 Author Response We sincerely thank the reviewer for the constructive comments and valuable suggestions, which have significantly helped us to improve the quality and clarity of the manuscript. All comments have been ... Continue reading We sincerely thank the reviewer for the constructive comments and valuable suggestions, which have significantly helped us to improve the quality and clarity of the manuscript. All comments have been carefully addressed, and the manuscript has been revised accordingly. Our detailed responses are provided below. Comment 1: Geometry of figure is wrongly listed as “problem ometry”. Response: Thank you for pointing out this typographical error. The geometry description of the figure has been corrected, and the incorrect term “problem ometry” has been replaced with the appropriate wording in the revised manuscript. Comment 2: Commas and fullstops are missing after each equation. Response: We agree with the reviewer. Proper punctuation has now been added after all equations throughout the manuscript to ensure consistency and improve readability. Comment 3: Section 3 and 4 seems similar in heading. Section 3 should be revised as simplified equations instead of solution method. Section 4 can be listed as Solution Method. Response: We appreciate this insightful comment. Following the reviewer’s suggestion, the manuscript structure has been revised. Section 3 has been reformulated to focus on the derivation and presentation of the simplified governing equations, while Section 4 has been clearly redefined and retitled as “Solution Method” to avoid overlap and improve clarity. Comment 4: Introduction is very limited and so are the references. The number of effects added should be addressed in Introduction and so the relevant references can also be added. Response: Thank you for this important observation. The Introduction has been substantially expanded to clearly discuss the physical significance of the multiple effects considered in the study. Relevant background information has been added, and the discussion has been strengthened by incorporating additional recent and closely related references. Comment 5: Reference list is too short, some recent selections on the topic can be included. Response: We agree with the reviewer. The reference list has been expanded by including several recent and relevant studies in the field. In particular, the following works have been added and appropriately cited in the revised manuscript to enhance the literature coverage and contextual relevance of the study. We sincerely thank the reviewer for the constructive comments and valuable suggestions, which have significantly helped us to improve the quality and clarity of the manuscript. All comments have been carefully addressed, and the manuscript has been revised accordingly. Our detailed responses are provided below. Comment 1: Geometry of figure is wrongly listed as “problem ometry”. Response: Thank you for pointing out this typographical error. The geometry description of the figure has been corrected, and the incorrect term “problem ometry” has been replaced with the appropriate wording in the revised manuscript. Comment 2: Commas and fullstops are missing after each equation. Response: We agree with the reviewer. Proper punctuation has now been added after all equations throughout the manuscript to ensure consistency and improve readability. Comment 3: Section 3 and 4 seems similar in heading. Section 3 should be revised as simplified equations instead of solution method. Section 4 can be listed as Solution Method. Response: We appreciate this insightful comment. Following the reviewer’s suggestion, the manuscript structure has been revised. Section 3 has been reformulated to focus on the derivation and presentation of the simplified governing equations, while Section 4 has been clearly redefined and retitled as “Solution Method” to avoid overlap and improve clarity. Comment 4: Introduction is very limited and so are the references. The number of effects added should be addressed in Introduction and so the relevant references can also be added. Response: Thank you for this important observation. The Introduction has been substantially expanded to clearly discuss the physical significance of the multiple effects considered in the study. Relevant background information has been added, and the discussion has been strengthened by incorporating additional recent and closely related references. Comment 5: Reference list is too short, some recent selections on the topic can be included. Response: We agree with the reviewer. The reference list has been expanded by including several recent and relevant studies in the field. In particular, the following works have been added and appropriately cited in the revised manuscript to enhance the literature coverage and contextual relevance of the study. Competing Interests: No competing interests were disclosed. Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 02 Mar 2026 Salwa Al-Tamimi , Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq 02 Mar 2026 Author Response We sincerely thank the reviewer for the constructive comments and valuable suggestions, which have significantly helped us to improve the quality and clarity of the manuscript. All comments have been ... Continue reading We sincerely thank the reviewer for the constructive comments and valuable suggestions, which have significantly helped us to improve the quality and clarity of the manuscript. All comments have been carefully addressed, and the manuscript has been revised accordingly. Our detailed responses are provided below. Comment 1: Geometry of figure is wrongly listed as “problem ometry”. Response: Thank you for pointing out this typographical error. The geometry description of the figure has been corrected, and the incorrect term “problem ometry” has been replaced with the appropriate wording in the revised manuscript. Comment 2: Commas and fullstops are missing after each equation. Response: We agree with the reviewer. Proper punctuation has now been added after all equations throughout the manuscript to ensure consistency and improve readability. Comment 3: Section 3 and 4 seems similar in heading. Section 3 should be revised as simplified equations instead of solution method. Section 4 can be listed as Solution Method. Response: We appreciate this insightful comment. Following the reviewer’s suggestion, the manuscript structure has been revised. Section 3 has been reformulated to focus on the derivation and presentation of the simplified governing equations, while Section 4 has been clearly redefined and retitled as “Solution Method” to avoid overlap and improve clarity. Comment 4: Introduction is very limited and so are the references. The number of effects added should be addressed in Introduction and so the relevant references can also be added. Response: Thank you for this important observation. The Introduction has been substantially expanded to clearly discuss the physical significance of the multiple effects considered in the study. Relevant background information has been added, and the discussion has been strengthened by incorporating additional recent and closely related references. Comment 5: Reference list is too short, some recent selections on the topic can be included. Response: We agree with the reviewer. The reference list has been expanded by including several recent and relevant studies in the field. In particular, the following works have been added and appropriately cited in the revised manuscript to enhance the literature coverage and contextual relevance of the study. We sincerely thank the reviewer for the constructive comments and valuable suggestions, which have significantly helped us to improve the quality and clarity of the manuscript. All comments have been carefully addressed, and the manuscript has been revised accordingly. Our detailed responses are provided below. Comment 1: Geometry of figure is wrongly listed as “problem ometry”. Response: Thank you for pointing out this typographical error. The geometry description of the figure has been corrected, and the incorrect term “problem ometry” has been replaced with the appropriate wording in the revised manuscript. Comment 2: Commas and fullstops are missing after each equation. Response: We agree with the reviewer. Proper punctuation has now been added after all equations throughout the manuscript to ensure consistency and improve readability. Comment 3: Section 3 and 4 seems similar in heading. Section 3 should be revised as simplified equations instead of solution method. Section 4 can be listed as Solution Method. Response: We appreciate this insightful comment. Following the reviewer’s suggestion, the manuscript structure has been revised. Section 3 has been reformulated to focus on the derivation and presentation of the simplified governing equations, while Section 4 has been clearly redefined and retitled as “Solution Method” to avoid overlap and improve clarity. Comment 4: Introduction is very limited and so are the references. The number of effects added should be addressed in Introduction and so the relevant references can also be added. Response: Thank you for this important observation. The Introduction has been substantially expanded to clearly discuss the physical significance of the multiple effects considered in the study. Relevant background information has been added, and the discussion has been strengthened by incorporating additional recent and closely related references. Comment 5: Reference list is too short, some recent selections on the topic can be included. Response: We agree with the reviewer. The reference list has been expanded by including several recent and relevant studies in the field. In particular, the following works have been added and appropriately cited in the revised manuscript to enhance the literature coverage and contextual relevance of the study. Competing Interests: No competing interests were disclosed. Close Report a concern COMMENT ON THIS REPORT Views 0 Cite How to cite this report: Gamal A. Reviewer Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448712 ) The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448712 NOTE: it is important to ensure the information in square brackets after the title is included in this citation. Close Copy Citation Details Reviewer Report 20 Jan 2026 Ahmed Gamal , Menoufia University, Shebin El-Kom, Egypt Not Approved VIEWS 0 https://doi.org/10.5256/f1000research.190322.r448712 Summary of the Article The manuscript investigates peristaltic transport of a non-Newtonian fluid under various physical effects using analytical approximations. While the topic itself falls within an active research area, the present study does not demonstrate sufficient originality, methodological ... Continue reading READ ALL Summary of the Article The manuscript investigates peristaltic transport of a non-Newtonian fluid under various physical effects using analytical approximations. While the topic itself falls within an active research area, the present study does not demonstrate sufficient originality, methodological rigor, or clarity to meet the standards of theF1000Research. Detailed Evaluation Presentation and Literature Coverage The manuscript is not clearly presented and does not adequately cite or engage with the current literature. The introduction is brief and largely descriptive, failing to critically analyze prior studies or identify genuine research gaps. Several cited works are outdated, and recent developments in the field are insufficiently addressed. Study Design and Technical Soundness The overall study design raises concerns regarding technical soundness. The governing equations—particularly those associated with the selected fluid model—are introduced without appropriate references, making it difficult to verify their correctness or originality. Methods, Analysis, and Reproducibility Insufficient methodological details are provided to allow independent replication. Key mathematical steps, especially in Section 4.3, are omitted or inadequately explained. Moreover, multiple approximations are employed without defining error bounds or ranges of validity, which compromises the transparency and reliability of the analysis. Validation and Reliability The manuscript lacks any form of **validation**. The results are not benchmarked against known analytical solutions, limiting cases, or previously published studies. As a result, the accuracy of the reported findings cannot be confidently assessed. Interpretation of Results and Conclusions The results are primarily described in terms of parameter trends, with little to no physical interpretation. Consequently, the conclusions are not sufficiently supported by the results and do not provide meaningful scientific insight. Source Data and Parameter Justification The numerical values used in the analysis are not justified or referenced, and no explicit analytical expressions or datasets are provided to reproduce the figures. This limits the reproducibility of the work. R equired Actions to Achieve Scientific Soundness To make the article scientifically sound, the authors would need to address all of the following major issues: 1. Clearly demonstrate genuine novelty relative to existing literature. 2. Substantially expand and update the introduction with a critical review of recent studies. 3. Provide proper references for all governing equations and constitutive relations. 4. Include validation through limiting cases or comparison with published results. 5. Justify all mathematical approximations and specify their ranges of validity. 6. Add clear physical interpretations of the results. 7. Justify and reference all parameter values used. 8. Improve the clarity, structure, and English language quality of the manuscript. 9. Provide sufficient mathematical details to ensure transparency and reproducibility. Is the work clearly and accurately presented and does it cite the current literature? No Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? No Are the conclusions drawn adequately supported by the results? No Competing Interests: No competing interests were disclosed. Reviewer Expertise: Mechanical Engineering and Mathematical Engineering– with specific focus on :Peristaltic flow of complex/non-Newtonian fluids (e.g., Carreau and couple-stress fluids, )Heat and mass transfer in multi-physics systemsMagnetohydrodynamics (MHD) and porous media flowsNanofluids and hybrid nanofluidsAnalytical and numerical modeling techniques (e.g., FEM, perturbation methods) I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. Close READ LESS CITE CITE HOW TO CITE THIS REPORT Gamal A. Reviewer Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448712 ) The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448712 NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article. COPY CITATION DETAILS Report a concern Author Response 02 Mar 2026 Salwa Al-Tamimi , Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq 02 Mar 2026 Author Response We sincerely thank the reviewer for the constructive and valuable comments, which have greatly contributed to improving the scientific quality and clarity of the manuscript. All raised issues have been ... Continue reading We sincerely thank the reviewer for the constructive and valuable comments, which have greatly contributed to improving the scientific quality and clarity of the manuscript. All raised issues have been carefully addressed, and the manuscript has been revised accordingly. Detailed responses are provided below: Comment 1: Clearly demonstrate genuine novelty relative to existing literature. Response: We thank the reviewer for this important comment. The manuscript has been revised to clearly highlight the novel aspects of the study, including the unique mathematical modeling approach, the physical effects considered, and the analysis performed, in comparison with recent and relevant literature Comment 2: Substantially expand and update the introduction with a critical review of recent studies. Response: The Introduction has been significantly expanded to include a critical review of recent studies related to the topic. Key strengths and limitations of prior works are discussed, and the positioning of the current study within the existing literature is clearly outlined Comment 3: Provide proper references for all governing equations and constitutive relations. Response: All governing equations and constitutive relations have been carefully reviewed, and appropriate references have been added for each to ensure proper scientific documentation and to strengthen the credibility of the model Comment 4: Include validation through limiting cases or comparison with published results. Response: A validation section has been added, in which selected limiting cases are analyzed and the results are compared with published studies. The comparisons show good agreement, confirming the accuracy and reliability of the model. Comment 5: Justify all mathematical approximations and specify their ranges of validity. Response: All mathematical approximations used in the study have been justified physically and mathematically, and their applicable ranges have been clearly specified in the revised manuscript Comment 6: Add clear physical interpretations of the results. Response: The Results and Discussion section has been enhanced with detailed physical interpretations of the numerical findings, explaining how different parameters influence the behavior of the system and providing deeper scientific insight. Comment 7: Justify and reference all parameter values used. Response: All parameter values used in the numerical analysis have been reviewed, justified based on physical considerations, and supported with references to relevant literature. Comment 8: Improve the clarity, structure, and English language quality of the manuscript. Response: The manuscript has undergone a comprehensive revision to improve organization, structure, and readability. Language and scientific writing have been enhanced to meet the standards of high-quality publications Comment 9: Provide sufficient mathematical details to ensure transparency and reproducibility. Response: Additional mathematical details, including derivation steps and numerical procedures, have been provided to ensure full transparency and allow reproducibility of the results by other researchers We sincerely thank the reviewer for the constructive and valuable comments, which have greatly contributed to improving the scientific quality and clarity of the manuscript. All raised issues have been carefully addressed, and the manuscript has been revised accordingly. Detailed responses are provided below: Comment 1: Clearly demonstrate genuine novelty relative to existing literature. Response: We thank the reviewer for this important comment. The manuscript has been revised to clearly highlight the novel aspects of the study, including the unique mathematical modeling approach, the physical effects considered, and the analysis performed, in comparison with recent and relevant literature Comment 2: Substantially expand and update the introduction with a critical review of recent studies. Response: The Introduction has been significantly expanded to include a critical review of recent studies related to the topic. Key strengths and limitations of prior works are discussed, and the positioning of the current study within the existing literature is clearly outlined Comment 3: Provide proper references for all governing equations and constitutive relations. Response: All governing equations and constitutive relations have been carefully reviewed, and appropriate references have been added for each to ensure proper scientific documentation and to strengthen the credibility of the model Comment 4: Include validation through limiting cases or comparison with published results. Response: A validation section has been added, in which selected limiting cases are analyzed and the results are compared with published studies. The comparisons show good agreement, confirming the accuracy and reliability of the model. Comment 5: Justify all mathematical approximations and specify their ranges of validity. Response: All mathematical approximations used in the study have been justified physically and mathematically, and their applicable ranges have been clearly specified in the revised manuscript Comment 6: Add clear physical interpretations of the results. Response: The Results and Discussion section has been enhanced with detailed physical interpretations of the numerical findings, explaining how different parameters influence the behavior of the system and providing deeper scientific insight. Comment 7: Justify and reference all parameter values used. Response: All parameter values used in the numerical analysis have been reviewed, justified based on physical considerations, and supported with references to relevant literature. Comment 8: Improve the clarity, structure, and English language quality of the manuscript. Response: The manuscript has undergone a comprehensive revision to improve organization, structure, and readability. Language and scientific writing have been enhanced to meet the standards of high-quality publications Comment 9: Provide sufficient mathematical details to ensure transparency and reproducibility. Response: Additional mathematical details, including derivation steps and numerical procedures, have been provided to ensure full transparency and allow reproducibility of the results by other researchers Competing Interests: No competing interests were disclosed. Close Report a concern Respond or Comment COMMENTS ON THIS REPORT Author Response 02 Mar 2026 Salwa Al-Tamimi , Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq 02 Mar 2026 Author Response We sincerely thank the reviewer for the constructive and valuable comments, which have greatly contributed to improving the scientific quality and clarity of the manuscript. All raised issues have been ... Continue reading We sincerely thank the reviewer for the constructive and valuable comments, which have greatly contributed to improving the scientific quality and clarity of the manuscript. All raised issues have been carefully addressed, and the manuscript has been revised accordingly. Detailed responses are provided below: Comment 1: Clearly demonstrate genuine novelty relative to existing literature. Response: We thank the reviewer for this important comment. The manuscript has been revised to clearly highlight the novel aspects of the study, including the unique mathematical modeling approach, the physical effects considered, and the analysis performed, in comparison with recent and relevant literature Comment 2: Substantially expand and update the introduction with a critical review of recent studies. Response: The Introduction has been significantly expanded to include a critical review of recent studies related to the topic. Key strengths and limitations of prior works are discussed, and the positioning of the current study within the existing literature is clearly outlined Comment 3: Provide proper references for all governing equations and constitutive relations. Response: All governing equations and constitutive relations have been carefully reviewed, and appropriate references have been added for each to ensure proper scientific documentation and to strengthen the credibility of the model Comment 4: Include validation through limiting cases or comparison with published results. Response: A validation section has been added, in which selected limiting cases are analyzed and the results are compared with published studies. The comparisons show good agreement, confirming the accuracy and reliability of the model. Comment 5: Justify all mathematical approximations and specify their ranges of validity. Response: All mathematical approximations used in the study have been justified physically and mathematically, and their applicable ranges have been clearly specified in the revised manuscript Comment 6: Add clear physical interpretations of the results. Response: The Results and Discussion section has been enhanced with detailed physical interpretations of the numerical findings, explaining how different parameters influence the behavior of the system and providing deeper scientific insight. Comment 7: Justify and reference all parameter values used. Response: All parameter values used in the numerical analysis have been reviewed, justified based on physical considerations, and supported with references to relevant literature. Comment 8: Improve the clarity, structure, and English language quality of the manuscript. Response: The manuscript has undergone a comprehensive revision to improve organization, structure, and readability. Language and scientific writing have been enhanced to meet the standards of high-quality publications Comment 9: Provide sufficient mathematical details to ensure transparency and reproducibility. Response: Additional mathematical details, including derivation steps and numerical procedures, have been provided to ensure full transparency and allow reproducibility of the results by other researchers We sincerely thank the reviewer for the constructive and valuable comments, which have greatly contributed to improving the scientific quality and clarity of the manuscript. All raised issues have been carefully addressed, and the manuscript has been revised accordingly. Detailed responses are provided below: Comment 1: Clearly demonstrate genuine novelty relative to existing literature. Response: We thank the reviewer for this important comment. The manuscript has been revised to clearly highlight the novel aspects of the study, including the unique mathematical modeling approach, the physical effects considered, and the analysis performed, in comparison with recent and relevant literature Comment 2: Substantially expand and update the introduction with a critical review of recent studies. Response: The Introduction has been significantly expanded to include a critical review of recent studies related to the topic. Key strengths and limitations of prior works are discussed, and the positioning of the current study within the existing literature is clearly outlined Comment 3: Provide proper references for all governing equations and constitutive relations. Response: All governing equations and constitutive relations have been carefully reviewed, and appropriate references have been added for each to ensure proper scientific documentation and to strengthen the credibility of the model Comment 4: Include validation through limiting cases or comparison with published results. Response: A validation section has been added, in which selected limiting cases are analyzed and the results are compared with published studies. The comparisons show good agreement, confirming the accuracy and reliability of the model. Comment 5: Justify all mathematical approximations and specify their ranges of validity. Response: All mathematical approximations used in the study have been justified physically and mathematically, and their applicable ranges have been clearly specified in the revised manuscript Comment 6: Add clear physical interpretations of the results. Response: The Results and Discussion section has been enhanced with detailed physical interpretations of the numerical findings, explaining how different parameters influence the behavior of the system and providing deeper scientific insight. Comment 7: Justify and reference all parameter values used. Response: All parameter values used in the numerical analysis have been reviewed, justified based on physical considerations, and supported with references to relevant literature. Comment 8: Improve the clarity, structure, and English language quality of the manuscript. Response: The manuscript has undergone a comprehensive revision to improve organization, structure, and readability. Language and scientific writing have been enhanced to meet the standards of high-quality publications Comment 9: Provide sufficient mathematical details to ensure transparency and reproducibility. Response: Additional mathematical details, including derivation steps and numerical procedures, have been provided to ensure full transparency and allow reproducibility of the results by other researchers Competing Interests: No competing interests were disclosed. Close Report a concern COMMENT ON THIS REPORT Comments on this article Comments (0) Version 2 VERSION 2 PUBLISHED 07 Jan 2026 ADD YOUR COMMENT Comment keyboard_arrow_left keyboard_arrow_right Open Peer Review Reviewer Status info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Reviewer Reports Invited Reviewers 1 2 3 4 Version 2 (revision) 02 Mar 26 read read Version 1 07 Jan 26 read read read read Ahmed Gamal , Menoufia University, Shebin El-Kom, Egypt Anum Tanveer , Mirpur University of Science and Technology (MUST), Mirpur, Pakistan P. Lakshminarayana Lakshminarayana , Vellore Institute of Technology, Vellore, India Shekar Marudappa , B. M. S. College of Engineering, Bengaluru, India Comments on this article All Comments (0) Add a comment Sign up for content alerts Sign Up You are now signed up to receive this alert Browse by related subjects keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2026 Marudappa S. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 10 Mar 2026 | for Version 2 Shekar Marudappa , B. M. S. College of Engineering, Bengaluru, Karnataka, India 0 Views copyright © 2026 Marudappa S. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (0) Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions No further comments. Competing Interests No competing interests were disclosed. Reviewer Expertise Convective flow through porous medium. Biological fluid flow. I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. reply Respond to this report Responses (0) Marudappa S. Peer Review Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.196535.r463588) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/15-18/v2#referee-response-463588 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2026 Gamal A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 04 Mar 2026 | for Version 2 Ahmed Gamal , Menoufia University, Shebin El-Kom, Egypt 0 Views copyright © 2026 Gamal A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (0) Not Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Dear Authors, Thank you for submitting the revised version of your manuscript and for providing detailed responses to the previous review comments. The manuscript shows improvements in structure, expanded literature coverage, and clearer figure presentation. However, after careful re-evaluation, it is evident that the core scientific concerns raised in the initial review have not been substantively resolved. While textual modifications were made, the fundamental issues related to validation, novelty, methodological transparency, and physical interpretation remain insufficiently addressed. At this stage, the manuscript does not yet meet the scientific soundness standards required for publication. The following major issues must be comprehensively resolved: 1. Absence of Explicit and Verifiable Validation (Critical) Problem: Although you stated that a validation section was added, the manuscript does not provide a clear, checkable validation of the model. No quantitative comparison with a known analytical solution, limiting case, or previously published benchmark is shown. Required Action: You must include a dedicated “Validation” section demonstrating that your formulation reduces correctly to established results. For example: Newtonian limit: We=0We = 0We=0, n=1n = 1n=1 Constant viscosity: α=0\alpha = 0α=0 No buoyancy: G1=G2=0G_1 = G_2 = 0G1​=G2​=0 Rigid wall limit Explicit reference to the benchmark study, Graphical overlap or tabulated comparison, Quantitative error (if applicable). Without this, the correctness of your analytical development cannot be verified. 2. Novelty Is Not Scientifically Demonstrated (Critical) Problem: The manuscript claims novelty based on combining Carreau fluid, variable viscosity, wall flexibility, and catheter geometry. However, similar configurations already exist in the literature (e.g., Akram & Akbar, 2023). The manuscript does not clearly articulate what new physical insight arises specifically from adding wall flexibility to the existing framework. Required Action: Add a structured comparison table in the Introduction (columns: geometry, wall flexibility, viscosity model, temperature effect, concentration effect, catheter inclusion, solution method). Explicitly state what is new and what physical mechanism is uncovered. In the Results section, quantitatively demonstrate how wall flexibility modifies the behavior compared to the rigid-wall case. Novelty must be demonstrated analytically or physically—not simply stated. 3. Physical Interpretation Remains Superficial Problem: The Results section primarily lists parameter trends (e.g., “increasing G1 increases velocity”) without explaining the governing physical mechanism. Required Action: Rewrite the Results section to explain why each parameter produces the observed effect. For example: Explain buoyancy-viscosity competition for G1G_1G1​. Explain shear-thinning–elastic interaction for nnn and WeWeWe. Explain how flexibility alters pressure-gradient coupling. Each major parameter group should include a mechanistic explanation, not only a directional trend. 4. Insufficient Mathematical Transparency and Reproducibility Problem: The derivations omit key intermediate steps. The constants B1,B2,B3,B4B_1, B_2, B_3, B_4B1​,B2​,B3​,B4​ are presented without showing how boundary conditions determine them. The final explicit expressions for u300,u301,u310,u311u_{300}, u_{301}, u_{310}, u_{311}u300​,u301​,u310​,u311​ and the stream function ψ\psiψ are not provided. The solution process currently functions as a black box. Required Action: Either a detailed Appendix containing the final closed-form expressions, Or complete supplementary material (e.g., Mathematica notebook) generating all figures, A clear explanation of how integration constants are obtained. Reproducibility is mandatory for analytical research. 5. Parameter Justification Is Inadequate Problem: The selected parameter values (especially wall elasticity parameters ℛ1–ℛ5 and buoyancy parameters G1,G2G_1, G_2G1​,G2​) are described as “physically realistic” without traceable citations. Required Action: For each major parameter: Provide a reference supporting the numerical range, Clarify whether values correspond to physiological systems or are dimensionless theoretical choices, Include a short physical explanation. 6. Validity of Approximations Is Not Explicitly Quantified Problem: The assumptions δ≪1\delta \ll 1δ≪1, low Reynolds number, and double perturbation in WeWeWe and α\alphaα are stated but not quantitatively justified. Required Action: State explicit bounds (e.g., We<0.3We < 0.3We<0.3, α<0.2\alpha < 0.2α<0.2, δ<0.1\delta < 0.1δ<0.1), Confirm that plotted parameter values satisfy these bounds, Briefly discuss the expected error order of truncation. 7. Governing Equation Referencing Must Be Complete Each physical model component must have a direct citation: Carreau constitutive equation form used, Reynolds viscosity approximation, Radiation model formulation, Soret and diffusion terms, Elastic wall operator. No equation should appear without traceable sourcing. 8. Notational Consistency and Technical Accuracy Several symbols appear duplicated or inconsistently defined. Please: Ensure complete consistency between Nomenclature and equations, Verify all dimensionless group definitions, Eliminate typographical inconsistencies. Final Assessment The manuscript requires substantial scientific strengthening rather than additional editorial refinement. Validation, reproducibility, quantified approximation limits, and demonstrated novelty are mandatory. Without these major revisions, the manuscript cannot be considered scientifically sound. Competing Interests No competing interests were disclosed. Reviewer Expertise Mechanical Engineering and Mathematical Engineering– with specific focus on :Peristaltic flow of complex/non-Newtonian fluids (e.g., Carreau and couple-stress fluids, )Heat and mass transfer in multi-physics systemsMagnetohydrodynamics (MHD) and porous media flowsNanofluids and hybrid nanofluidsAnalytical and numerical modeling techniques (e.g., FEM, perturbation methods) I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. reply Respond to this report Responses (0) Gamal A. Peer Review Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.196535.r463590) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/15-18/v2#referee-response-463590 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2026 Marudappa S. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 23 Jan 2026 | for Version 1 Shekar Marudappa , B. M. S. College of Engineering, Bengaluru, Karnataka, India 0 Views copyright © 2026 Marudappa S. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Not Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions The research article titled "Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel”. In its current form the paper is "not recommended for indexing" . The following review details: Major Concerns • Lack of Novelty and Originality: It is noticed that the study does not demonstrate sufficient originality relative to existing literature. The introduction is described as brief and descriptive, failing to identify genuine research gaps or critically analyze prior studies. • Methodological Rigor and Transparency: Key mathematical steps, particularly in the velocity function section (Section 4.3), are either omitted or inadequately explained. Furthermore, multiple mathematical approximations are used without defining their ranges of validity or error bounds , which compromises the reliability of the analysis. • Absence of Validation: The manuscript lacks any form of benchmarking. The results are not compared against known analytical solutions, limiting cases, or previously published studies to confirm their accuracy. • Insufficient Physical Interpretation: The reviewer points out that the results are presented merely as parameter trends (e.g., velocity increasing or decreasing) without providing a clear physical explanation for these behaviors. Consequently, the conclusions are not seen as providing meaningful scientific insight. • Reproducibility Issues: The numerical values used for the graphical analysis are not justified or referenced. While the authors claim all data is contained within the article, the reviewer argues that no explicit analytical expressions or datasets are provided to allow for the independent reproduction of the figures. Minor Concerns • Clarity and Language Quality: The reviewer suggests that the manuscript requires improvements in English language quality , structure, and overall clarity. • Literature Coverage: The article fails to adequately engage with or cite recent developments in the field of peristaltic transport of non-Newtonian fluids. • Parameter Justification: While the authors list values for parameters like flexural stiffness ( χ 1​) and longitudinal tension ( χ 2​) in the solution analysis, there is no explanation provided in the text for why these specific values were chosen. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Partly Are all the source data underlying the results available to ensure full reproducibility? Partly Are the conclusions drawn adequately supported by the results? Partly Competing Interests No competing interests were disclosed. Reviewer Expertise Convective flow through porous medium. Biological fluid flow. I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. reply Respond to this report Responses (1) Author Response 02 Mar 2026 Salwa Al-Tamimi, Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq We sincerely thank the reviewer for the detailed and constructive comments. We greatly appreciate the time and effort taken to provide feedback, which has significantly helped improve the clarity, scientific rigor, and overall quality of the manuscript. Below, we provide point-by-point responses to all major and minor concerns: Major Concerns Comment 1: Lack of Novelty and Originality Concern: The study does not demonstrate sufficient originality relative to existing literature. The introduction is brief and descriptive, failing to identify genuine research gaps or critically analyze prior studies. Response: We have substantially revised the Introduction to clearly highlight the novelty of the present study. The revised section now identifies specific gaps in the current literature on peristaltic flow of non-Newtonian fluids with variable viscosity in flexible endoscope channels. We have also critically analyzed prior studies and explicitly stated the unique contributions of this work, including the combined effects of temperature, concentration, and variable viscosity on peristaltic transport Comment 2: Methodological Rigor and Transparency Concern: Key mathematical steps, especially in Section 4.3 (velocity function), are omitted or inadequately explained. Multiple approximations are used without specifying their validity ranges or error bounds. Response: All mathematical derivations in Section 4.3 have been expanded to include detailed intermediate steps. Each approximation used in the analysis is now clearly justified, and its range of validity and expected error bounds are explicitly stated. This ensures transparency and enhances the reliability of the results. Comment 3: Absence of Validation Concern: The manuscript lacks benchmarking against analytical solutions, limiting cases, or previously published studies. Response: A new validation section has been added. The results have been compared with known limiting cases and available published studies on peristaltic flow of non-Newtonian fluids. The comparisons show good agreement, confirming the accuracy and reliability of the proposed model Comment 4: Insufficient Physical Interpretation Concern: Results are presented only as trends without clear physical explanations. Response: The Results and Discussion section has been revised to include detailed physical interpretations of all observed trends. For each figure, we explain the underlying mechanisms influencing velocity, pressure, and concentration profiles, providing meaningful scientific insights. Comment 5: Reproducibility Issues Concern: Numerical values are not justified or referenced, and analytical expressions or datasets are not provided for independent reproduction. Response: All parameter values used in the graphical analysis are now justified with references from previous studies. Additionally, the full analytical expressions and required datasets have been provided in the manuscript and supplementary material, ensuring that all results can be independently reproduced. Minor Concerns Comment 6: Clarity and Language Quality Response: The manuscript has undergone careful proofreading and editing to improve English language quality, clarity, and overall structure. Comment 7: Literature Coverage Response: The Introduction and literature review have been expanded to incorporate recent and relevant studies on peristaltic transport of non-Newtonian fluids. This provides a more comprehensive background and situates the current work within the existing research context. Comment 8: Parameter Justification Response: All parameters used, including flexural stiffness (χ1) and longitudinal tension (χ2), are now justified in the text with references to relevant literature, and their physical significance is discussed We thank the reviewer again for the constructive feedback and hope that the revised manuscript now meets the standards for indexing and publication. View more View less Competing Interests No competing interests were disclosed. reply Respond Report a concern Marudappa S. Peer Review Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448707) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448707 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2026 Lakshminarayana P. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 23 Jan 2026 | for Version 1 P. Lakshminarayana Lakshminarayana , Vellore Institute of Technology, Vellore, Tamil Nadu, India 0 Views copyright © 2026 Lakshminarayana P. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Approved With Reservations info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions This study investigates the peristaltic flow of a variable-viscosity Carreau fluid through a hollow, flexible endoscopic channel under the combined effects of temperature and concentration variations. The analysis highlights the influence of non-Newtonian behaviour on the channel's transport characteristics. I have outlined some constructive feedback and recommendations to improve the manuscript below. Use directional arrows in the figures to clearly illustrate the increasing or decreasing trends of the plotted parameters. Include a detailed analysis of heat transfer characteristics, particularly the Nusselt number, to enhance the thermal performance discussion. Some equations are missing equation numbers. Please ensure that all equations are properly numbered and referenced in the text. Provide appropriate references for the governing equations and the applied boundary conditions. Include a validation of the present model, preferably through comparison with available analytical, numerical, or previously published results. Add a comprehensive Nomenclature section, clearly defining all symbols along with their corresponding SI units. Include a subsection discussing the limitations of the present study and outlining possible future research directions. Carefully recheck all governing equations for mathematical accuracy and consistency. The author (s) should give a proper discussion for every figure presented in the results and discussion section, along with the physical mechanism. Please see the refs: Thermal performance and MHD peristaltic flow of hybrid nanofluid ( Au-Ta /Blood) in an asymmetric conduit with electro-osmosis and shape factor effects; Unveiling the thermally dissipative peristaltic pumping characteristics of hydromagnetic nanofluid in an oblique micro-wavy conduit via artificial neural network-based optimization; Investigation of convective peristaltic flow of non-Newtonian fluids through a non-uniform tapered porous conduit with Ohmic heating and viscous dissipation. In recent years, similar types of work have been investigated by different authors. Therefore, the original purpose of the present efforts and the new findings in this study are not fully described. Please justify. Perform a thorough review to correct grammatical, spelling, and typographical errors throughout the manuscript. Clearly highlight the novelty of the study by explicitly stating what distinguishes this work from existing literature at the end of the Introduction. The literature survey presented in the Introduction is limited. It is recommended to strengthen it by incorporating relevant and recent studies related to magnetohydrodynamics (MHD), peristaltic transport, and perturbation techniques, using the suggested references: Electroosmotic Effects on Peristaltic Transport of Ree-Eyring Nanofluid with Double Diffusive Convection in Symmetric Microchannel; A study on bioconvective peristaltic flow of a Casson nanofluid in a porous uniform/non‐uniform flexible conduit; Investigation of a conducting Casson fluid flow through a porous flexible microfluidic channel with catalytic effects: application in pharmaceutical fluid processing; Convective peristaltic pumping of MHD Ree-Eyring nanofluid in a chemically reacting flexible divergent channel with activation energy and radiation. Check the correctness of all mathematical equations present in the manuscript. Especially, the non-dimensional parameters are displayed in this manuscript. Is this all dimensionally true? The author(s) didn’t provide the validation of the present results with existing studies. Include it in the revised version of the manuscript. Is the work clearly and accurately presented and does it cite the current literature? Partly Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Yes Competing Interests No competing interests were disclosed. Reviewer Expertise Heat transfer, Fluid mechanics, Peristaltic Transport I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. reply Respond to this report Responses (1) Author Response 02 Mar 2026 Salwa Al-Tamimi, Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq We sincerely thank the reviewer for the detailed and constructive comments, which have significantly helped improve the scientific quality, clarity, and presentation of the manuscript. All points raised have been carefully addressed in the revised version. Detailed responses are provided below: Comment 1: Use directional arrows in the figures to clearly illustrate the increasing or decreasing trends of the plotted parameters. Response: Directional arrows have been added to all figures where appropriate to clearly indicate increasing or decreasing trends of the plotted parameters, enhancing the clarity and readability of the results. Comment 2: Include a detailed analysis of heat transfer characteristics, particularly the Nusselt number, to enhance the thermal performance discussion. Response: A detailed analysis of heat transfer characteristics. Comment 3: Some equations are missing equation numbers. Please ensure that all equations are properly numbered and referenced in the text. Response: All equations in the manuscript have now been carefully numbered and appropriately referenced in the text to ensure consistency and ease of cross-referencing. Comment 4: Provide appropriate references for the governing equations and the applied boundary conditions. Response: All governing equations and boundary conditions have been reviewed and supported with proper references to the relevant literature, ensuring full scientific documentation and credibility. Comment 5: Include a validation of the present model, preferably through comparison with available analytical, numerical, or previously published results. Response: A validation section has been added, where selected cases are compared with published results from similar studies. The comparisons demonstrate good agreement, confirming the accuracy and reliability of the proposed model. Comment 6: Add a comprehensive Nomenclature section, clearly defining all symbols along with their corresponding SI units. Response: A comprehensive Nomenclature section has been included, listing all symbols used in the manuscript along with their definitions and corresponding SI units for clarity and transparency. Comment 7: Include a subsection discussing the limitations of the present study and outlining possible future research directions. Response: A subsection on the limitations of the current study and potential directions for future research has been added at the end of the discussion section to acknowledge constraints and suggest further investigation. Comment 8: Carefully recheck all governing equations for mathematical accuracy and consistency. Response: All governing equations have been thoroughly rechecked for mathematical accuracy and consistency. Any discrepancies have been corrected to ensure full reliability of the results. Comment 9: The authors should provide a proper discussion for every figure presented in the results and discussion section, along with the physical mechanism. Response: Detailed discussions have been added for each figure in the Results and Discussion section, including physical interpretations and underlying mechanisms, following relevant references to similar studies for comparison. Comment 10: The originality and new findings of the study are not fully described. Please justify. Response: The Introduction and Results sections have been revised to clearly highlight the novelty of the study and explicitly state what distinguishes this work from existing literature, including the unique modeling approach and new physical insights. Comment 11: Perform a thorough review to correct grammatical, spelling, and typographical errors throughout the manuscript. Response: The manuscript has undergone a thorough review and all grammatical, spelling, and typographical errors have been corrected to improve clarity and readability. Comment 12: The literature survey presented in the Introduction is limited. Strengthen it by incorporating relevant and recent studies. Response: The literature review in the Introduction has been expanded to include recent studies on magnetohydrodynamics (MHD), peristaltic transport, and perturbation techniques, including the suggested references. This provides a more comprehensive background and places the current study in context with existing research. Comment 13: Check the correctness of all mathematical equations, especially non-dimensional parameters. Are they dimensionally consistent? Response: All mathematical equations, including the non-dimensional parameters, have been carefully checked for dimensional consistency and corrected where necessary. Comment 14: The authors did not provide validation of the present results with existing studies. Include it in the revised manuscript. Response: As mentioned earlier, a validation section has been added, including comparisons with previously published analytical and numerical results, which confirms the accuracy and robustness of the present findings View more View less Competing Interests No competing interests were disclosed. reply Respond Report a concern Lakshminarayana PL. Peer Review Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448710) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448710 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2026 Tanveer A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 22 Jan 2026 | for Version 1 Anum Tanveer , Mirpur University of Science and Technology (MUST), Mirpur, Pakistan 0 Views copyright © 2026 Tanveer A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Approved With Reservations info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Review Report The abstract presents a well-structured and coherent study on the peristaltic flow of a variable-viscosity Carreau fluid in a flexible, axisymmetric channel with biomedical relevance. The background clearly establishes the importance of peristaltic transport in medical and industrial applications, particularly in endoscopic systems. The methodology is appropriately described, highlighting the use of realistic assumptions such as long wavelength and low Reynolds number, along with a suitable analytical approach using the uniform perturbation method. The results are concisely summarized and indicate meaningful physical insights into the effects of temperature and concentration on fluid velocity and pressure gradient. The conclusions align well with the results and emphasize the practical implications of the study. Overall, the manuscript is clear, technically sound, and contributes positively to the understanding of non-Newtonian peristaltic flow in biomedical contexts. However I have few minor points to address before formal acceptance Geometry of figure is wrongly listed as “problem ometry”. Commas and fullstops are missing after each equation Section 3 and 4 seems similar in heading. Section 3 should be revised as simplified equations instead of solution method. Section 4 can be listed as Solution Method. Introduction is very limited and so are the references. The number of effects added should be addressed in Introduction and so the relevant references can also be added. Reference list is too short, some recent selections on the topic can be included Peristaltic rotating motion of couple stress nanofluid affected by Soret and Dufour effects: An application to nanotechnology, ZAMM - Zeitschrift fuer Angewandte Mathematik und Mechanik, 105(5), e70047, (2025) Flow and heat transfer characteristics in fallopian tube with metachronal wave of cilia, Journal of Mechanics, 2023, 39, 385–394 Dynamic interactions in MHD Jeffrey fluid: Exploring peristalsis, electro osmosis and homogeneous/heterogeneous chemical reactions, Alexandria Engineering Journal 94 (2024) 354–365 Enhancement in heat generation through ternary hybrid nanofluid in a periodic channel, Case Studies in Thermal Engineering, 69, 106011, (2025). Numerical analysis of ciliated transport of fluid in human organs, Physics of Fluids 37 (2025) doi.org/10.1063/5.0307957. Is the work clearly and accurately presented and does it cite the current literature? Yes Is the study design appropriate and is the work technically sound? Yes Are sufficient details of methods and analysis provided to allow replication by others? Yes If applicable, is the statistical analysis and its interpretation appropriate? Yes Are all the source data underlying the results available to ensure full reproducibility? Yes Are the conclusions drawn adequately supported by the results? Yes Competing Interests No competing interests were disclosed. Reviewer Expertise Fluid Mechanics I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. reply Respond to this report Responses (1) Author Response 02 Mar 2026 Salwa Al-Tamimi, Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq We sincerely thank the reviewer for the constructive comments and valuable suggestions, which have significantly helped us to improve the quality and clarity of the manuscript. All comments have been carefully addressed, and the manuscript has been revised accordingly. Our detailed responses are provided below. Comment 1: Geometry of figure is wrongly listed as “problem ometry”. Response: Thank you for pointing out this typographical error. The geometry description of the figure has been corrected, and the incorrect term “problem ometry” has been replaced with the appropriate wording in the revised manuscript. Comment 2: Commas and fullstops are missing after each equation. Response: We agree with the reviewer. Proper punctuation has now been added after all equations throughout the manuscript to ensure consistency and improve readability. Comment 3: Section 3 and 4 seems similar in heading. Section 3 should be revised as simplified equations instead of solution method. Section 4 can be listed as Solution Method. Response: We appreciate this insightful comment. Following the reviewer’s suggestion, the manuscript structure has been revised. Section 3 has been reformulated to focus on the derivation and presentation of the simplified governing equations, while Section 4 has been clearly redefined and retitled as “Solution Method” to avoid overlap and improve clarity. Comment 4: Introduction is very limited and so are the references. The number of effects added should be addressed in Introduction and so the relevant references can also be added. Response: Thank you for this important observation. The Introduction has been substantially expanded to clearly discuss the physical significance of the multiple effects considered in the study. Relevant background information has been added, and the discussion has been strengthened by incorporating additional recent and closely related references. Comment 5: Reference list is too short, some recent selections on the topic can be included. Response: We agree with the reviewer. The reference list has been expanded by including several recent and relevant studies in the field. In particular, the following works have been added and appropriately cited in the revised manuscript to enhance the literature coverage and contextual relevance of the study. View more View less Competing Interests No competing interests were disclosed. reply Respond Report a concern Tanveer A. Peer Review Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448711) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. The direct URL for this report is: https://f1000research.com/articles/15-18/v1#referee-response-448711 keyboard_arrow_left Back to all reports Reviewer Report 0 Views copyright © 2026 Gamal A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 20 Jan 2026 | for Version 1 Ahmed Gamal , Menoufia University, Shebin El-Kom, Egypt 0 Views copyright © 2026 Gamal A. This is an open access peer review report distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. format_quote Cite this report speaker_notes Responses (1) Not Approved info_outline Alongside their report, reviewers assign a status to the article: Approved The paper is scientifically sound in its current form and only minor, if any, improvements are suggested Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit. Not approved Fundamental flaws in the paper seriously undermine the findings and conclusions Summary of the Article The manuscript investigates peristaltic transport of a non-Newtonian fluid under various physical effects using analytical approximations. While the topic itself falls within an active research area, the present study does not demonstrate sufficient originality, methodological rigor, or clarity to meet the standards of theF1000Research. Detailed Evaluation Presentation and Literature Coverage The manuscript is not clearly presented and does not adequately cite or engage with the current literature. The introduction is brief and largely descriptive, failing to critically analyze prior studies or identify genuine research gaps. Several cited works are outdated, and recent developments in the field are insufficiently addressed. Study Design and Technical Soundness The overall study design raises concerns regarding technical soundness. The governing equations—particularly those associated with the selected fluid model—are introduced without appropriate references, making it difficult to verify their correctness or originality. Methods, Analysis, and Reproducibility Insufficient methodological details are provided to allow independent replication. Key mathematical steps, especially in Section 4.3, are omitted or inadequately explained. Moreover, multiple approximations are employed without defining error bounds or ranges of validity, which compromises the transparency and reliability of the analysis. Validation and Reliability The manuscript lacks any form of **validation**. The results are not benchmarked against known analytical solutions, limiting cases, or previously published studies. As a result, the accuracy of the reported findings cannot be confidently assessed. Interpretation of Results and Conclusions The results are primarily described in terms of parameter trends, with little to no physical interpretation. Consequently, the conclusions are not sufficiently supported by the results and do not provide meaningful scientific insight. Source Data and Parameter Justification The numerical values used in the analysis are not justified or referenced, and no explicit analytical expressions or datasets are provided to reproduce the figures. This limits the reproducibility of the work. R equired Actions to Achieve Scientific Soundness To make the article scientifically sound, the authors would need to address all of the following major issues: 1. Clearly demonstrate genuine novelty relative to existing literature. 2. Substantially expand and update the introduction with a critical review of recent studies. 3. Provide proper references for all governing equations and constitutive relations. 4. Include validation through limiting cases or comparison with published results. 5. Justify all mathematical approximations and specify their ranges of validity. 6. Add clear physical interpretations of the results. 7. Justify and reference all parameter values used. 8. Improve the clarity, structure, and English language quality of the manuscript. 9. Provide sufficient mathematical details to ensure transparency and reproducibility. Is the work clearly and accurately presented and does it cite the current literature? No Is the study design appropriate and is the work technically sound? Partly Are sufficient details of methods and analysis provided to allow replication by others? Partly If applicable, is the statistical analysis and its interpretation appropriate? Not applicable Are all the source data underlying the results available to ensure full reproducibility? No Are the conclusions drawn adequately supported by the results? No Competing Interests No competing interests were disclosed. Reviewer Expertise Mechanical Engineering and Mathematical Engineering– with specific focus on :Peristaltic flow of complex/non-Newtonian fluids (e.g., Carreau and couple-stress fluids, )Heat and mass transfer in multi-physics systemsMagnetohydrodynamics (MHD) and porous media flowsNanofluids and hybrid nanofluidsAnalytical and numerical modeling techniques (e.g., FEM, perturbation methods) I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above. reply Respond to this report Responses (1) Author Response 02 Mar 2026 Salwa Al-Tamimi, Department of Fluid Mechanics, University of Al-Qadisiya, AL-Qadisiya, 58001, Iraq We sincerely thank the reviewer for the constructive and valuable comments, which have greatly contributed to improving the scientific quality and clarity of the manuscript. All raised issues have been carefully addressed, and the manuscript has been revised accordingly. Detailed responses are provided below: Comment 1: Clearly demonstrate genuine novelty relative to existing literature. Response: We thank the reviewer for this important comment. The manuscript has been revised to clearly highlight the novel aspects of the study, including the unique mathematical modeling approach, the physical effects considered, and the analysis performed, in comparison with recent and relevant literature Comment 2: Substantially expand and update the introduction with a critical review of recent studies. Response: The Introduction has been significantly expanded to include a critical review of recent studies related to the topic. Key strengths and limitations of prior works are discussed, and the positioning of the current study within the existing literature is clearly outlined Comment 3: Provide proper references for all governing equations and constitutive relations. Response: All governing equations and constitutive relations have been carefully reviewed, and appropriate references have been added for each to ensure proper scientific documentation and to strengthen the credibility of the model Comment 4: Include validation through limiting cases or comparison with published results. Response: A validation section has been added, in which selected limiting cases are analyzed and the results are compared with published studies. The comparisons show good agreement, confirming the accuracy and reliability of the model. Comment 5: Justify all mathematical approximations and specify their ranges of validity. Response: All mathematical approximations used in the study have been justified physically and mathematically, and their applicable ranges have been clearly specified in the revised manuscript Comment 6: Add clear physical interpretations of the results. Response: The Results and Discussion section has been enhanced with detailed physical interpretations of the numerical findings, explaining how different parameters influence the behavior of the system and providing deeper scientific insight. Comment 7: Justify and reference all parameter values used. Response: All parameter values used in the numerical analysis have been reviewed, justified based on physical considerations, and supported with references to relevant literature. Comment 8: Improve the clarity, structure, and English language quality of the manuscript. Response: The manuscript has undergone a comprehensive revision to improve organization, structure, and readability. Language and scientific writing have been enhanced to meet the standards of high-quality publications Comment 9: Provide sufficient mathematical details to ensure transparency and reproducibility. Response: Additional mathematical details, including derivation steps and numerical procedures, have been provided to ensure full transparency and allow reproducibility of the results by other researchers View more View less Competing Interests No competing interests were disclosed. reply Respond Report a concern Gamal A. Peer Review Report For: Analysis of the peristaltic flow of a variable viscosity Carreau fluid affected by temperature and concentration through an endoscope hollow flexible channel [version 1; peer review: 2 approved with reservations, 2 not approved] . F1000Research 2026, 15 :18 ( https://doi.org/10.5256/f1000research.190322.r448712) NOTE: it is important to ensure the information in square brackets after the title is included in this citation. 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