Numerical study of radiating Casson fluid past a permeable stretching sheet in a Darcy-Forchheimer porous medium
DOI:
https://doi.org/10.24425/ather.2025.154918Abstract
This research investigates the mixed convection of an incompressible, non-Newtonian radiating Casson fluid in a Darcy-Forchheimer porous medium over a slippery, permeable, stretching surface. The study further examines the influences of thermal buoyancy and viscous dissipation. Through appropriate similarity transformations, the governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved using MATLAB with the fourth-order Runge-Kutta method combined with the shooting technique. This work aims to assess the influence of Casson parameter, porosity parameter, radiation parameter, suction parameter, Eckert number, mixed convection parameter, local inertia coefficient, Prandtl number and slip parameter on the velocity and temperature. The findings show that increasing Casson parameter results in decreased velocity and temperature, while an increase in the radiation parameter leads to a rise in temperature. Velocity decreases with an increase in slip parameter for velocity, but as the similarity variable exceeds 2.4, it experiences a slight increase due to the stretching effect of the sheet. Conversely, temperature is directly proportional to slip parameter for velocity.References
[1] Gupta, P., & Gupta, P. (1977). Heat and mass transfer on a stretching sheet with suction or blowing. Canadian Journal of Chemical Engineering, 55(6), 744–746. https://doi.org/10.1002/cjce.5450550619
[2] Magyari, E., & Keller, B. (1999). Heat and mass transfer in boundary layers on an exponentially stretching surface. Journal of Physics D: Applied Physics, 32(5), 577–585. https://doi.org/10.1088/0022-3727/32/5/012
[3] Elbashbeshy, E.M.A. (2001). Heat transfer over an exponentially stretching continuous surface with suction. Archives of Mechanics, 53(6), 643–651.
[4] Pramanik, S. (2014). Casson fluid flow over an exponentially stretching porous surface with radiation. Ain Shams Engineering Journal, 5(1), 205–212. https://doi.org/10.1016/j.asej.2013.05.003
[5] Jain, R., Mehta, R., Mehta, T., & Yadav, R.S. (2020). Numerical study of reactive MHD boundary layer flow with slip. Advances in Mathematics: Scientific Journal, 9(9), 7057–7064. https://doi.org/10.37418/amsj.9.9.55
[6] Partha, M.K., Murthy, P.V., & Rajasekhar, G.P. (2005). Effect of viscous dissipation on convection from exponentially stretching surface. Heat and Mass Transfer, 41, 360–366. https://doi.org/10.1007/s00231-004-0552-2
[7] Khan, S.K. (2006). Boundary layer viscoelastic fluid flow over an exponentially stretching sheet. International Journal of Applied Mechanics and Engineering, 11(2), 321–335.
[8] Sajid, M., & Hayat, T. (2008). Thermal radiation effects on flow due to exponentially stretching sheet. International Communications in Heat and Mass Transfer, 35(3), 347–356. https://doi.org/10.1016/j.icheatmasstransfer.2007.08.006
[9] Bejawada, S.G., Reddy, Y.D., Jamshed, W., Nisar, K.S., Alharbi, A.N., & Chouikh, R. (2022). Radiation effect on MHD Casson fluid flow in porous medium. Alexandria Engineering Journal, 61(10), 8207–8220. https://doi.org/10.1016/j.aej.2022.01.043
[10] Rasool, G., Chamkha, A.J., Muhammad, T., Shafiq, A., & Khan, I. (2020). Darcy-Forchheimer Casson MHD nanofluid flow. Propulsion and Power Research, 9(2), 159–168. https://doi.org/10.1016/j.jppr.2020.04.003
[11] Bilal Ashraf, M., Hayat, T., & Alsaedi, A. (2017). Mixed convection Casson fluid flow with Hall effect. Boundary Value Problems, 137. https://doi.org/10.1186/s13661-017-0869-7
[12] Raju, C.S., Hoque, M.M., & Sivasankar, T. (2017). Radiative Casson fluid flow over wedge with microorganisms. Advanced Powder Technology, 28(2), 575–583. https://doi.org/10.1016/j.apt.2016.10.026
[13] Mehmood, R., Rana, S., Akbar, N.S., & Nadeem, S. (2018). Non-aligned stagnation point flow of Casson fluid. Alexandria Engineering Journal, 57(2), 939–946. https://doi.org/10.1016/j.aej.2017.01.010
[14] Sinha, S., & Yadav, R.S. (2022). MHD slip flow along inclined porous plate with radiation. Trends in Sciences, 19(4), 2685. https://doi.org/10.48048/tis.2022.2685
[15] Loganathan, P., & Deepa, K. (2019). Electromagnetic Casson fluid flow over Riga plate. Journal of Theoretical and Applied Mechanics, 57(4), 987–998. https://doi.org/10.15632/jtam-pl/112421
[16] Kumar, K.A., Sugunamma, V., & Sandeep, N. (2020). Radiation effect on MHD Casson fluid flow over curved sheet. Journal of Thermal Analysis and Calorimetry, 140, 2377–2385. https://doi.org/10.1007/s10973-019-08977-0
[17] Samrat, S.P., Reddy, M.G., & Sandeep, N. (2021). Buoyancy effects on radiative Casson fluid flow. EPJ Special Topics, 230, 1273–1281. https://doi.org/10.1140/epjs/s11734-021-00043-x
[18] Gebhart, B. (1962). Effects of viscous dissipation in natural convection. Journal of Fluid Mechanics, 14(2), 225–232. https://doi.org/10.1017/S0022112062001196
[19] Al-Hadhrami, A., Elliott, L., & Ingham, D. (2003). Model for viscous dissipation in porous media. Transport in Porous Media, 53, 117–122. https://doi.org/10.1023/A:1023557332542
[20] Hayat, T., Khan, M.I., Waqas, M., Yasmeen, T., & Alsaedi, A. (2016). Viscous dissipation in magnetonanofluid flow. Journal of Molecular Liquids, 222, 47–54. https://doi.org/10.1016/j.molliq.2016.06.096
[21] Kumar, P., Yadav, R.S., & Makinde, O.D. (2023). Williamson fluid flow over stretching cylinder with Joule heating. Heat Transfer, 52(4), 3372–3388. https://doi.org/10.1002/htj.22832
[22] Koo, J., & Kleinstreuer, C. (2004). Viscous dissipation effects in microchannels. International Journal of Heat and Mass Transfer, 47(14–16), 3159–3169. https://doi.org/10.1016/j.ijheatmasstransfer.2004.02.017
[23] Winter, H.H. (1987). Viscous dissipation term in energy equations. AIChE Modular Instruction, Series C, Vol. 7, 27–34.
[24] Khan, M.I., Alzahrani, F., & Hobiny, A. (2020). Micropolar ferrofluid flow with Darcy-Forchheimer medium. Journal of Materials Research and Technology, 9(4), 7335–7340. https://doi.org/10.1016/j.jmrt.2020.04.079
[25] Mukhopadhyay, S., De, P.R., Bhattacharyya, K., & Layek, G.C. (2012). Convective flow over porous plate in Darcy-Forchheimer medium. Meccanica, 47, 153–161. https://doi.org/10.1007/s11012-011-9423-3
[26] Kumar, K.G., Reddy, M.G., Khan, M.I., Alzahrani, F., El-Zahar, E.R. (2021). Heat transfer and melting in Darcy-Forchheimer medium. Case Studies in Thermal Engineering, 28, 101649. https://doi.org/10.1016/j.csite.2021.101649
[27] Prasad, D.K., Chaitanya, G.K., & Raju, R.S. (2019). Double diffusive Casson fluid flow over wavy plate. Results in Engineering, 3, 100019. https://doi.org/10.1016/j.rineng.2019.100019
[28] Shoaib, M., Kausar, M., Nisar, K.S., Raja, M.A.Z., & Morsy, A. (2022). MHD Casson fluid through porous medium with soft computing. Alexandria Engineering Journal, 61(12), 12211–12228. https://doi.org/10.1016/j.aej.2022.06.014
[29] Bansal, S., & Yadav, R.S. (2024). Slip velocity effect on Newtonian fluid in porous medium. Journal of Engineering and Applied Science, 71, 153. https://doi.org/10.1186/s44147-024-00481-z
[30] Sahoo, B., & Poncet, S. (2011). Third grade fluid over exponential stretching sheet with slip. International Journal of Heat and Mass Transfer, 54(23–24), 5010–5019. https://doi.org/10.1016/j.ijheatmasstransfer.2011.07.015
[31] Bidin, B., & Nazar, R. (2009). Numerical solution of flow over exponential stretching sheet with radiation. European Journal of Scientific Research, 33(4), 710–717.
