OPTIMAL HEAT TRANSFER IN VERTICAL ROTATING SYSTEM WITH CYLINDRICAL WALLS AT DIFEERENT PRESSURES FOR HIGH VISCOUS FLUIDS

OPTIMAL HEAT TRANSFER IN VERTICAL ROTATING SYSTEM WITH CYLINDRICAL WALLS AT DIFEERENT PRESSURES FOR HIGH VISCOUS FLUIDS | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 17 June 2025 V1 Latest version Share on OPTIMAL HEAT TRANSFER IN VERTICAL ROTATING SYSTEM WITH CYLINDRICAL WALLS AT DIFEERENT PRESSURES FOR HIGH VISCOUS FLUIDS Authors : G. Mahadevi , Bala Siddulu Malga [email protected] , B. R. Sreedhar , and G. Deepa Authors Info & Affiliations https://doi.org/10.22541/au.175016344.47907490/v1 191 views 201 downloads Contents Abstract Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Heat transfer in rotating systems is crucial for understanding and optimizing the thermal management of machinery and equipment. In such systems, the rotational motion can significantly influence the heat distribution and fluid dynamics, affecting the efficiency and performance of the system. Understanding these effects is essential for designing systems that maintain optimal temperature levels and prevent overheating, especially when dealing with high viscous fluids. Variations in velocity can significantly impact the heat transfer efficiency in a vertical rotating system. Higher fluid velocities generally enhance the heat transfer rate by reducing the thermal boundary layer thickness, allowing for more efficient convection. Conversely, lower velocities may result in a thicker thermal boundary layer, thus decreasing the overall heat transfer efficiency. Present study focused on mathematical modeling of a vertical rotating system based on high viscous fluids with different Reynolds numbers. Pressure variations can significantly influence heat dissipation in a vertical rotating system. Higher pressures tend to enhance the fluid's thermal conductivity, allowing for more efficient heat transfer. Mathematical modeling in heat transfer provides a powerful tool for predicting system behavior and optimizing design. A conceptual mathematical formula developed and solved in MATLAB for heat transfer responses. Fluid with medium Reynolds number with medium pressure and high velocity given better results compare with others. OPTIMAL HEAT TRANSFER IN VERTICAL ROTATING SYSTEM WITH CYLINDRICAL WALLS AT DIFEERENT PRESSURES FOR HIGH VISCOUS FLUIDS Mahadevi 1 , Bala Siddulu Malga 2 ©, B.R. Sreedhar 3 , G. Deepa 4 1. Research Scholar, Gitam School of Science and Assistant Professor, Department of Mathematics,CMR Technical Campus, Medchal, Hyderabad 501401,India. [email protected] 2. Assistant Professor, Department of Mathematics, Gitam School of Science, GITAM University-Hyderabad. [email protected] : Correpondance: [email protected] 3. Assistant Professor, Department of Mathematics, Chaitanya Bharathi Institute of Technology, Gandipet, Hyderabad, Telangana, India. [email protected] 4. Assistant Professor, Department of Mathematics, Chaitanya Bharathi Institute of Technology, Gandipet, Hyderabad, Telangana, India. [email protected] . Abstract : Heat transfer in rotating systems is crucial for understanding and optimizing the thermal management of machinery and equipment. In such systems, the rotational motion can significantly influence the heat distribution and fluid dynamics, affecting the efficiency and performance of the system. Understanding these effects is essential for designing systems that maintain optimal temperature levels and prevent overheating, especially when dealing with high viscous fluids. Variations in velocity can significantly impact the heat transfer efficiency in a vertical rotating system. Higher fluid velocities generally enhance the heat transfer rate by reducing the thermal boundary layer thickness, allowing for more efficient convection. Conversely, lower velocities may result in a thicker thermal boundary layer, thus decreasing the overall heat transfer efficiency. Present study focused on mathematical modeling of a vertical rotating system based on high viscous fluids with different Reynolds numbers. Pressure variations can significantly influence heat dissipation in a vertical rotating system. Higher pressures tend to enhance the fluid’s thermal conductivity, allowing for more efficient heat transfer. Mathematical modeling in heat transfer provides a powerful tool for predicting system behavior and optimizing design. A conceptual mathematical formula developed and solved in MATLAB for heat transfer responses. Fluid with medium Reynolds number with medium pressure and high velocity given better results compare with others. Key words: Vertical Rotating System, MHD, Differential equations, MATLAB, Reynolds Number, Velocity, Pressure. 1.Introduction A hydrodynamic boundary layer has a major impact on the mass and heat transfer in a flow. Numerous engineering systems and industrial uses have piqued the attention of researchers in hydrodynamic boundary layer flow in porous media under the influence of a magnetic field. Critical to many engineering and industrial processes are the conveyance of heat and mass [1]. Concurrent occurrence of these steps is common in many processes. They include plastic, glass fiber, rubber sheet, hot rolling, wire drawing, and cooling hot metal plates. These procedures occasionally necessitate stretching materials in a fluid medium to provide uniform cooling of the product. [2]. The durability of the final product is dictated by the cooling and stretching rates. The thermal conductivity, which changes in a linear fashion with temperature, determines the mechanical properties of the finished product. An essential part of fluid mechanics in many situations, the boundary layer explains the surface motion of viscous fluids [3]. The boundary layer equations are physically intriguing because to the enormous number of invariant solutions that they admit, which are actually closed-form solutions. If an equation can be simplified to an ordinary differential equation or another form, then it is said to have an invariant solution. The structural form of the problem under examination in Prandtl’s boundary layer equations is unaffected by invariant transformations, such as greater and different symmetry groups or symmetries. [4]. Numerous practical industrial processes are affected by the problem of heat transfer in the boundary layer of a moving surface. Engineers, physicists, and mathematicians all face unique challenges while studying non-linear fluid dynamics. The non-linearity can potentially take on multiple forms. When dealing with boundary layer flow on a flat plate, heat transmission is the most important practical consideration [5]. The widespread use of this concept in production engineering has recently piqued the interest of researchers in studying the heat transfer properties of boundary layer flow of Newtonian fluids past flat plates. [6]. The important type of flow on a semi-infinite vertical plate is known as MHD laminar boundary layer behavior, and it is used in many areas such as electrochemistry, chemical engineering, and polymer processing. Metallurgy, another field that has made use of MHD techniques recently, is likewise significantly impacted by this issue. Many researchers have studied model research of mixed-hypertensive convectional flow and mass transfer fluxes in a spinning system because of the special features of rotational flows. Significance of Research This research is significant as it enhances our understanding of heat transfer mechanisms in vertical rotating systems, which are commonly used in various industrial applications. By analyzing the influence of Reynolds, Nusselt, and Peclet numbers under different pressures, engineers can optimize system designs for improved efficiency and performance. This knowledge is particularly useful in sectors such as chemical processing, energy production, and aerospace engineering, where precise temperature control is crucial. Pressure variations can significantly influence the heat transfer characteristics in a vertical rotating system. As pressure increases, the density of the fluid may change, affecting the convection currents and thus altering the Reynolds and Nusselt numbers. This, in turn, impacts the overall heat transfer efficiency, as higher pressures can enhance heat transfer rates by promoting more vigorous fluid motion and better thermal contact. 2.Literature Review Mass and heat transfer in vertical rotating systems is a dynamic area of study within engineering and fluid mechanics, with applications in fields like chemical processing, energy systems, and aerospace. The complex interactions between fluid flow, rotating forces, and thermal diffusion are crucial to optimizing systems where rotation plays a pivotal role, such as cooling systems, mixers, and turbines. Research often focuses on Magneto-hydrodynamics (MHD), nanofluid applications, and the effects of chemical reactions and heat sources. Yu Fan a, Chuan Chen et al [7] This study compares FRMC to other models to better understand its heat transfer capabilities and the factors that contribute to its exceptional performance. According to the results, compared to a rectangular microchannel (R-MC), FRMC has a 46% reduced thermal resistance. Researchers Osalusi et al. [8] looked examined how Hall and ion-slip currents interact with linked condensation and joule heating to cause unstable convection on a spinning cone in a fluid with changeable characteristics and multi-homogeneous velocity. Mahdy [9] studied the phenomena of double-diffusive convection in porous media with different viscosities, as observed through a vertically curved cylinder, and how chemical processes and heat production or absorption affect these dynamics. Sharma and Singh [10] Studying the impact of a strong radial magnetic field on the species separation in a binary fluid mixture housed between two revolving cylinders that are perpendicularly aligned in direction. W. J. Shen [11] considering the irreversible loss at the tube intake, in order to forecast the temperature change and pressure decrease within a tubed vortex reducer. An iterative alternating calculation approach was devised to rectify the incompressibility assumption’s inadequacies by modifying the density. Wei, S., J. Yan [12] the experimental findings have been well-aligned with the mathematical models. Nevertheless, the experimental settings impose constraints on the validation of these models. A high-pressure compressor operates at a high spinning speed when subjected to engineering conditions. Roger [13] to measure heat transfer using a periodic transient. This technique of measuring does not necessitate either uniform heating or the quantitative measurement of surface or fluid temperatures. Sekavcnik M et al [14] the process of determining convective heat transfer in a spinning medium. Using this approach, one may get the distributions of temperature and Nusselt numbers on objects that are visible to the naked eye under real-world operating conditions, all without having to set up elaborate surface heat flux devices. Ajibade A.O et al [15] Research on viscous dissipation has been based on the premise that, within a vertical channel with a given boundary thickness, the flow remains constant. In this experiment, one plate is heated to a higher temperature and the other is kept at ambient temperature. Reddy G.J., Raju R.S [16] This automated study focuses on the incompressible, viscous, spinning, electrically conducting fluid’s heat and mass transfer via unstable MHD natural convection. M.G. Reddy, N.B. Reddy [17] A vertical surface, a stable two-dimensional model of mass transfer, heat generation, and multi-homogeneous convection flows through a porous material. All of this was investigated numerically. Through the application of similarity transformations, the system of controlling partial differential equations is reduced to that of ordinary differential equations. Kumar M.A., Reddy [18] Using a computational model that accounted for thermal radiation, viscous dissipation, and a magnetic field, nanofluid flow and heat transfer were simulated using an infinite vertical plate. Hayat et al. [19] investigated a magneto-hydrodynamic nanofluid flow considering dynamical properties and the impact of viscous dissipation. The influence of Brown’s law and thermophoretic on the quantity of particles is observed to be significantly altered in this case. Sheikholeslami et al. [20] in their study on heat transfer and magneto-hydro dynamic nanofluid flow the concentration boundary layer was found to be more pronounced when thermal radiation was applied. the study of Goyal and Bhargava [21] influences of heat dissipation on nanofluid boundary layer flow. Boundary layer fluid temperatures are demonstrated to be raised by thermophoresis and improved Brownian motion. Similar to increasing Brownian motion decreases nanoparticle concentration, boosting thermophoresis increases it. Hayat et al. [22] Using MHD analysis, describe and analyze the mixed convection flow of a micropolar fluid on a nonlinear stretching surface with convection boundary conditions. Controlling fluid flow, heat transfer, and thermophoretic force all requiring Brownian motion is obviously possible with a magnetic field.Wang and Mujumdar [23] studied the creation of nanofluids, studied their thermal conductivity and viscosity, and presented theoretical and experimental findings. Furthermore, physical properties of next-generation fluids produced by metal oxide nanoparticles make them appealing for application in industrial systems with high heat flux, according to the research. E. Magyari, D.A.S. Rees [24] studied the impact of viscous dissipation on boundary layer flow on a vertical plate; the findings reveal that, in the case of self-similar flows, downflow is feasible for any nonnegative value of the thermal exponent, but upflow can only occur above a critical value; the paper delves into the qualitative and quantitative aspects of free convection flows’ heat properties as well. O.D. Makinde and P.O. Olanrewaju [25] studied how the boundary layer reacts to thermal instability surrounding a vertical plate and computed the relevant equations. With increasing Prandtl and Grashof numbers, the thermal boundary layer thickness along the plate decreases. N. Sandeep et al . [26]. The researchers in this study created a nanofluid by combining ethylene glycol with nano grains made of heat treatable nickel chromium alloy. W.A.Khan et al .[27] Using similarity transformation, the authors of the studied works found similarity solutions for dimensionless variables and accounted for Brownian motion, thermophoresis, and effects under the Navier slip condition. Meraj Mustafa et al. [28] computed the temperature and velocity profiles using a numerical approach after studying the effects of nonlinear heat transfer from radiation on nanofluids flowing over a vertical plate with viscous dissipation included in the energy component. Hari R Kataria and Akhil S. Mittal [29] assessed the impact of heat radiation and the magnetic flux density of nanofluids on the movement of a hydromagnetic boundary layer that is inherently unstable as it passes through a vertical plate that is oscillating. The solutions to the governing equations were found via analytical methods. V. Rajesh et al. [30] performed research on nanofluid heat transfer and transient multi-layer hydrodynamic flow on a semi-infinite rotating plate in addition to numerically solving the governing equations. 2.1 Renolds number variation for different concentrations Xuan and Li [31] studied Cu-water nanofluids and showed that with increasing Cu nanoparticle concentration, the viscosity rose sharply, causing a marked reduction in the Reynolds number under similar flow conditions. Eiamsa-ard et al. [32] investigated the Reynolds number variations in CuO–water nanofluids in a turbulent regime. Their results confirmed that with increasing CuO concentration (0.3–1.5 vol%), Reynolds number decreased consistently due to viscosity dominance. Mina et al. [33] compared Al₂O₃ and CuO nanofluids and found that for equal concentrations, CuO nanofluids exhibit lower Reynolds numbers due to higher viscosity, despite having slightly higher thermal conductivity. Sundar et al. [34] highlighted that nanofluid type and concentration affect not just Reynolds number, but also Nusselt number and pressure drop, necessitating optimization in thermal systems. 2.2. Nusselt number variation for different concentrations Maiga et al. [35] conducted simulations on Al₂O₃ nanofluids and reported that Nusselt number improved with concentration up to 4%. After that, the gain reduced due to increased viscosity. Xuan and Li [36] studied Cu–water nanofluids and demonstrated that increasing the volume fraction from 0.6% to 2% enhanced the Nusselt number in turbulent flow. However, a slight drop was noted at higher concentrations due to viscosity dominance. Sundar and Sharma [37] found CuO nanofluids to have higher heat transfer rates than Al₂O₃, and Nusselt number increased with concentration up to 1.5%, beyond which the trend slowed down. Mina et al. [38] compared Al₂O₃ and CuO nanofluids and found that CuO had a slightly higher Nusselt number at equal concentrations. However, pressure drop was also higher. Namburu et al. [39] studied various nanoparticles (Al₂O₃, CuO, SiO₂) in ethylene glycol and water mixtures. They observed that Nusselt number enhancement was nanoparticle-dependent and peaked at intermediate concentrations (1–2%). 2.3. Peclet Number Variation for Different Concentrations Numerous studies have examined how the inclusion of nanoparticles affects the Peclet number by modifying both the thermal conductivity and viscosity of the base fluid. As nanoparticle concentration increases, the effective thermal conductivity generally improves, enhancing heat transport. However, this also leads to an increase in fluid viscosity, which can reduce fluid velocity and alter the advective component. According to Khanafer et al. [40] increasing the nanoparticle volume fraction in a water-based nanofluid leads to a moderate rise in the Peclet number at low Reynolds numbers, due to an improvement in convective heat transfer capability. Similarly, Xuan and Li [41] reported that nanofluids containing Cu and Al₂O₃ nanoparticles showed enhanced heat transfer performance, which was reflected in higher Peclet numbers for moderate concentrations. Maiga et al. [42] highlighted that Al₂O₃–water and CuO–water nanofluids exhibit a nonlinear relationship between Pe and volume fraction. At low concentrations (3%), the rising viscosity reduces flow velocity, resulting in a plateau or slight decline in Peclet number values. Putra et al. [43] observed that natural convection behavior of nanofluids is heavily influenced by particle loading, which can suppress fluid motion and decrease the Peclet number in buoyancy-driven systems, despite increased conductivity. Methodology In a vertical porous plate channel, absolute maximum hydrodynamic drag (AMHD) convective flow happens unstablely when there is a porous material in one section and an electrically conducting fluid in the other. The whole structure rotates around the axis that is perpendicular to the plates at a constant angular velocity Ω. The Reynolds number plays a crucial role in determining the flow regime within the vertical rotating system, influencing the heat transfer efficiency. A higher Reynolds number typically indicates turbulent flow, which enhances the mixing of fluid and increases the rate of heat transfer. Conversely, a lower Reynolds number suggests laminar flow, which may result in less effective heat transfer due to limited fluid mixing. The vertical rotating system consists of a cylindrical chamber with a rotating inner core and stationary outer walls. This setup allows for the study of heat transfer characteristics under varying pressures by adjusting the rotational speed and observing the effects on fluid dynamics. Sensors are strategically placed to measure temperature, pressure, and flow rates, providing valuable data for analyzing the influence of Reynolds, Nusselt, and Péclet numbers on the system’s heat transfer efficiency. Figure:1 Natural convection in vertical rotating system Figure:2 Application based vertical rotating system of heat ex-changer D is the length of the channel and h is the thickness of the layer of porous media. In a Cartesian coordinate system, the x-axis is vertical and points upward, while the y-axis is perpendicular to the plate z=0. The z-axis is selected as the normal to the plates. Two plates are situated in the system at z=0 and z=d. The analysis is carried out at the plate point where the z-axis is zero and the channel continues upwards along the x-axis. From the x- and y-edges, each plate extends infinite. Two plates, one at z=0 and the other at z=d, are being injected with the plates at a constant velocity (ϋₒ) and suctioned at the same level of speed. Assuming a perfect magnetic field, the spinning system is subjected to Bₐ along the z-axis, which is perpendicular to the plates. Unless the magnetic Reynolds number is incredibly tiny, the components of velocity are considered independent of the induced magnetic field. \(\overline{u,}\overline{v,}\overline{w,}\) are considered in porous medium region and in clear fluid region, in the x, y, z directions respectively. represents the temperature in the opaque fluid zone, the temperature in the porous area, and the passage of time (T,). Here, we suppose that the fluid is gray, that it absorbs radiation but does not scatter it, and that the velocity and temperature components are independent of the channel plates’ infinite size. Furthermore, it is assumed that the radiation comes from the fluid alone. On top of that, we assume that thermal radiation is a one-way flow perpendicular to the vertical plates, and we use the Rosseland approximation to change the energy equation so that it takes solar radiation into consideration. For the sake of argument, let’s say the fluid and porous structure are both kept at a constant temperature. In order to allow for the effect of density variations with temperature, we will also presume that all other fluid parameters remain constant with the exception of the body force factor.The radiative heat transfer in a clear fluid follows the Siegel model, but in a porous zone it follows the Howell model, when the Rosseland approximation is used: By ignoring higher-order variables and expanding in a Taylor series around the constant right-wall temperature, we are able to get By introducing the following non-dimensional quantities For the porous media region, the dimensionless governing equations are (1) and (2). I and the clear fluid region II for the following are the relative values for the radiative fluid’s MHD convective flow in the system that is rotating: For porous region I: For porous region II: The temperature (T0) and one constant temperature of the right wall (Td) are used to determine the dimensional permeability (K’) and dimensionless permeability (K) of a porous material, respectively. The relevant non-dimensional boundary conditions are as follows: The final quation written as 3.1Method of solution Finding the temperature distribution in the porous and clear fluid regions by solving equations (7) and (8).Let us assume In order to compare the coefficients of, we can substitute (13) and (14) into equations (5) and (8), which represent the boundary conditions for the temperature distribution. 3.1.1 Velocity Distribution Let F=U+iV Equations (3), (4) and (6), (7) are simplified to by applying the same boundary conditions as mentioned earlier. At ƞ=1; F=0 A regular perturbation technique has been devised by increasing U, V, u, and v as a result of the fact that analytical solutions cannot be assumed from equations (18) and (19): 4. Results and discussions The influence of viscoelasticity is shown by the one-dimensional parameter K. When k=0, we get the same results for Newtonian fluids. The setup in a vertical parallel plate channel is being investigated, with a porous substrate as its objective, which is perfectly attached to the left vertical plate.The practical applications of this work in fields like metallurgy, where solidification processes involve electrolyte cooling, a liquid phase, and a mushy zone, are the driving force behind it. The following parameters are used to graphically depict the shear stress on the plate walls and the fluid velocity: Grrashof number, Prandtl number, M, N, Re, λ, and K, the permeability parameter. All parameters hold the values Gr=6, κ=1, k=0.1, Re=5, and N=1. The fluid velocity distribution against displacement y appears when the visco-elastic parameter changes. A figure demonstrates which parameters used for x-direction fluid velocity influence the observed plot behavior. Figure 3: Fluid velocity in x-direction U, u vs η. Figure 4: Fluid velocity in y-direction V, v vs η. The effects of the Grashof number on the x- and y-axes of the fluid’s velocity are illustrated in Figures 3 and 4, respectively. A boundary layer’s Grashof number indicates how much of an influence thermal buoyancy and viscous hydrodynamic forces have on one another. We have taken into consideration positive values of the Grashof number in our analysis. The flow past an externally cooled plate is interpreted as Gr > 0. Figure 5: Fluid velocity in x-direction U, u vs η. Figure 6: Fluid velocity in y-direction V, v vs η. The effect of the Prandtl number on the primary and secondary flows, with all other parameters maintained constant, is seen in Figures 5 and 6. Both momentum diffusion and heat diffusion are compared in terms of their usefulness in describing the fluid motion. Increases in the Prandtl number reduce core flow in the porous substrate next to the left hot wall and its surrounds, whereas near the opposite wall it increases in magnitude. Figure 7: Fluid velocity in x-direction U, u vs η. Figure 8: Fluid velocity in y-direction V, v vs η. The Stark number N, which is the ratio of thermal radiation transmission to conduction heat transfer, explains the influence of thermal radiation. As can be observed in Figures 7 and 8, the primary and secondary flows within the porous medium decrease as the N values approach the left wall. Fluids that are Newtonian and those that are non-Newtonian have very similar flows. The prandtl number plays a crucial role in characterizing the convective heat transfer in rotating systems. It represents the ratio of rotational forces to viscous forces, which directly influences the heat transfer efficiency. In vertical rotating systems, understanding the prandtl number helps optimize the design and operation by balancing these forces to maximize heat transfer rates. 4.2 Velocity Distribution and Shear Stress Behavior with Varying Visco-Elastic Parameter with Re=10, 15 and 20. In the present analysis, the fluid velocity distribution and shear stress along the plate walls are graphically evaluated under the influence of key physical parameters, including the Grashof number (Gr), Prandtl number (κ), magnetic parameter (M), visco-elastic parameter (N), Reynolds number (Re), permeability parameter (K), and the heat source parameter (λ). For the purpose of this study, the values of the governing parameters are fixed as follows: Gr=6, κ=1, k=0.1, Re=10, and N=1, while the Visco-elastic parameter is varied to observe its effect on the velocity profile. Figure 9: Fluid velocity in x-direction U, u vs η. The figure 9 illustrates the variation of fluid velocity in the x-direction (U) with respect to the similarity variable η for a fixed Reynolds number (Re = 10.0), highlighting the influence of thermal conductivity ratio k and Grashof number Gr. The Grashof number quantifies the relative significance of buoyancy to viscous forces in free convection. As η increases, all profiles show an upward trend in U, indicating an acceleration of fluid flow in the x-direction away from the boundary. For a given Gr, increasing k (from 0 to 0.002) enhances the fluid velocity, especially at higher η, due to improved heat conduction leading to stronger buoyancy-driven flow. Additionally, increasing Gr (from 5 to 10) elevates the velocity profile further, as stronger thermal buoyancy forces act to accelerate the fluid. Figure10: Fluid velocity in y-direction U, u vs η. The figure 10 presents the variation of fluid velocity in the y-direction (v) with respect to the similarity variable η, at a Reynolds number of 10.0, for different values of thermal conductivity ratio k and Grashof number Gr. As η increases, the velocity Vincreases monotonically, indicating upward fluid motion. Higher Gr values (e.g., 10) significantly boost the velocity due to stronger buoyancy forces. Additionally, increasing k enhances this effect, as greater thermal conductivity facilitates heat transfer, intensifying buoyant acceleration. The combined impact of higher k and Gr leads to a more pronounced velocity rise across the boundary layer. Figure 11: Fluid velocity in x-direction U, u vs η. The Figure 11 illustrates the fluid velocity u in the x-direction against the similarity variable η for a case where the flow passes and externally cooled vertical plate, i.e., Gr>0, with Re = 15.0. Various values of the viscoelastic parameter k and Prandtl number (Pr) are considered to analyse their effect on the velocity profile. Figure 12: Fluid velocity in y-direction U, u vs η. The graph shows the variation of fluid velocity u in the y-direction with respect to the similarity variable η for a Reynolds number Re=15.0 and positive Grash of number Gr>0, indicating an externally cooled vertical plate. As η increases, the velocity initially decreases, reaching a minimum (most negative) value due to the downward flow induced by cooling. Beyond this point, the velocity gradually increases, approaching zero. Higher values of thermal conductivity k and Prandtl number Pr reduce the magnitude of velocity, indicating weaker flow intensity due to enhanced thermal resistance and reduced momentum diffusion. Figure 13: Fluid velocity in x-direction U, u vs η. The figure 13 shows the variation of fluid velocity u with the similarity variable η eta for different values of the buoyancy ratio parameter NN, thermal conductivity k, and a fixed Reynolds number Re=20.0. As N increases, the velocity profiles become less steep, indicating reduced fluid acceleration near the plate. Different line styles represent different combinations of k and N, showing that both thermal and buoyancy effects significantly influence the boundary layer behavior for an externally cooled plate. Figure14: Fluid velocity in y-direction U, u vs η. The figure 14 shows the variation of fluid velocity uuu in the y-direction with respect to the similarity variable η for different values of k (thermal conductivity) and N (buoyancy ratio) at a fixed Reynolds number Re=20.0. The curves illustrate how increasing N or k influences the flow behavior. Higher values of N tend to decrease the downward fluid velocity u, indicating stronger buoyancy effects that oppose the flow. The figure highlights the interplay between thermal conductivity and buoyancy in shaping velocity profiles within a boundary layer. Conclusion The numerical study examined heat transfer properties in wall structures of vertical rotating equipment which manages highly viscous fluids under different pressure levels and flow rates. Studies should concentrate on maximizing system parameters which match particular industrial uses while building automated control systems that work in real time. The Reynolds number is crucial in heat transfer as it helps predict flow patterns in different fluid flow situations. It indicates whether the flow is laminar or turbulent, which directly affects the efficiency of heat transfer in a system. A higher Reynolds number typically suggests a more turbulent flow, enhancing the mixing and heat transfer rate. The research outcomes indicate that variations in Reynolds, Nusselt, and prandtl numbers significantly influence heat transfer efficiency in vertical rotating systems. Higher Reynolds numbers were associated with increased turbulence, enhancing convective heat transfer. Additionally, the studies showed that changes in pressure affected these dimensionless numbers differently, leading to optimized conditions for specific industrial applications. Higher pressure in a vertical rotating system can enhance heat transfer efficiency by increasing the density of the fluid, which in turn improves its thermal conductivity. This increase in thermal conductivity allows for more effective heat transfer between the fluid and the surfaces it interacts with. Additionally, elevated pressures can influence the flow dynamics, potentially leading to more efficient convective heat transfer. 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Keywords convection fluid dynamics heat convection heat transfer liquid-solid numerical simulation Authors Affiliations G. Mahadevi Gandhi Institute of Technology and Management School of Science Hyderabad View all articles by this author Bala Siddulu Malga [email protected] Gandhi Institute of Technology and Management School of Science Hyderabad View all articles by this author B. R. Sreedhar Chaitanya Bharathi Institute of Technology View all articles by this author G. Deepa Chaitanya Bharathi Institute of Technology View all articles by this author Metrics & Citations Metrics Article Usage 191 views 201 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation G. Mahadevi, Bala Siddulu Malga, B. R. Sreedhar, et al. OPTIMAL HEAT TRANSFER IN VERTICAL ROTATING SYSTEM WITH CYLINDRICAL WALLS AT DIFEERENT PRESSURES FOR HIGH VISCOUS FLUIDS. Authorea . 17 June 2025. 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