Thermal performance of MHD radiative nanofluid convection over an exponentially stretching surface in a porous medium
DOI:
https://doi.org/10.24425/ather.2025.156596Abstract
This study investigates the hydromagnetic convection of a radiating nanofluid flowing over an exponentially stretched sheet embedded in a porous medium, with emphasis on the influences of thermal radiation, magnetic fields, Joule heating, viscous dissipation, porous permeability, and nanoparticle volume fraction on flow and heat transfer behaviour. The governing momentum and energy equations are formulated using boundary layer theory and reduced to nonlinear ordinary differential equations via similarity transformations. We numerically solve these equations using the shooting method in conjunction with the Runge-Kutta-Fehlberg integration scheme. The analysis looks at how important factors like the strength of the magnetic field, thermal radiation, Prandtl number, and how easily fluid can flow through a porous material impact the system, showing how magnetic and thermal effects play a big role in how fluids move. One of the main discoveries is that stronger magnetic fields and more thermal radiation together lower the Nusselt number, highlighting the balance between heat transfer through radiation and convection, which is important in high-temperature industrial processes. The study offers important insights for optimising a range of engineering applications, including nanomaterial-based thermal coatings, energy systems, and magnetically influenced flow control that ultimately aid advancements in energy efficiency, manufacturing processes, and environmental technologies.References
1. Abbas, N., Shatanawi, W., Hasan, F., & Shatnawi Taqi, A.M. (2025). Investigation of MHD radiative Casson micropolar hybrid nanofluid over an exponential curved stretching sheet. Journal of Radiation Research and Applied Sciences, 18(1), 101269. doi:10.1016/j.jrras.2024.101269
2. Nayak, M.K., Pandey, V.S., Tripathi, D., Akbar, N.S., & Makinde, O.D. (2020). 3D MHD cross flow over an exponential stretching porous surface. Heat Transfer, 49(3), 1256–1280. doi:10.1002/htj.21661
3. Crane, L.J. (1970). Flow past a stretching plate. Journal of Applied Mathematics and Physics (Zeitschrift für Angewandte Mathematik und Physik), 21, 645–647. doi:10.1007/BF01587695
4. Elbashbeshy, E.M.A. (1998). Heat transfer over a stretching surface with variable surface heat flux. Journal of Physics D: Applied Physics, 31(16), 1951–1954.
5. Mahapatra, T.R., & Gupta, A.S. (2002). Heat transfer in stagnation-point flow towards a stretching sheet. Heat and Mass Transfer, 38, 517–521. doi:10.1007/s002310100215
6. Chaudhary, S., Choudhary, M.K., & Sharma, R. (2015). Effects of thermal radiation on hydromagnetic flow over an unsteady stretching sheet embedded in a porous medium in the presence of a heat source or sink. Meccanica, 50, 1977–1987. doi:10.1007/s11012-015-0137-9
7. Alkaoud, A., Khader, M.M., Eid, A., & Megahed, A.M. (2024). Numerical simulation of the flow of a tangent hyperbolic fluid over a stretching sheet within a porous medium, accounting for slip conditions. Heliyon, 10, e28683. doi:10.1016/j.heliyon.2024.e28683
8. Nawaz, Y., Arif, M.S., Nazeer, A., Abbasi, J.N., & Abodayeh, K. (2024). A two-stage reliable computational scheme for stochastic unsteady mixed convection flow of Casson nanofluid. International Journal for Numerical Methods in Fluids, 96(5), 719–737. doi:10.1002/fld.5264
9. Saleem, M., Hussain, M., & Inc, M. (2023). Significance of Darcy–Forchheimer law and magnetic field on the comparison of Williamson–Casson fluid subject to an exponential stretching sheet. International Journal of Modern Physics B, 37(27), 2350315. doi:10.1142/S0217979223503150
10. Vajravelu, K., & Roper, T. (1999). Flow and heat transfer in a second-grade fluid over a stretching sheet. International Journal of Non-linear Mechanics, 34(6), 1031–1036. doi:10.1016/S0020-7462(98)00073-0
11. Sajid, M., Ali, N., Javed, T., & Abbas, Z. (2010). Stretching a curved surface in a viscous fluid. Chinese Physics Letters, 27(2), 024703. doi:10.1088/0256-307X/27/2/024703
12. Abbas, Z., Naveed, M., & Sajid, M. (2016). Hydromagnetic slip flow of nanofluid over a curved stretching surface with heat generation and thermal radiation. Journal of Molecular Liquids, 215, 756–762. doi:10.1016/j.molliq.2016.01.012
13. Hussain, Z., Hayat, T., Alsaedi, A., & Anwar, M.S. (2021). Mixed convective flow of CNTs nanofluid subject to varying viscosity and reactions. Scientific Reports, 11, 22838. doi:10.1038/s41598-021-02228-9
14. Othman, M.N., Jedi, A., & Bakar, N.A.A. (2021). MHD stagnation point on nanofluid flow and heat transfer of carbon nanotube over a shrinking surface with heat sink effect. Molecules, 26, 7441. doi:10.3390/molecules26247441
15. Majeed, A., Zeeshan, A., & Alam, T. (2023). Mathematical analysis of MHD CNTs of rotating nanofluid flow over a permeable stretching surface. Arab J. Sci. Eng., 48, 727–737. doi:10.1007/s13369-022-06871-w
16. Choudhary, P., Choudhary, S., Jat, K., Loganathan, K., & Eswaramoorthi, S. (2024). Impacts of unsteady MHD hybrid nanofluid over a non-linear stretchable porous sheet with thermal radiation and gyrotactic microorganisms. International Journal of Thermofluids, 23, 100788. doi:10.1016/j.ijft.2024.100788
17. Sharma, R.P., Baag, S., Mishra, S.R., & Sahoo, P. (2023). On the radiative heat transport phenomena in MHD Williamson nanofluid flow past an expanding surface with an interaction of inclined magnetic field. Journal of Thermal Analysis and Calorimetry, 148(14). doi:10.1007/s10973-023-12206-0
18. Sakkaravarthi, K., & Reddy, B.A. (2023). Entropy generation on MHD Casson and Williamson hybrid nanofluid over a curved stretching sheet with the Cattaneo–Christov heat flux model: Semi-analytical and numerical simulations. International Journal of Ambient Energy, 44(1). doi:10.1080/01430750.2023.2190338
19. Makinde, O.D., & Eegunjobi, A.S. (2017). MHD couple stress nanofluid flow in a permeable wall channel with entropy generation and nonlinear radiative heat. Journal of Thermal Science and Technology, 12(2). doi:10.1299/jtst.2017jtst0033
20. Srinivasulu, T., & Goud, B.S. (2021). Effect of inclined magnetic field on flow, heat, and mass transfer of Williamson nanofluid over a stretching sheet. Case Studies in Thermal Engineering, 23, 100819. doi:10.1016/j.csite.2020.100819
21. Kiwan, S., & Ali, M.E. (2008). Near-slit effects on the flow and heat transfer from a stretching plate in a porous medium. Numerical Heat Transfer, Part A: Applications, 54(1), 93–108. doi:10.1080/10407780802025275
22. Tamayol, A., Hooman, K., & Bahrami, M. (2010). Thermal analysis of flow in a porous medium over a permeable stretching wall. Transport in Porous Media, 85(3), 661–676. doi:10.1007/s11242-010-9584-x
23. Pal, D., & Chatterjee, S. (2010). Heat and mass transfer in MHD non-Darcian flow of a micropolar fluid over a stretching sheet embedded in a porous medium with non-uniform heat source and thermal radiation. Communications in Nonlinear Science and Numerical Simulation, 15(7), 1843–1857. doi:10.1016/j.cnsns.2009.07.024
24. Krishna, M.V., Ahammad, N.A., & Chamkha, A.J. (2021). Radiative MHD flow of Casson hybrid nanofluid over an infinite exponentially accelerated vertical porous surface. Case Studies in Thermal Engineering, 27, 101229. doi:10.1016/j.csite.2021.101229
25. Eegunjobi, A.S., & Makinde, O.D. (2014). Second law analysis for MHD permeable channel flow with variable electrical conductivity and asymmetric Navier slips. Open Physics, 13(1), 100–110. doi:10.1515/phys-2015-0014
26. Chamkha, A.J., Issa, C., & Khanafer, K. (2002). Natural convection from an inclined plate embedded in a variable porosity porous medium due to solar radiation. International Journal of Thermal Sciences, 41(1), 73–81. doi:10.1016/S1290-0729(01)01305-9
27. Makinde, O.D., & Sibanda, P. (2008). Magnetohydrodynamic mixed convective flow and heat and mass transfer past a vertical plate in a porous medium with constant wall suction. Journal of Heat Transfer, 130(11). doi:10.1115/1.2955471
28. Hayat, T., Qasim, M., & Mesloub, S. (2011). MHD flow and heat transfer over permeable stretching sheet with slip conditions. International Journal for Numerical Methods in Fluids, 66, 963–975. doi:10.1002/fld.2294
29. Khan, M.S., Karim, I., Islam, M.S., & Wahiduzzaman, M. (2014). MHD boundary layer radiative, heat-generating, and chemical reacting flow past a wedge moving in a nanofluid. Nano Convergence, 1(20). doi:10.1186/s40580-014-0020-8
30. Cebeci, T., & Bradshaw, P. (1988). Physical and computational aspects of convective heat transfer. New York, USA: Springer.
31. Na, T.Y. (1979). Computational methods in engineering boundary value problems. New York, USA: Academic Press.
32. Brinkman, H.C. (1952). The viscosity of concentrated suspensions and solutions. The Journal of Chemical Physics, 20(4), 571–571. doi:10.1063/1.1700493
33. Kefene, Z.M., Makinde, O.D., & Enyadene, G.L. (2022). Magnetic effects of ferrofluid flow in a heated micro-channel with permeable walls. Latin American Applied Research, 52(3), 247–257. doi:10.52292/j.laar.2022.666
34. Eegunjobi, A.S., & Makinde, O.D. (2017). Irreversibility analysis of hydromagnetic flow of couple stress fluid with radiative heat in a channel filled with a porous medium. Results in Physics, 7, 459–469. doi:10.1016/j.rinp.2017.01.002
35. Putra, N., Roetzel, W., & Das, S.K. (2003). Natural convection of nanofluids. Heat and Mass Transfer, 39, 775–784. doi:10.1007/s00231-002-0382-z
36. Waqas, H., Kafait, A., Muhammad, T., & Farooq, U. (2022). Numerical study for bio-convection flow of tangent hyperbolic nanofluid over a Riga plate with activation energy. Alexandria Engineering Journal, 61(2), 1803–1814. doi:10.1016/j.aej.2021.06.068
37. Amjad, M., Khan, M.N., Ahmed, K., Ahmed, I., Akbar, T., & Eldin, S.M. (2023). Magnetohydrodynamics tangent hyperbolic nanofluid flow over an exponentially stretching sheet: Numerical investigation. Case Studies in Thermal Engineering, 45, 102900. doi:10.1016/j.csite.2023.102900
38. Chamkha, A.J., & Pop, I. (2004). Effect of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium. International Communications in Heat and Mass Transfer, 31(3), 421–430. doi:10.1016/j.icheatmasstransfer.2004.02.012
