Numerical studies on thermo-hydraulic performance of solar air heater with quarter circle roughness ribs

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The fluid flow and heat transfer properties of a roughened solar air heater with quarter-circle-shaped ribs were examined in-depth using numerical analysis. The k–e RNG turbulence model was used to conduct 2D steady-state numerical simulations, and the findings showed excellent agreement with the smooth duct and related literatures. The impact of rib spacing was explored by changing the rib relative pitch (p/e) from 6.67 to 13.3 for Reynolds numbers (Re) between 4,000 and 20,000. The thermo-hydraulic performance factor was found to be 1.63. Additionally, it was shown that an increase in relative pitch (p/e) of 6.67 to 10 resulted in an increase in the Nusselt number for all Re values examined. At Re of 16,000, an enhancement of 2.42 times the Nu was made for p/e = 6.67. It was also noted that for all Re values taken into consideration, Nu falls with an increase in p/e from 10 to 13.3. solar air heater heat transfer thermal performance quarter circle ribs CFD Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction Solar air heaters have a straightforward construction and design. They are frequently employed as drying crops and heating spaces. The reason for the low efficiency of flat plate solar air heaters is poor convective heat transfer coefficient between the flowing air and the absorber plate which increases heat losses to the environment. The existence of a laminar sub-layer, which can be broken by adding artificial roughness to the heat-transferring surface, is the cause of the low heat transfer coefficient [ 1 ]. The intention of enhancing heat transfer has been tried by deliberately disturbing this laminar sub-layer. To induce turbulence close to walls or disrupt laminar sub-layers, artificial roughness in the shape of ribs has been employed in a variety of configurations. Artificial roughness increases frictional losses, which raises the power needed for fluid flow. To break the viscous sub-layer, turbulence must therefore be produced in the area immediately surrounding the heat-transferring surface. The flow of core fluid should not be excessively disrupted in order to prevent an increase in pumping demand. In order to do this, roughness element heights are kept low relative to duct size [ 2 ]. Several investigations have been carried out to study the effect of artificial roughness on heat transfer and friction factor with roughened surface. Yadav and Bhagoria [ 3 , 4 ] examined the impact of transverse circular, square, and equilateral triangular ribs using 2D computational fluid dynamics (CFD) analysis on the enhancement of heat transfer. They found that the ribs situated beneath the absorber could increase the convective heat transfer coefficient in a fluid field of solar air heater. Mishra et al [ 5 ] investigated triangular-shaped SAH with V-shaped ribs on the absorber plate. They changed the angle of attack from 45° to 60° and Re from 4,000 to 20,000. Nu was found to be 2.26 times higher than the smooth duct. Dongxu Jin et’al [ 25 ] also investigated solar air heater duct with multi V-shaped ribs on the absorber plate numerically and the maximum value of the thermal performance parameter was found to be 1.93 for the range of parameters investigated. This research was studied further in 2019 with a finding of maximum thermo-hydraulic performance factor of 2.35 [ 26 ]. Extrusion on the absorber plate shaped like tiny wires is studied by Prasad and Saini [ 6 ], investigated whether identical roughness geometries have an equivalent impact on heat transfer, friction factor, and thermal performance. And other more related researches are reviewed as shown in Table 1 . The motivation behind this study stems from the need to enhance the efficiency and effectiveness of solar air heater systems by exploring the effects of novel rib configurations, such as quarter-circle roughness ribs, on heat transfer and fluid flow characteristics. Despite the existing body of research on solar air heaters and roughened surfaces, limited attention has been given to the unique geometric features and potential advantages offered by quarter-circle ribs in enhancing heat transfer performance. By investigating the thermo-hydraulic behavior of solar air heaters equipped with quarter-circle roughness ribs through numerical simulations, this study aims to fill a critical gap in understanding the intricacies of heat transfer augmentation in swirling confined flows. Specifically, the proposed numerical investigations will focus on quantifying the thermal performance enhancements, pressure drop characteristics, and flow distribution patterns associated with quarter-circle roughness ribs in solar air heater channels. By elucidating the impact of these innovative rib geometries on heat transfer efficiency and flow dynamics, this study seeks to provide valuable insights for optimizing solar air heater design and operation in renewable energy systems. Through comprehensive numerical analyses and comparisons with conventional rib configurations, the research aims to identify the advantages and limitations of utilizing quarter-circle ribs for enhancing the thermo-hydraulic performance of solar air heaters. 2. Methodology 2.1. Numerical Modeling ANSYS Fluent 19.2 was used to model the quarter-circle ribbed surface schematic arrangement of the proposed numerical setup as shown in Fig. 1 . We want to study the impact of rib shape on airflow and heat transfer enhancement in solar air heater quantitatively and qualitatively in this work. We have selected the 2D geometry of a rectangular duct with quarter circle ribs at the bottom of the absorber for numerical simulation. A duct consists of three sections which are intake part spanning 245 mm, a test portion comprising 300 mm, an exit section measuring 115 mm. The solar air heater duct's hydraulic diameter is 33.33 mm and the duct aspect ratio (W/H) is maintained at 5. The entry and exit sections' lengths are determined by the ASHRAE Standard 93 [ 15 ] to minimize flow disturbances at the inlet and to capture the airflow behavior downstream of the absorber plate respectively. Therefore, fully developed turbulent flow will be created in the test section. In order to reduce the impact of flow passage obstruction [ 16 ], the rib height is maintained at 1.5 mm. A constant heat flux of 1000 W/m 2 is delivered to the test section's upper surface and the rib pitch to its height ratio (P/e) is maintained between 6.67 and 13.33. We used Reynolds number ranging from 4,000 to 20,000 in this simulation. Table 2 presents the geometric parameters of solar air heater duct. Table 2 Geometrical Parameters for numerical simulation [ 15 , 27 ] Parameters Values Entry length, L 1 245 mm Test section, L 2 300 mm Exit length, L 3 115 mm Width of duct, W 100 mm Height of duct, H 20 mm Hydraulic diameter of duct, D h 33.33 mm Roughness height, e 1.5 mm Relative roughness height RRH, e/D h 0.045 Roughness pitch, p 10, 15, 20 mm Relative roughness pitch RRP, p/e 6.67, 10, 13.33 (3 Values) Number of ribs, n (L 2 /p) 30, 20, 15 2.2. Mesh Generation As shown in Fig. 2 , the laminar sub-layer along the boundary of the solar air heater duct is solved using a structured mesh with element size of 0.1 mm (481,424 number of elements as discussed in Table 5 ). Tetrahedral element type is chosen because it is better for rectangular SAH duct model simulation. The left side of the wall is a velocity inlet that receives a uniform, constant velocity ranging from 1.75 to 8.76 m/s. The right-side wall of the fluid domain serves as an ambient pressure outlet. There is a steady 1,000 W/m 2 heat flux at the top wall. The bottom plate belongs to the adiabatic boundary constraint. The boundary conditions of no-slip applied to the fluid domain walls as described in Table 3 . Table 3 Boundary conditions of SAH model Boundary Parameter Values Inlet Inlet velocity, (u i = u inlet ) Reynolds number, Re 1.75–8.76 m/s 4,000–20,000 (5 values) Outlet Outlet pressure, (P out = 0) 101,325 Pa Wall (Top surface (absorber)) Heat flux (-k \(\:\frac{\partial\:T}{\partial\:x}\) = \(\:\ddot{q}\) ) 1,000 W/m 2 Other walls (bottom, sides of absorber) Adiabatic ( (-k \(\:\frac{\partial\:T}{\partial\:x}\) = 0 ) 0 Solid-fluid interface No-slip (u i = 0) 0 2.3. Numerical Solution ANSYS Fluent 19.2 was used in this study to examine the heat transfer enhancement and fluid flow properties of a 2D simulation. The 2D model was solved by applying the previously indicated boundary conditions as shown in Table 3 . Pressure and momentum equations are connected using the SIMPLE algorithm and all equations are discretized using the second-order upwind scheme. For energy and other equations, the convergence criteria values were chosen at 10 − 6 and 10 − 3 respectively. The RNG k-ε turbulence model is used because of high accuracy for simulating complex flows such as swirling motions, which is created due to quarter circle ribs in this study. It has improved predictive accuracy and computational efficiency for such study than other turbulence models. Table 4 displays the thermo-physical characteristics of the absorber plate and working fluid. Table 4 Thermo-physical properties of air and absorber Properties Air Absorber (Al) Density, ρ 1.225 kg/m 3 2719 kg/m 3 Specific heat, C p 1006.43 J/kgk 871 J/kgk Thermal conductivity, K 0.0242 W/mk 202.4 W/mk Viscosity, µ 1.789x10 -5 kg/ms - Prantl number, Pr 0.744 - 2.3.1. Governing equations The governing equations for steady-state, 2D airflow in a solar air heater with artificial roughness can be expressed using the continuity, momentum, and energy equations [ 17 , 24 ]. Continuity Equation: $$\:\frac{\partial\:}{\partial\:{x}_{i}}\:\left(\rho\:{u}_{i}\right)\hspace{0.17em}=\hspace{0.17em}0$$ 1 Momentum conservation equation: \(\:\frac{\partial\:}{\partial\:{x}_{i}}\) ( \(\:\rho\:{u}_{i}{u}_{j}\) ) = - \(\:\frac{\partial\:\rho\:}{\partial\:{x}_{i}}\) + µ \(\:\frac{\partial\:}{\partial\:{x}_{j}}\left(\frac{\partial\:{u}_{i}}{\partial\:{x}_{j}}+\frac{\partial\:{u}_{j}}{\partial\:{x}_{i}}\right)\) (2) Energy conservation equation: $$\:\frac{\partial\:{(\rho\:u}_{j}T)}{\partial\:{x}_{i}}\:=\:\frac{\partial\:}{\partial\:{x}_{j}}\left(Г+\:{Г}_{t}\frac{\partial\:T}{\partial\:{x}_{j}}\:\right)$$ 3 Reynolds number [ 22 ]: Re = \(\:\frac{\rho\:u{D}_{h}}{\mu\:}\) (4) Where, D h = \(\:\frac{4A}{P}\) Nusselt number: This research examines how the addition of a quarter circle rib to the duct surface improves heat transfer and pressure drop. The FLUENT post-processing software is employed to determine the heat transfer coefficient (h) and pressure drop (∆P) within the duct, allowing for the calculation of the average Nusselt number and friction factor using Eqs. 5 & 7 respectively [ 18 ]. Nu r = \(\:\frac{h{.D}_{h}}{k}\) (5) Where, the average convective heat transfer coefficient (h) is h = \(\:\frac{{q}^{{\prime\:}{\prime\:}}}{{T}_{w}-{T}_{m}}\) (6) The friction factor for solar air heater with roughened ribs is $$\:{f}_{r}\:=\:\frac{(\varDelta\:p/l)D}{2\rho\:{u}^{2}}$$ 7 Where, ∆P = \(\:{P}_{in}-{P}_{out}\) The Nusselt number for a smooth solar air heater duct may be determined using the Dittus Boelter equation [ 19 ]. Nu s = 0.023 \(\:{R}_{e}^{0.8}{P}_{r}^{0.4}\) (8) And friction factor for a smooth solar air heater may be computed using the Blasius eqn, [ 17 ]. f s = 0.00791 \(\:{R}_{e}^{-0.25}\) (9) Thermo-hydraulic performance factor [ 20 ] THP = \(\:\frac{{Nu}_{r}\:/\:{Nu}_{s}\:}{{{(f}_{r}/{f}_{s})}^{1/3}\:}\) (10) 3. Results & Discussion In this research, heat transfer and flow characteristics in the solar air heater with a ribbed duct were analyzed and the governing equations were solved using ANSYS Fluent 19.2. The 2D model was created in Solid Work, imported and then irregularly meshed with Fluent. 3.1. Grid Independency Test A grid-independency investigation was performed to validate variations in flow friction and Nusselt number for various element sizes. As indicated in Table 5, it was discovered that the element size of 0.1 mm resulted in the least difference (< 1%) when compared to other element sizes at Re of 12,000 and relative pitch (p/e) of 6.67. As a result, 0.1 mm element size was taken into consideration for further investigations. Table 5 Grid independence test of ANSYS fluent element size No of cells Nu ∆Nu f ∆f 0.15 332,642 82.86 - 0.0328 - 0.12 413,531 84.14 1.521274 0.0332 1.3253 0.10 481,424 84.9 0.895171 0.0334 0.5988 0.08 513,146 85.53 0.736584 0.0335 0.29851 3.2. Validation of Numerical Model The 2D model of solar air heater is validated by contrasting the CFD results with the findings derived from the correlations reported in the literatures [17, 19]. Equations 8 & 9 show how to use the correlations to calculate the friction and Nusselt number for smooth solar air heater. The CFD findings are shown to be in good agreement (< 5%) with the empirical equations as shown in Figs. 3 and 4 which lends credence to the validity of the study and suggests potential for future investigations. 3.3. Qualitative and Quantitative Analysis a. Nusselt Number The heat transfer and fluid flow properties of a quarter circular rib surface at different pitch distances and Reynolds numbers are presented in Fig. 5. According to the findings, greater Reynolds numbers were associated with higher Nusselt numbers, while lower Reynolds numbers were associated with lower Nusselt numbers. Lower Nusselt numbers for Re of 4,000 and maximum Nusselt numbers for higher Reynolds numbers were seen in the numerical investigation. Furthermore, a higher heat transfer rate was obtained at the minimal pitch ratio of p/e = 6.7 as compared to p/e = 10 and p/e = 13.3. As shown in Fig. 6, velocity contour plot findings show how heat flow is distributed at different pitch distances. A powerful vortex is created close to the first pair of ribs and then the heat is distributed in the direction of fluid flow. Additionally, as the Reynolds number rises, a greater vortex size is created inside the duct which causes normal fluid disturbances creating higher heat transfer. Among these, the fluid flow experienced more turbulence at the relative pitch p/e of 6.67 than other pitch values. b. Flow Friction In this study, the pressure drop at different Reynolds numbers caused by the rib surface was recorded as Fig. 7 illustrates. As the Reynolds number increased, the friction factor was found to decrease and as the Reynolds number decreased, it increased. Figure 8 displays the pressure contour plot results, which clearly indicate the pressure drop between the rib surfaces. It was found that a powerful vortex with a closer pitch distance of p/e = 6.7 was generated at higher Reynolds numbers. Progressive vortices were formed by other relative pitch distances. The lowest pressure drop and friction were seen at relative pitch distance of p/e = 13.3. Using a turbulence kinetic energy (k-e) model, the heat dissipation between rib surfaces in the direction of fluid flow was examined. The findings are shown in Fig. 9 for all pitch distances with Reynolds numbers ranging from 4,000 to 20,000. The results show that when the Reynolds number grew, the rib surface with the closer pitch distance generated a larger heat transfer rate than the other surfaces. The turbulence intensity clearly showed the highest heat dissipation between the wall surface and rib surface. e. Thermo-hydraulic Performance Factor (THPF) The heat transfer efficiency in the fluid field of solar air heater is increased by adding a quarter-circle rib on the bottom of the absorber. However, when the rib is present, there is also a discernible rise in pressure drop. As a result, this section evaluates the THPF taking into account both an improvement in heat transmission and a rise in pressure drop as shown in Fig. 10. The values of the THPF were found in the range of 0.85 to 1.63. The THPF rises in conjunction with relative pitch and Re. The lower relative pitch and higher Reynolds number are considered to be more advantageous for higher solar air heater efficiency. The maximum THPF of 1.63 was found at the relative pitch of 6.67 which is lying within the acceptable range of roughness pitch as reported by other scientific papers [3, 14, 21]. According to the numerical study, the maximum Nusselt number is produced around 2.42 times higher compared with plain duct, at a Re of 16,000 and p/e = 6.67. Conclusions In solar air heater, the heat transmission, friction factor and thermo-hydraulic performance of quarter circle ribs at different pitch distances were the main subjects of the 2D numerical study. According to the numerical data, when the Reynolds number increased, the average Nusselt number increased and the average friction factor decreased. The numerical study revealed the following: Compared to a smooth surface, applying artificial roughness to the absorber plate greatly increased the Nusselt number. The minimum friction factor of 0.007 was obtained at relative pitch (p/e) of 13.3 and Reynolds number of 20,000. Nusselt number was improved 2.42 times higher in quarter circle roughened duct at p/e = 6.67 and Reynolds number of 16,000 than smooth duct. For square circle roughness, the thermo-hydraulic performance factor (THPF) of 1.63 was obtained at relative pitch p/e of 6.67. Therefore, adding quarter circle roughness to solar air heaters can help to improve heat transfer and system performance. This can contribute to advancements in solar energy utilization, and sustainable heating solutions. Collaboration with industry partners, academia, and governmental agencies can further catalyze the development and commercialization of innovative solar air heating technologies based on the findings from the present work. Abbreviations e roughness height, mm e/d relative roughness height p roughness pitch, m p/e relative roughness pitch H height of air channel, m h heat transfer coefficient, W/m 2 K k thermal conductivity of air, W/Mk f friction factor f r friction factor for rough surface f s friction factor for a smooth surface Nu Nusselt number Nu r Nusselt number for rough duct Nu s Nusselt number for smooth duct THPF Thermo-hydraulic performance factor SAH Solar air heater P r Prandtl number R e Reynolds number µ Dynamic viscosity, Ns/m 2 Declarations Declaration of competing interest The authors declare that there is no conflict of competing interest. Declaration of funding This research was not funded by any grant. Data availability The data that support the findings of this study are available from the corresponding author, [Tazebew Dires Kassie], upon reasonable request. Author contributions statement Yaregal Eneyew Bizuneh: Writing original draft, Visualization, Validation, Project administration, Methodology, Investigation, Formal analysis, Conceptualization. Tazebew Dires Kassie: Writing, review & editing, Supervision, Data curation, Investigation. Atalay Enyew Bizuneh: Writing, review & editing, Supervision, Resources, Investigation. References Bhatti MS, Shah RK; Turbulent and transition flow convective heat transfer; Handbook of single phase convective heat transfer, Chapter 4, New York: John Wiley & Sons Inc; 1987. Saini JS; Use of artificial roughness for enhancing performance of solar air heater; Proceedings of XVII National and VI ISHME/ASME heat and mass transfer conference; Kalpakkam (India); January 05e07 2004; p.103e12. Yadav, A.S.; Bhagoria, J.L. A CFD (Computational Fluid Dynamics) Based Heat Transfer and Fluid Flow Analysis of a Solar Air Heater Provided with Circular Transverse Wire Rib Roughness on the Absorber Plate. 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Supplementary Files Table1.docx Cite Share Download PDF Status: Published Journal Publication published 23 Jul, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 16 Apr, 2025 Reviews received at journal 11 Apr, 2025 Reviewers agreed at journal 18 Mar, 2025 Reviews received at journal 07 Mar, 2025 Reviewers agreed at journal 01 Mar, 2025 Reviews received at journal 05 Feb, 2025 Reviewers agreed at journal 15 Jan, 2025 Reviewers agreed at journal 13 Jan, 2025 Reviewers invited by journal 13 Jan, 2025 Editor assigned by journal 13 Jan, 2025 Editor invited by journal 13 Jan, 2025 Submission checks completed at journal 10 Jan, 2025 First submitted to journal 02 Jan, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5749527","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":400496643,"identity":"e7c05574-48d8-4ff9-920f-6146d9e0db39","order_by":0,"name":"Yaregal Eneyew Bizuneh","email":"","orcid":"","institution":"Debre Markos University","correspondingAuthor":false,"prefix":"","firstName":"Yaregal","middleName":"Eneyew","lastName":"Bizuneh","suffix":""},{"id":400496644,"identity":"c6e0e7b0-557e-4adc-b719-ed9585ee2be0","order_by":1,"name":"Tazebew Dires Kassie","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYJACZjB5GERUQNgS+JTzoGo5g9CCUxtCywEgZmwjQos9+/GHjwsqDjPwHed9+PDnPOtogwPMB2/zMNjU4bSFJyHZeMaZwwySh9mNjXm3peduOMCWbM3DkIbHYQnHpHnbbjMYHGZjk2bcdhiohcdMmofhMG4t/A/bf/P+A2th//lzDkgL/zeglv+4tUgkszHzNkBsYeBtANvCBtRyALeWG8+YpWcc+88jeZiNWZrnWHruzMNsxpZzDJIlG3BoYe9Pf/i5oCZNju/8McaPP2qsc/uONz+88abCjh+XLYhggANw1BgQ0jAKRsEoGAWjAB8AAI+FT4PYbFcSAAAAAElFTkSuQmCC","orcid":"","institution":"Debre Markos University","correspondingAuthor":true,"prefix":"","firstName":"Tazebew","middleName":"Dires","lastName":"Kassie","suffix":""},{"id":400496645,"identity":"cb619950-fc76-4bfc-86de-b3cb6dda0a67","order_by":2,"name":"Atalay Enyew Bizuneh","email":"","orcid":"","institution":"Debre Berhan University","correspondingAuthor":false,"prefix":"","firstName":"Atalay","middleName":"Enyew","lastName":"Bizuneh","suffix":""}],"badges":[],"createdAt":"2025-01-02 07:08:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5749527/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5749527/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-10620-y","type":"published","date":"2025-07-23T15:57:44+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":73661382,"identity":"7fb59f85-f50a-4c3f-bc45-ab85c09a2556","added_by":"auto","created_at":"2025-01-13 11:10:36","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":49474,"visible":true,"origin":"","legend":"\u003cp\u003eNumerical model of SAH duct\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/d8d16ce468957bd3b6888992.png"},{"id":73660183,"identity":"3da9753e-52af-4f20-8934-2adc19f27dd7","added_by":"auto","created_at":"2025-01-13 11:02:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":464738,"visible":true,"origin":"","legend":"\u003cp\u003eMeshing of SAH duct model\u003c/p\u003e","description":"","filename":"floatimage12.png","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/b25bd8b74dece3e9991fc1ec.png"},{"id":73660176,"identity":"e8642ab3-05d4-411a-89da-6d62d57fdbf8","added_by":"auto","created_at":"2025-01-13 11:02:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":45152,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of numerical values with a Dittus–Boelter equation\u003c/p\u003e","description":"","filename":"floatimage13.png","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/ab7b95c84f98dcac0c234910.png"},{"id":73661383,"identity":"0470d298-8fd8-49b0-8824-aa03bfc3d9f3","added_by":"auto","created_at":"2025-01-13 11:10:37","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":51669,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of numerical values with Blasius equation\u003c/p\u003e","description":"","filename":"floatimage14.png","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/8adca910f245ecabcec02c40.png"},{"id":73661380,"identity":"ad83341b-403e-4667-a4b6-6e22fb384055","added_by":"auto","created_at":"2025-01-13 11:10:36","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":52947,"visible":true,"origin":"","legend":"\u003cp\u003eNusselt number versus Reynolds number\u003c/p\u003e","description":"","filename":"floatimage15.png","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/05bdec9075411b52ced1a7de.png"},{"id":73660195,"identity":"4daa9501-30bc-478a-a84b-746cb12aeced","added_by":"auto","created_at":"2025-01-13 11:02:38","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":86718,"visible":true,"origin":"","legend":"\u003cp\u003eVelocity contour (a) Re=4,000, p/e=6.67; (b) Re=16,000, p/e=6.67; (c) Re=4,000, p/e=13.3; (d) Re=16,000, p/e=13.3\u003c/p\u003e","description":"","filename":"floatimage16.png","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/1dc33c7209230ccc1974b521.png"},{"id":73660164,"identity":"5d2b45ce-fa47-4a6c-bf30-effa87e41d92","added_by":"auto","created_at":"2025-01-13 11:02:36","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":65616,"visible":true,"origin":"","legend":"\u003cp\u003eFriction Factor versus Reynolds number\u003c/p\u003e","description":"","filename":"floatimage17.png","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/d37320c2001274ff428b894c.png"},{"id":73660181,"identity":"c8d23226-ae4d-436c-a6b6-065ac832d601","added_by":"auto","created_at":"2025-01-13 11:02:37","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":80824,"visible":true,"origin":"","legend":"\u003cp\u003eContour of pressure (a) Re=4,000, p/e=6.67; (b) Re=16,000, p/e=6.67; (c) Re=4,000, p/e=13.3; (d) Re=16,000, p/e=13.3\u003c/p\u003e","description":"","filename":"floatimage18.png","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/b4e6a6dd12d6fb2179f6f078.png"},{"id":73661387,"identity":"a36157c6-971e-4b7a-9ff0-d77c3ae786a5","added_by":"auto","created_at":"2025-01-13 11:10:37","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":101916,"visible":true,"origin":"","legend":"\u003cp\u003eContour of turbulence kinetic energy (a) Re=4,000, p/e=6.67; (b) Re=16,000, p/e=6.67; (c) Re=4,000, p/e=13.3; (d) Re=16,000, p/e=13.3\u003c/p\u003e","description":"","filename":"floatimage19.png","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/584594e9e476bcdb7ca421c8.png"},{"id":73660185,"identity":"f8b36aa7-220a-496c-80d6-cc8cbd7420c1","added_by":"auto","created_at":"2025-01-13 11:02:37","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":55119,"visible":true,"origin":"","legend":"\u003cp\u003eThermo-hydraulic performance factor versus Reynolds number\u003c/p\u003e","description":"","filename":"floatimage20.png","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/700676e50c07ed01bc57ae95.png"},{"id":87757515,"identity":"527c77e0-9ce2-4238-a1d7-a3eb61e837e2","added_by":"auto","created_at":"2025-07-28 16:11:01","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1734813,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/aba50e74-3a38-482f-88c5-803eff3e0aaf.pdf"},{"id":73660160,"identity":"d4eb3dfe-effd-45cf-825b-bf3da0f58700","added_by":"auto","created_at":"2025-01-13 11:02:36","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":69869,"visible":true,"origin":"","legend":"","description":"","filename":"Table1.docx","url":"https://assets-eu.researchsquare.com/files/rs-5749527/v1/98bb120883ea0a5bd173c0b0.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Numerical studies on thermo-hydraulic performance of solar air heater with quarter circle roughness ribs","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eSolar air heaters have a straightforward construction and design. They are frequently employed as drying crops and heating spaces. The reason for the low efficiency of flat plate solar air heaters is poor convective heat transfer coefficient between the flowing air and the absorber plate which increases heat losses to the environment. The existence of a laminar sub-layer, which can be broken by adding artificial roughness to the heat-transferring surface, is the cause of the low heat transfer coefficient [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e]. The intention of enhancing heat transfer has been tried by deliberately disturbing this laminar sub-layer. To induce turbulence close to walls or disrupt laminar sub-layers, artificial roughness in the shape of ribs has been employed in a variety of configurations. Artificial roughness increases frictional losses, which raises the power needed for fluid flow. To break the viscous sub-layer, turbulence must therefore be produced in the area immediately surrounding the heat-transferring surface. The flow of core fluid should not be excessively disrupted in order to prevent an increase in pumping demand. In order to do this, roughness element heights are kept low relative to duct size [\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e]. Several investigations have been carried out to study the effect of artificial roughness on heat transfer and friction factor with roughened surface. Yadav and Bhagoria [\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e] examined the impact of transverse circular, square, and equilateral triangular ribs using 2D computational fluid dynamics (CFD) analysis on the enhancement of heat transfer. They found that the ribs situated beneath the absorber could increase the convective heat transfer coefficient in a fluid field of solar air heater. Mishra et al [\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e] investigated triangular-shaped SAH with V-shaped ribs on the absorber plate. They changed the angle of attack from 45\u0026deg; to 60\u0026deg; and Re from 4,000 to 20,000. Nu was found to be 2.26 times higher than the smooth duct. Dongxu Jin et\u0026rsquo;al [\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e] also investigated solar air heater duct with multi V-shaped ribs on the absorber plate numerically and the maximum value of the thermal performance parameter was found to be 1.93 for the range of parameters investigated. This research was studied further in 2019 with a finding of maximum thermo-hydraulic performance factor of 2.35 [\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eExtrusion on the absorber plate shaped like tiny wires is studied by Prasad and Saini [\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e], investigated whether identical roughness geometries have an equivalent impact on heat transfer, friction factor, and thermal performance. And other more related researches are reviewed as shown in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The motivation behind this study stems from the need to enhance the efficiency and effectiveness of solar air heater systems by exploring the effects of novel rib configurations, such as quarter-circle roughness ribs, on heat transfer and fluid flow characteristics. Despite the existing body of research on solar air heaters and roughened surfaces, limited attention has been given to the unique geometric features and potential advantages offered by quarter-circle ribs in enhancing heat transfer performance. By investigating the thermo-hydraulic behavior of solar air heaters equipped with quarter-circle roughness ribs through numerical simulations, this study aims to fill a critical gap in understanding the intricacies of heat transfer augmentation in swirling confined flows. Specifically, the proposed numerical investigations will focus on quantifying the thermal performance enhancements, pressure drop characteristics, and flow distribution patterns associated with quarter-circle roughness ribs in solar air heater channels. By elucidating the impact of these innovative rib geometries on heat transfer efficiency and flow dynamics, this study seeks to provide valuable insights for optimizing solar air heater design and operation in renewable energy systems. Through comprehensive numerical analyses and comparisons with conventional rib configurations, the research aims to identify the advantages and limitations of utilizing quarter-circle ribs for enhancing the thermo-hydraulic performance of solar air heaters.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Numerical Modeling\u003c/h2\u003e \u003cp\u003eANSYS Fluent 19.2 was used to model the quarter-circle ribbed surface schematic arrangement of the proposed numerical setup as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. We want to study the impact of rib shape on airflow and heat transfer enhancement in solar air heater quantitatively and qualitatively in this work. We have selected the 2D geometry of a rectangular duct with quarter circle ribs at the bottom of the absorber for numerical simulation. A duct consists of three sections which are intake part spanning 245 mm, a test portion comprising 300 mm, an exit section measuring 115 mm. The solar air heater duct's hydraulic diameter is 33.33 mm and the duct aspect ratio (W/H) is maintained at 5. The entry and exit sections' lengths are determined by the ASHRAE Standard 93 [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] to minimize flow disturbances at the inlet and to capture the airflow behavior downstream of the absorber plate respectively. Therefore, fully developed turbulent flow will be created in the test section.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn order to reduce the impact of flow passage obstruction [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], the rib height is maintained at 1.5 mm. A constant heat flux of 1000 W/m\u003csup\u003e2\u003c/sup\u003e is delivered to the test section's upper surface and the rib pitch to its height ratio (P/e) is maintained between 6.67 and 13.33. We used Reynolds number ranging from 4,000 to 20,000 in this simulation. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the geometric parameters of solar air heater duct.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGeometrical Parameters for numerical simulation [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValues\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEntry length, L\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e245 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest section, L\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e300 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExit length, L\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e115 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth of duct, W\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e100 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHeight of duct, H\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHydraulic diameter of duct, D\u003csub\u003eh\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e33.33 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRoughness height, e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.5 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative roughness height RRH, e/D\u003csub\u003eh\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.045\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRoughness pitch, p\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10, 15, 20 mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRelative roughness pitch RRP, p/e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.67, 10, 13.33 (3 Values)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of ribs, n (L\u003csub\u003e2\u003c/sub\u003e/p)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30, 20, 15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Mesh Generation\u003c/h2\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the laminar sub-layer along the boundary of the solar air heater duct is solved using a structured mesh with element size of 0.1 mm (481,424 number of elements as discussed in Table \u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Tetrahedral element type is chosen because it is better for rectangular SAH duct model simulation.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe left side of the wall is a velocity inlet that receives a uniform, constant velocity ranging from 1.75 to 8.76 m/s. The right-side wall of the fluid domain serves as an ambient pressure outlet. There is a steady 1,000 W/m\u003csup\u003e2\u003c/sup\u003e heat flux at the top wall. The bottom plate belongs to the adiabatic boundary constraint. The boundary conditions of no-slip applied to the fluid domain walls as described in Table \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBoundary conditions of SAH model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBoundary\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eValues\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInlet\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInlet velocity, (u\u003csub\u003ei\u003c/sub\u003e = u\u003csub\u003einlet\u003c/sub\u003e)\u003c/p\u003e \u003cp\u003eReynolds number, Re\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.75\u0026ndash;8.76 m/s\u003c/p\u003e \u003cp\u003e4,000\u0026ndash;20,000 (5 values)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOutlet\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOutlet pressure, (P\u003csub\u003eout\u003c/sub\u003e = 0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e101,325 Pa\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWall (Top surface (absorber))\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHeat flux \u003cem\u003e(-k\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:T}{\\partial\\:x}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e=\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\ddot{q}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1,000 W/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOther walls (bottom, sides of absorber)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAdiabatic (\u003cem\u003e(-k\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:T}{\\partial\\:x}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e= 0\u003c/em\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSolid-fluid interface\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo-slip (u\u003csub\u003ei\u003c/sub\u003e = 0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Numerical Solution\u003c/h2\u003e \u003cp\u003eANSYS Fluent 19.2 was used in this study to examine the heat transfer enhancement and fluid flow properties of a 2D simulation. The 2D model was solved by applying the previously indicated boundary conditions as shown in Table \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Pressure and momentum equations are connected using the SIMPLE algorithm and all equations are discretized using the second-order upwind scheme. For energy and other equations, the convergence criteria values were chosen at 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e and 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e respectively. The RNG k-ε turbulence model is used because of high accuracy for simulating complex flows such as swirling motions, which is created due to quarter circle ribs in this study. It has improved predictive accuracy and computational efficiency for such study than other turbulence models. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e displays the thermo-physical characteristics of the absorber plate and working fluid.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThermo-physical properties of air and absorber\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eProperties\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAir\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAbsorber (Al)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDensity, ρ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.225 kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2719 kg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpecific heat, C\u003csub\u003ep\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1006.43 J/kgk\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e871 J/kgk\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThermal conductivity, K\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0242 W/mk\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e202.4 W/mk\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eViscosity, \u0026micro;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.789x10\u003csup\u003e-5\u003c/sup\u003e kg/ms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePrantl number, Pr\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.744\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1. Governing equations\u003c/h2\u003e \u003cp\u003eThe governing equations for steady-state, 2D airflow in a solar air heater with artificial roughness can be expressed using the continuity, momentum, and energy equations [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eContinuity Equation:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\frac{\\partial\\:}{\\partial\\:{x}_{i}}\\:\\left(\\rho\\:{u}_{i}\\right)\\hspace{0.17em}=\\hspace{0.17em}0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eMomentum conservation equation:\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:}{\\partial\\:{x}_{i}}\\)\u003c/span\u003e \u003c/span\u003e \u003cem\u003e(\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\rho\\:{u}_{i}{u}_{j}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e) = -\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:\\rho\\:}{\\partial\\:{x}_{i}}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e+ \u0026micro;\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\partial\\:}{\\partial\\:{x}_{j}}\\left(\\frac{\\partial\\:{u}_{i}}{\\partial\\:{x}_{j}}+\\frac{\\partial\\:{u}_{j}}{\\partial\\:{x}_{i}}\\right)\\)\u003c/span\u003e\u003c/span\u003e (2)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eEnergy conservation equation:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\frac{\\partial\\:{(\\rho\\:u}_{j}T)}{\\partial\\:{x}_{i}}\\:=\\:\\frac{\\partial\\:}{\\partial\\:{x}_{j}}\\left(Г+\\:{Г}_{t}\\frac{\\partial\\:T}{\\partial\\:{x}_{j}}\\:\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eReynolds number [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]: \u003cem\u003eRe =\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\rho\\:u{D}_{h}}{\\mu\\:}\\)\u003c/span\u003e\u003c/span\u003e (4) \u003cem\u003eWhere, D\u003c/em\u003e\u003csub\u003e\u003cem\u003eh\u003c/em\u003e\u003c/sub\u003e \u003cem\u003e=\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{4A}{P}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eNusselt number: This research examines how the addition of a quarter circle rib to the duct surface improves heat transfer and pressure drop. The FLUENT post-processing software is employed to determine the heat transfer coefficient (h) and pressure drop (∆P) within the duct, allowing for the calculation of the average Nusselt number and friction factor using Eqs.\u0026nbsp;5 \u0026amp; \u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e7\u003c/span\u003e respectively [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e \u003cem\u003eNu\u003c/em\u003e \u003csub\u003e \u003cem\u003er\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e=\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{h{.D}_{h}}{k}\\)\u003c/span\u003e\u003c/span\u003e (5)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, the average convective heat transfer coefficient (h) is\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e \u003cem\u003eh =\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{q}^{{\\prime\\:}{\\prime\\:}}}{{T}_{w}-{T}_{m}}\\)\u003c/span\u003e\u003c/span\u003e (6)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe friction factor for solar air heater with roughened ribs is\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{f}_{r}\\:=\\:\\frac{(\\varDelta\\:p/l)D}{2\\rho\\:{u}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003e \u003cem\u003eWhere, ∆P =\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{in}-{P}_{out}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe Nusselt number for a smooth solar air heater duct may be determined using the Dittus Boelter equation [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e \u003cem\u003eNu\u003c/em\u003e \u003csub\u003e \u003cem\u003es\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e= 0.023\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{e}^{0.8}{P}_{r}^{0.4}\\)\u003c/span\u003e\u003c/span\u003e (8)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAnd friction factor for a smooth solar air heater may be computed using the Blasius eqn, [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e \u003cem\u003ef\u003c/em\u003e \u003csub\u003e \u003cem\u003es\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e= 0.00791\u003c/em\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{e}^{-0.25}\\)\u003c/span\u003e\u003c/span\u003e (9)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThermo-hydraulic performance factor [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e \u003cem\u003eTHP =\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{Nu}_{r}\\:/\\:{Nu}_{s}\\:}{{{(f}_{r}/{f}_{s})}^{1/3}\\:}\\)\u003c/span\u003e\u003c/span\u003e (10)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Results \u0026 Discussion","content":"\u003cp\u003eIn this research, heat transfer and flow characteristics in the solar air heater with a ribbed duct were analyzed and the governing equations were solved using ANSYS Fluent 19.2. The 2D model was created in Solid Work, imported and then irregularly meshed with Fluent.\u003c/p\u003e\n\u003cdiv id=\"Sec8\"\u003e\n \u003ch2\u003e3.1. Grid Independency Test\u003c/h2\u003e\n \u003cp\u003eA grid-independency investigation was performed to validate variations in flow friction and Nusselt number for various element sizes. As indicated in Table 5, it was discovered that the element size of 0.1 mm resulted in the least difference (\u0026lt; 1%) when compared to other element sizes at Re of 12,000 and relative pitch (p/e) of 6.67. As a result, 0.1 mm element size was taken into consideration for further investigations.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 5\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eGrid independence test of ANSYS fluent\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eelement size\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eNo of cells\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003eNu\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003e∆Nu\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003ef\u003c/p\u003e\n \u003c/th\u003e\u003cth align=\"left\"\u003e\n \u003cp\u003e∆f\u003c/p\u003e\n \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e332,642\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e82.86\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0328\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.12\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e413,531\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e84.14\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e1.521274\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0332\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e1.3253\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e481,424\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e84.9\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.895171\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0334\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5988\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e513,146\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e85.53\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.736584\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"char\"\u003e\n \u003cp\u003e0.0335\u003c/p\u003e\n \u003c/td\u003e\u003ctd align=\"left\"\u003e\n \u003cp\u003e0.29851\u003c/p\u003e\n \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\"\u003e\n \u003ch2\u003e3.2. Validation of Numerical Model\u003c/h2\u003e\n \u003cp\u003eThe 2D model of solar air heater is validated by contrasting the CFD results with the findings derived from the correlations reported in the literatures [17, 19]. Equations\u0026nbsp;8 \u0026amp; 9 show how to use the correlations to calculate the friction and Nusselt number for smooth solar air heater. The CFD findings are shown to be in good agreement (\u0026lt; 5%) with the empirical equations as shown in Figs.\u0026nbsp;3 and 4 which lends credence to the validity of the study and suggests potential for future investigations.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\"\u003e\n \u003ch2\u003e3.3. Qualitative and Quantitative Analysis\u003c/h2\u003e\n \u003cp\u003e\u003cstrong\u003ea. Nusselt Number\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eThe heat transfer and fluid flow properties of a quarter circular rib surface at different pitch distances and Reynolds numbers are presented in Fig.\u0026nbsp;5. According to the findings, greater Reynolds numbers were associated with higher Nusselt numbers, while lower Reynolds numbers were associated with lower Nusselt numbers. Lower Nusselt numbers for Re of 4,000 and maximum Nusselt numbers for higher Reynolds numbers were seen in the numerical investigation. Furthermore, a higher heat transfer rate was obtained at the minimal pitch ratio of p/e = 6.7 as compared to p/e = 10 and p/e = 13.3.\u003c/p\u003e\n \u003cp\u003eAs shown in Fig.\u0026nbsp;6, velocity contour plot findings show how heat flow is distributed at different pitch distances. A powerful vortex is created close to the first pair of ribs and then the heat is distributed in the direction of fluid flow.\u003c/p\u003e\n \u003cp\u003eAdditionally, as the Reynolds number rises, a greater vortex size is created inside the duct which causes normal fluid disturbances creating higher heat transfer. Among these, the fluid flow experienced more turbulence at the relative pitch p/e of 6.67 than other pitch values.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eb. Flow Friction\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eIn this study, the pressure drop at different Reynolds numbers caused by the rib surface was recorded as Fig.\u0026nbsp;7 illustrates. As the Reynolds number increased, the friction factor was found to decrease and as the Reynolds number decreased, it increased.\u003c/p\u003e\n \u003cp\u003eFigure 8 displays the pressure contour plot results, which clearly indicate the pressure drop between the rib surfaces. It was found that a powerful vortex with a closer pitch distance of p/e = 6.7 was generated at higher Reynolds numbers. Progressive vortices were formed by other relative pitch distances. The lowest pressure drop and friction were seen at relative pitch distance of p/e = 13.3.\u003c/p\u003e\n \u003cp\u003eUsing a turbulence kinetic energy (k-e) model, the heat dissipation between rib surfaces in the direction of fluid flow was examined. The findings are shown in Fig.\u0026nbsp;9 for all pitch distances with Reynolds numbers ranging from 4,000 to 20,000. The results show that when the Reynolds number grew, the rib surface with the closer pitch distance generated a larger heat transfer rate than the other surfaces. The turbulence intensity clearly showed the highest heat dissipation between the wall surface and rib surface.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003ee. Thermo-hydraulic Performance Factor (THPF)\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eThe heat transfer efficiency in the fluid field of solar air heater is increased by adding a quarter-circle rib on the bottom of the absorber. However, when the rib is present, there is also a discernible rise in pressure drop. As a result, this section evaluates the THPF taking into account both an improvement in heat transmission and a rise in pressure drop as shown in Fig.\u0026nbsp;10. The values of the THPF were found in the range of 0.85 to 1.63. The THPF rises in conjunction with relative pitch and Re. The lower relative pitch and higher Reynolds number are considered to be more advantageous for higher solar air heater efficiency. The maximum THPF of 1.63 was found at the relative pitch of 6.67 which is lying within the acceptable range of roughness pitch as reported by other scientific papers [3, 14, 21]. According to the numerical study, the maximum Nusselt number is produced around 2.42 times higher compared with plain duct, at a Re of 16,000 and p/e = 6.67.\u003c/p\u003e\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn solar air heater, the heat transmission, friction factor and thermo-hydraulic performance of quarter circle ribs at different pitch distances were the main subjects of the 2D numerical study. According to the numerical data, when the Reynolds number increased, the average Nusselt number increased and the average friction factor decreased. The numerical study revealed the following:\u003c/p\u003e\u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eCompared to a smooth surface, applying artificial roughness to the absorber plate greatly increased the Nusselt number.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eThe minimum friction factor of 0.007 was obtained at relative pitch (p/e) of 13.3 and Reynolds number of 20,000.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eNusselt number was improved 2.42 times higher in quarter circle roughened duct at p/e = 6.67 and Reynolds number of 16,000 than smooth duct.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eFor square circle roughness, the thermo-hydraulic performance factor (THPF) of 1.63 was obtained at relative pitch p/e of 6.67.\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\u003cp\u003eTherefore, adding quarter circle roughness to solar air heaters can help to improve heat transfer and system performance. This can contribute to advancements in solar energy utilization, and sustainable heating solutions. Collaboration with industry partners, academia, and governmental agencies can further catalyze the development and commercialization of innovative solar air heating technologies based on the findings from the present work.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003ee roughness height, mm\u003c/p\u003e\u003cp\u003ee/d relative roughness height\u003c/p\u003e\u003cp\u003ep roughness pitch, m\u003c/p\u003e\u003cp\u003ep/e relative roughness pitch\u003c/p\u003e\u003cp\u003eH height of air channel, m\u003c/p\u003e\u003cp\u003eh heat transfer coefficient, W/m\u003csup\u003e2\u003c/sup\u003e K\u003c/p\u003e\u003cp\u003ek thermal conductivity of air, W/Mk\u003c/p\u003e\u003cp\u003ef friction factor\u003c/p\u003e\u003cp\u003ef\u003csub\u003er\u003c/sub\u003e friction factor for rough surface\u003c/p\u003e\u003cp\u003ef\u003csub\u003es\u003c/sub\u003e friction factor for a smooth surface\u003c/p\u003e\u003cp\u003eNu Nusselt number\u003c/p\u003e\u003cp\u003eNu\u003csub\u003er\u003c/sub\u003e Nusselt number for rough duct\u003c/p\u003e\u003cp\u003eNu\u003csub\u003es\u003c/sub\u003e Nusselt number for smooth duct\u003c/p\u003e\u003cp\u003eTHPF Thermo-hydraulic performance factor\u003c/p\u003e\u003cp\u003eSAH Solar air heater\u003c/p\u003e\u003cp\u003eP\u003csub\u003er\u003c/sub\u003e Prandtl number\u003c/p\u003e\u003cp\u003eR\u003csub\u003ee\u003c/sub\u003e Reynolds number\u003c/p\u003e\u003cp\u003eµ Dynamic viscosity, Ns/m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDeclaration of competing interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that there is no conflict of competing interest.\u003c/p\u003e\n\n\n\u003cp\u003e\u003cstrong\u003eDeclaration of funding\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was not funded by any grant.\u003c/p\u003e\n\n\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author, [Tazebew Dires Kassie], upon reasonable request.\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eAuthor contributions statement\u003c/strong\u003e\u003c/p\u003e\n\n\n\n\u003cp\u003eYaregal Eneyew Bizuneh: Writing original draft, Visualization, Validation, Project administration, Methodology, Investigation, Formal analysis, Conceptualization.\u003c/p\u003e\n\u003cp\u003eTazebew Dires Kassie: Writing, review \u0026amp; editing, Supervision, Data curation, Investigation.\u003c/p\u003e\n\u003cp\u003eAtalay Enyew Bizuneh: Writing, review \u0026amp; editing, Supervision, Resources, Investigation.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBhatti MS, Shah RK; Turbulent and transition flow convective heat transfer; Handbook of single phase convective heat transfer, Chapter 4, New York: John Wiley \u0026amp; Sons Inc; 1987.\u003c/li\u003e\n\u003cli\u003eSaini JS; Use of artificial roughness for enhancing performance of solar air heater; Proceedings of XVII National and VI ISHME/ASME heat and mass transfer conference; Kalpakkam (India); January 05e07 2004; p.103e12.\u003c/li\u003e\n\u003cli\u003eYadav, A.S.; Bhagoria, J.L. A CFD (Computational Fluid Dynamics) Based Heat Transfer and Fluid Flow Analysis of a Solar Air Heater Provided with Circular Transverse Wire Rib Roughness on the Absorber Plate. Energy 2013, 55, 1127\u0026ndash;1142.\u003c/li\u003e\n\u003cli\u003eYadav AS, Bhagoria JL. A numerical investigation of square sectioned transverse rib roughened solar air heater. Int J Therm Sci. 2014; 79:111‐131.\u003c/li\u003e\n\u003cli\u003eMisra R, Singh J, Jain SK, et al, Prediction of behavior of triangular solar air heater duct using V‐down rib with multiple gaps and turbulence promoters as artificial roughness: a CFD analysis, Int J Heat Mass Transfer. 2020; 162: 120376. \u003c/li\u003e\n\u003cli\u003eM.K. Mittal, Varun, R.P. Saini, S.K. Singal, Effective efficiency of solar air heaters having different types of roughness elements on the absorber plate, Energy 32 (2007) 739\u0026ndash;745.\u003c/li\u003e\n\u003cli\u003eSingh Patel S, Lanjewar A. Experimental and numerical investigation of solar air heater with novel v‐rib geometry, J Energy Storage. 2019; 21:750‐764.\u003c/li\u003e\n\u003cli\u003eRavi RK, Saini RP. Nusselt number and friction factor correlations for forced convective type counter flow solar air heater having discrete multi V shaped and staggered rib roughness on both sides of the absorber plate. Appl Therm Eng. 2018; 129:735‐746.\u003c/li\u003e\n\u003cli\u003eMahanand Y, Senapati JR. Thermal enhancement study of a transverse inverted‐T shaped ribbed solar air heater. Int Commun Heat Mass Transfer. 2020.\u003c/li\u003e\n\u003cli\u003eMehdi A. Ehyaei, Suresh Gogada, Sujit Roy, Ankur Gupta, Biplab Das; Energy and exergy analysis of solar air heater with trapezoidal ribs based absorber: A comparative analysis, Energy Sci Eng. 2023; 11:585\u0026ndash;605, DOI: 10.1002/ese3.1347.\u003c/li\u003e\n\u003cli\u003eA.Boulemtafes-Boukadoum, R.Boualbani, A.Benzaoui and S.El Mokretar; 3D Numerical Investigation of Convective Heat Transfer and Friction in Solar Air Collector\u0026apos;s Channel Roughened by Triangular Ribs, Environment and Sustainability, AIP Conf. Proc. 2190, 020037-1\u0026ndash;020037-13; https://doi.org/10.1063/1.5138523.\u003c/li\u003e\n\u003cli\u003eRanjan E., et al, CFD based Analysis of a Solar Air Heater having Isosceles Right Triangle Rib Roughness on the Absorber Plate, Int. Energy Journal 17,2017, 57 \u0026ndash; 74.\u003c/li\u003e\n\u003cli\u003eYadav A.S et al; A Numerical Investigation of an Artificially Roughened Solar Air Heater, Energies 2022, 15, 8045. https://doi.org/10.3390/en15218045\u003c/li\u003e\n\u003cli\u003eAssaye et al., umerical investigation of convection heat transfer in solar air heater with semi-circular shape transverse rib, Cogent Engineering (2022), 9: 2106930, doi: 10.1080/23311916. 2022.2106930.\u003c/li\u003e\n\u003cli\u003eASHRAE Standard 93; Method of Testing to Determine the Thermal Performance of Solar Collectors. 30329. American Society of Heating, Refrigeration and Air Conditioning Engineers: Atlanta, GA, USA, 2003.\u003c/li\u003e\n\u003cli\u003eYadav, A. S. (2015); CFD investigation of effect of relative roughness height on Nusselt number and friction factor in an artificially roughened solar air heater; Journal of the Chinese Institute of Engineers, 38(4), 494\u0026ndash;502. https://doi.org/10.1080/02533839.2014. 998165.\u003c/li\u003e\n\u003cli\u003eFox, R.W.; McDonald, A.T.; Pritchard, P.J. Introduction to Fluid Mechanics; John Wiley \u0026amp; Sons: New York, NY, USA, 1985.\u003c/li\u003e\n\u003cli\u003eF. p. Incropera; Fundamentals of heat and mass transfer, Wiley Inc, 6\u003csup\u003eth\u003c/sup\u003e edition, 2007.\u003c/li\u003e\n\u003cli\u003eMcAdams, W.H, Heat Transmission; McGraw-Hill Book Co.: New York, USA, 1942.\u003c/li\u003e\n\u003cli\u003eWebb, R.L.; Eckert, E.R.G; Application of rough surfaces to heat exchanger design. Int. J. Heat Mass Transf. 1972, 15, 1647\u0026ndash;1658.\u003c/li\u003e\n\u003cli\u003eGawande, V. B., Dhoble, A., Zodpe, D., \u0026amp; Sunil Chamoli. (2016). Experimental and CFD investigation of convection heat transfer in solar air heater with reverse L-shaped ribs. Solar Energy, 131, 275\u0026ndash;295. http://dx.doi.org/10.1016/j.solener.2016.02.040.\u003c/li\u003e\n\u003cli\u003eVipin B. Gawande , A. S. Dhoble , D. B. Zodpe \u0026amp; Chidanand Mangrulkar (2020) A comparative analysis of thermo-hydraulic performance of a roughened solar air heater using various rib shapes, Australian Journal of Mechanical Engineering, 18:3, 331-350, DOI: 10.1080/14484846.2018.1525171.\u003c/li\u003e\n\u003cli\u003eR. K. Kakac, S. Shah, and W. Aung, \u0026ldquo;Hand Book of Single-Phase Convective Heat Transfer,\u0026rdquo; Wiley, New York, 1987.\u003c/li\u003e\n\u003cli\u003eJan Taler et al; Investigation of Thermo-Hydraulic Performances of Artificial Ribs Mounted in a Rectangular Duct; Energies 2023; https://doi.org/10.3390/en16114404. \u003c/li\u003e\n\u003cli\u003eDongxu Jin et\u0026rsquo;al; Numerical investigation of heat transfer and fluid flow in a solar air heater duct with multi V-shaped ribs on the absorber plate; Energy, Vol 89 (2015) pp. 178\u0026ndash;190. https://doi.org/10.1016/j.energy.2015.07.069.\u003c/li\u003e\n\u003cli\u003eDongxu Jin et\u0026rsquo;al; Numerical investigation of heat transfer enhancement in a solar air heater roughened by multiple V-shaped ribs; Renewable energy 134 (2019) pp. 78\u0026ndash;88; https://doi.org/10.1016/j.renene.2018.11.016.\u003c/li\u003e\n\u003cli\u003eNaveen K. Gupta, et\u0026rsquo;al; A case study on thermal performance of solar air heater with down apex position of open trapezoidal ribs with gaps; Case Studies in Thermal Engineering, Vol 51, Nov 2023. https://doi.org/10.1016/j.csite.2023.103572.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Table 1","content":"\u003cp\u003eTable 1 is available in the Supplementary Files section.\u003c/p\u003e\n"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"solar air heater, heat transfer, thermal performance, quarter circle ribs, CFD","lastPublishedDoi":"10.21203/rs.3.rs-5749527/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5749527/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWith their diverse range of applications, solar air heaters transform renewable solar energy into useful heat. The fluid flow and heat transfer properties of a roughened solar air heater with quarter-circle-shaped ribs were examined in-depth using numerical analysis. The k\u0026ndash;e RNG turbulence model was used to conduct 2D steady-state numerical simulations, and the findings showed excellent agreement with the smooth duct and related literatures. The impact of rib spacing was explored by changing the rib relative pitch (p/e) from 6.67 to 13.3 for Reynolds numbers (Re) between 4,000 and 20,000. The thermo-hydraulic performance factor was found to be 1.63. Additionally, it was shown that an increase in relative pitch (p/e) of 6.67 to 10 resulted in an increase in the Nusselt number for all Re values examined. At Re of 16,000, an enhancement of 2.42 times the Nu was made for p/e\u0026thinsp;=\u0026thinsp;6.67. It was also noted that for all Re values taken into consideration, Nu falls with an increase in p/e from 10 to 13.3.\u003c/p\u003e","manuscriptTitle":"Numerical studies on thermo-hydraulic performance of solar air heater with quarter circle roughness ribs","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-13 11:02:31","doi":"10.21203/rs.3.rs-5749527/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-04-16T05:43:22+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-11T16:39:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"74840117775094821275488492516655313419","date":"2025-03-18T10:56:45+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-03-07T11:35:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"192967807154662826726109695218100428593","date":"2025-03-01T11:48:13+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-02-05T19:54:39+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"227439909655145670815919048919423636135","date":"2025-01-15T12:08:02+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"331748019825096265310301182152309220281","date":"2025-01-13T11:12:39+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-01-13T10:21:24+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-01-13T10:20:35+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-01-13T09:56:54+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-01-10T13:18:39+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-01-02T07:03:23+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7363a6e1-5f8c-47be-83c0-7667bdae90d8","owner":[],"postedDate":"January 13th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-07-28T16:09:41+00:00","versionOfRecord":{"articleIdentity":"rs-5749527","link":"https://doi.org/10.1038/s41598-025-10620-y","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-07-23 15:57:44","publishedOnDateReadable":"July 23rd, 2025"},"versionCreatedAt":"2025-01-13 11:02:31","video":"","vorDoi":"10.1038/s41598-025-10620-y","vorDoiUrl":"https://doi.org/10.1038/s41598-025-10620-y","workflowStages":[]},"version":"v1","identity":"rs-5749527","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5749527","identity":"rs-5749527","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}