MAGNETOHYDRODYNAMICS EFFECTS ON STEADY NATURAL CONVECTION COUETTE FLOW OF HEAT GENERATING/ABSORBING FLUID IN A VERTICAL CHANNEL WITH VISCOUS DISSIPATION
Abstract
This study investigates the impact of magnetohydrodynamics (MHD) on steady natural convection Couette flow of a heat generating/absorbing fluid in a vertical channel in the presence of viscous dissipation. The dimensionless governing equations for momentum and energy were analytically solved using the Homotopy perturbation method. The influence of various physical parameters on the flow behavior is illustrated through graphical results. Moreover, the effects of these parameters on skin friction, rate of heat transfer, mass flux and mean temperature are analyzed and presented numerically in tabular form. Findings from the study show that, the magnetic field intensity on the velocity and temperature distributions of the fluid. It is worth highlighting that increasing the permeability enhances the fluid velocity and also the temperature near the heated plate rises, while a steeper temperature gradient is observed across the channel. Increasing the Eckert number significantly enhances both fluid velocity and temperature. The findings of this study are important due to its application in magnetohydrodynamics Power Generation, Metallurgy and Materials Processing, Cooling Systems in Nuclear Reactors, Electromagnetic Pumps, Plasma Propulsion and Aerospace and Food and Chemical Industries.
References
Ajibade, A. O. and Tafida, M. K. (2019a). Viscous dissipation effect on steady natural convection Couette flow of heat generating fluid in a vertical channel. Journal of Advances in Mathematics and Computer Science. 30(1): 1 16. https://doi.org/10.9734/JAMSC/2019/45020. DOI: https://doi.org/10.9734/JAMCS/2019/45020
Ajibade, A. O. and Tafida, M. K. (2019b). Viscous dissipation effect on a steady generalised Couette flow of heat-generating/absorbing fluid in a vertical channel. Z. Naturforsch. 74(7)a: 605 616. https://doi.org/10.1515/zna-2018-0537 DOI: https://doi.org/10.1515/zna-2018-0537
Ajibade, A. O. and Tafida, M. K. (2020). The combined effect of variable viscosity and variable thermal conductivity on natural convection Couette ow. International Journal of Thermouids. 100036, 5 6. https://doi.org/10.1016/j.ijft.2020.100036 DOI: https://doi.org/10.1016/j.ijft.2020.100036
Ajibade, A. O., Gambo, J. J. and Jha, B. K. (2024). Effects of Darcy and viscous dissipation on natural convection flow in a vertical tube partially filled with porous material under convective boundary condition. Int. J. Appl. Comput. Math. 10:84. https://doi.org/10.1007/s40819-023-01623-2. DOI: https://doi.org/10.1007/s40819-023-01623-2
Akbar, N., Hussain, S.M. and Khan, R.U. (2022). Numerical solution of Casson fluid flow under viscous dissipation and radiation phenomenon. Journal of Applied Mathematics and Physics, 10: 475 - 490. https://doi.org/10.4236/jamp.2022.102036 DOI: https://doi.org/10.4236/jamp.2022.102036
Alam, Md. M., Begum, R., Islam, M. M. and Parvez, M. M. (2018). Numerical study of temperature dependent viscosity and thermal conductivity on a natural convection flow over a sphere in presence of magneto hydrodynamics. Current Journal of Applied Science and Technology. 28(4): 1 13. https://doi.org/10.9734/CJAST/2018/42677 DOI: https://doi.org/10.9734/CJAST/2018/42677
Chillingo, K. J., Mnganga, J., Onyango, E. R. and Matoa, M. (2024). Influence of induced Mgnetic field and chemically reacting on hydromagnetic Couette flow of Jeffrey fluid in an inclined channel with variable viscosity and convective cooling: A caputo derivative approach. 22: 100627. DOI: https://doi.org/10.1016/j.ijft.2024.100627
Eswaran, R. and Jagadeesh-Kumar, M. S. (2025). Influence of MHD flow on forced convection in a saturated porous duct with Ohmic heating. Discover Applied Sciences. 7:36. https://doi.org/10.1007/s42452-024-06432-w DOI: https://doi.org/10.1007/s42452-024-06432-w
Farhood, A. K. and Mohammed, O. H. (2023). Homotopy Perturbation Method for solving time-fractional nonlinear variable-order delay partial differential equations. Partial Differential Equations in Applied Mathematics. 7: 100513. DOI: https://doi.org/10.1016/j.padiff.2023.100513
Gouder, P. M., Kolli, V. H., Page, Md. H., Chavaraddi, K. B. and Chandaragi, P. (2022). The Homotopy Perturbation Method to Solve a Wave Equation. Communications in Mathematics and Applications. 13(2): 691701. DOI: https://doi.org/10.26713/cma.v13i2.1764
Hamza, M. M., Suleiman, B. A., Ahmad, S. K. and Tasiu, A. R. (2024). Nonlinear-mixed convection flow with variable thermal conductivity impacted by asymmetric/symmetric heating/cooling conditions. Arabian Journal for Science and Engineering. https://doi.org/10.1007/s13369-024-08757-5 DOI: https://doi.org/10.1007/s13369-024-08757-5
Hassan, A., Hussain, A., Arshad, M., Gouadria, S., Awrejcewicz, J., Galal, A. M., Alharb, F. M. and Eswaramoorthi, S. (2022). Insight into the signicance of viscous dissipation and heat generation/absorption in magneto-hydrodynamic radiative Casson fluid flow with first-order chemical reaction. Frontiers in Physics. 10: https://doi.org/10.3389/fphy.2022.920372 DOI: https://doi.org/10.3389/fphy.2022.920372
Jha, B. K. and Aina, B. (2017). Impact of Induced Magnetic Field on MHD Mixed Convection Flow in Vertical Microchannel Formed by Non-Conducting and Conducting Innite Vertical Parallel Plates. Journal of Nanouids. 6: 960 970. https://doi.org/10.1166/jon.2017.1376 DOI: https://doi.org/10.1166/jon.2017.1376
Jha, B. K. and Samaila, G. (2022). Mixed convection ow from a convectively heated vertical porous plate with combined effects of suction/injection, internal heat generation and nonlinear thermal radiation. Proc IMechE Part E: Journal Process Mechanical Engineering. 110. https://doi.org/10.1177/09544089221116963. DOI: https://doi.org/10.1177/09544089221116963
Jassim, H. K. and Mohammed, M. G. (2021). Natural homotopy perturbation method for solving nonlinear fractional gas dynamics equations. Int. J. Nonlinear Anal. Appl. 12(1): 812 820. http://dx.doi.org/10.22075/IJNAA.2021.4936
Kaita, I. H., Zayyanu, S. Y., Masud, L., Hamsiu, A., Abdullahi, U. and Auwal, D. M. (2024). Heat and mass transfer flow in a channel filled with porous medium in the presence of variable thermal conductivity. FUDMA Journal of Sciences. 8(2): 225 234. https://doi.org/10.33003/fjs-2024-0802-223. DOI: https://doi.org/10.33003/fjs-2024-0802-2236
Khaleghizadeh, S. (2022). Homotopy perturbation method with the help of Adomian decomposition method for nonlinear problems. Mathematical Analysis and its Contemporary Applications. 4(1): 45 51.
Kumar, K. T., Kalyan, S., Kandagal, M., Tawade, M. J., Khan, U., Eldin, S. M., Chohan, J. S., Elattar, S. and Abed, A. M. (2023). Influence of heat generation/absorption on mixed convection flow field with porous matrix in a vertical channel. Case Studies in Thermal Engineering. 47: 103049. 1 18. https://doi.org/10.1016/j.csite.2023.103049 DOI: https://doi.org/10.1016/j.csite.2023.103049
Mishra, S., Swain, K. and Dalai, ND. R. (2023). Joule heating and viscous dissipation effects on heat transfer of hybrid nanofluids with thermal slip . Iranian Journal of Science and Technology, Transactions of Mechanical Engineering. https://doi.org/10.1007/s40997-023-00681-7 DOI: https://doi.org/10.1007/s40997-023-00681-7
Nabwey, H. A., Ashraf, M., Rashad, A. M. Chamkha, A. J. (2024). A review on magnetic permeability in heat and fluid flow characteristics: Applications in magnetized shielding. AIP Advances. 14, 120701 DOI: https://doi.org/10.1063/5.0238462
Omokhuale, E. and Dange M. S. (2023). Natural Convection Couette Flow in the Presence of Magnetic Field and Thermal Property. International Journal of Science for Global Sustainability. 9(2): 10 20. https://doi.org/10.57233/ijsgs.v9i2.453. DOI: https://doi.org/10.57233/ijsgs.v9i2.453
Oni, M. O. and Jha, B. K. (2019). Heat Generation/Absorption Effect on natural convection flow in a vertical annulus with time-periodic boundary conditions. Journal of Aircraft and Spacecraft Technology. 3: 183 196. https://doi.org/10.3844/jastsp.2019.183.196 DOI: https://doi.org/10.3844/jastsp.2019.183.196
Oni, M. O. and Jha, B. K. (2023). Heat generation/absorption effect on mixed convection flow in a vertical channel filled with a nanofluid: Exact solution. Journal of Oil and Gas Research Reviews. 3(1): 1 14. DOI: https://doi.org/10.33140/JOGRR.03.01.01
Ramesh, K. (2018). Effects of viscous dissipation and Joule heating on the Couette flow of a Jeffrey fluid with slip boundary conditions. Propulsion and Power Research. 3(4): 329 341. https://doi.org/10.1016/j.jppr.2018.11.008 DOI: https://doi.org/10.1016/j.jppr.2018.11.008
Razaa, Q., Qureshi, Z. A., Alkarni, S., Ali, B., Zain, A., Asogwa, K. K., Shah, N. A., and Yookh, S. (2023). Significance of viscous dissipation, nanoparticles, and Joule heat on the dynamics of water: The case of two porous orthogonal disk. Case Studies in Thermal Engineering. 45: 103008. DOI: https://doi.org/10.1016/j.csite.2023.103008
Sekhar, K. VC. (2023). Unsteady MHD free convection flow of a second grade casson fluid with ramped wall temperature. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences. 111(1): 80 95. https://doi.org/10.37934/arfmts.111.1.8095 DOI: https://doi.org/10.37934/arfmts.111.1.8095
Shabiha, N., Tamizharasi, R. (2025). Inuence of induced magnetic eld, electric load and viscous dissipation on electro-hydromagnetic Jerey uid owing in an insulated vertical channel: An application of electric power generation. Results in Engineering. 26: 104963. https://doi.org/10.1016/j.rineng.2025.104963 DOI: https://doi.org/10.1016/j.rineng.2025.104963
Sobamowo, M. G. (2023). Direct applications of homotopy perturbation method for solving nonlinear algebraic and transcendental equations. International Journal of Petrochemical Science & Engineering. 6(1): 10 22. DOI: https://doi.org/10.15406/ipcse.2023.06.00127
Srisailam, B., Reddy, K. S., Narender, G. and Malga, B. S. (2023). The Effect of viscous dissipation and chemical reaction on the flow of MHD nanofluid. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences. 107(2): 150 170. https://doi.org/10.37934/arfmts.107.2.150170 DOI: https://doi.org/10.37934/arfmts.107.2.150170
Tafida, M. K., Umar, A. M. and Umar, L. (2023). Magnetohydrodynamics free Convection Couette flow and heat transfer through a vertical porous plate with heat generation and absorption effect. Dutse Journal of Pure and Applied Sciences. 9(2a): 133 145. https://dx.doi.org/10.4314/dujopas.v9i2a.13 DOI: https://doi.org/10.4314/dujopas.v9i2a.13
Tafida, M. K., Umar, A. M. and Usman, M. I. (2024). Analytical study on fully developed mixed convection Couette flow in a vertical channel with viscous dissipation effect. FUDMA Journal of Sciences. 8(5): 193 200. DOI: https://doi.org/10.33003/fjs-2024-0805-2652 DOI: https://doi.org/10.33003/fjs-2024-0805-2652
Tafida, M. K. and Tajuddeen, A. (2024). Homotopy perturbation method for analyzing the effect of viscous dissipation on steady natural convection Couette flow with convective boundary conditions. International Journal of Fluid Mechanics and Thermal Sciences. 10(3), 45 56. https://doi.org/10.11648/j.ijfmts.20241003.11 DOI: https://doi.org/10.11648/j.ijfmts.20241003.11
Usman, A. (2024). Examinations of viscous dissipation, magnetic field and thermal radiation on the systematic flow of Casson fluid with gyrotactic microorganisms. ITM Web of Conferences 67: 01049. https://doi.org/10.1051/itmconf/20246701049 DOI: https://doi.org/10.1051/itmconf/20246701049
Waini, I., Alabdulhady, S., Ishak, A. and Pop, I. (2023). Viscous dissipation effects on hybrid nanofluid flow over a non-linearly shrinking sheet with power-law velocity. Heliyon. 9: e20910. DOI: https://doi.org/10.1016/j.heliyon.2023.e20910
Zigta, B. (2022). Thermal Radiation, chemical reaction and viscous dissipation effects on MHD mixed convection flow of micro polar fluid with stretching surface in the presence of heat generation/absorption. Journal of Fluid Dynamics. 3(2), 45 64. https://doi.org/10.36959/717/662. DOI: https://doi.org/10.36959/717/662
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