MHD Natural Convection Couette Flow in a Vertical Channel: Effects of Nonlinear Boussinesq Approximation and Suction/Injection
Keywords:
Couette flow, Magnetohydrodynamic, Natural convection, Nonlinear Boussinesq Approximation, Vertical channel
Abstract
This study analytically investigates buoyancy driven magnetohydrodynamic (MHD) natural convection Couette flow in a vertical channel, focusing on the effects of the nonlinear Boussinesq approximation, suction/injection and magnetic fields. The nonlinear Boussinesq term captures significant thermal variations beyond linear models, suction/injection modifies boundary-layer thickness and convective transport, and the magnetic field introduces Lorentz-force damping in electrically conducting flows. The governing momentum and energy equations are solved using the Homotopy Perturbation Method (HPM), and the influence of various parameters on velocity and temperature distributions is examined. Results indicate that the nonlinear Boussinesq parameter enhances fluid motion near the moving plate while suppressing it near the stationary plate. Increased Hartmann numbers uniformly dampen velocity due to stronger Lorentz forces, whereas suction/injection modulates flow development by adjusting the boundary layer. The findings highlight the interplay of buoyancy, magnetic suppression and boundary layer control, providing insights for optimizing flow stability and heat transfer in advanced thermal fluid systems.
References
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Jha, B. K., Aina, B., and Ajiya, A. T. (2015). Role of suction/injection on MHD natural convection flow in a vertical microchannel. International Journal of Energy and Technology. 7(2), 30-39.
Yale, I. D., and Musa, M. (2022). Unsteady MHD Couette flow in a vertical porous channel with effect of thermal radiation and variable temperature. Global Journal of Engineering and Technology Advances. 10(3), 85-94.
Anyanwu, E. O., and Raymond, D. (2023). Effects of Hartmann number on unsteady MHD flow in a porous medium bounded by parallel plate. Asian Journal of Pure and Applied Mathematics. 5(1), 396-41.
Ajibade, A. O., Umar, A. M., and Tafida, M. K. (2021). An analytical study on effect of viscous dissipation and suction/injection on a steady MHD natural convection Couette flow of heat generating/absorbing fluid. Advances in Mechanical Engineering. 13(5), 1-12.
Usman, H., Dogondaji, A. M. and Sammani, A. (2023). Effect of suction/injection on unsteady MHD natural convective radiative flow of heat mass transfer in a plumb frequency. Saudi Journal of Engineering and Technology. 8(7), 171-180.
Oni, M. O., and Rilwanu, U. (2023). Role of suction/injection on electromagnetohydrodynamic natural convection flow in a porous microchannel with electro osmotic effect. International Journal of Applied Mechanics and Engineering. 28(4), 94-113.
Ajibade, A. O., and Bolaji, S. (2020). Steady natural convection MHD flow in a vertical channel with induced magnetics field and variable fluid properties. Journal of Mathematical Science Series. 47(1), 176-192.
Jha, B. K. and Samaila, G. (2022). Nonlinear approach for natural convection and mass transfer in a vertical channel. doi:10.1002/htj.223443.
Raju, S. R., Reddy, G. J., Rao, J. A., and Rashidi, M. M. (2016). Thermo diffusion and diffusion thermo effects on an unsteady heat and mass transfer MHD natural convection Couette flow using FEM. Journal of Computational Design and Engineering, 3, 349-362.
Amouzadeh, F., Tondro, M., Asadi, Z., and Ganji, D. D. (2021). Suction and injection effect on MHD fluid flow within a vertical annulus for electrical wire cooling. Case Studies in Thermal Engineering, 27; 101241.
Chitra, M., and Suhasini, M. (2017). Effect of suction/injection on unsteady MHD oscillatory flow through a vertical channel filled with porous medium. Research Journal of Science and Technology, 9(4), 498-504.
Jha, B. K., and Malgwi, P. B. (2022). Hydromagnetic free convection flow in a vertical microporous channel with hall current and ion slip effect. Journal of the Egyptian Mathematical Society, 30(21), 2-26.
Yao, S. W. Ahmad, M. Mustafa, I., Ahmad, I., Asjad, M. I., and Nazar, M. (2022). Suction effect on MHD flow of Brinkman-type fluid with heat absorption and first-order chemical reaction. frontiers in energy research. 10:963583.
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Palai, D. P., Chaudhuri, S., and Das, B. (2025). Effects of uniform injection and suction on the flow of a rivlin-ericksen fluid of grade three through porous parallel plates: A semi-analytical study. Journal of Heat and Mass Transfer Research. 12(1), 45-60.
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Sajjan, K., Shah, N. A., Ahammad, N. A., Raju, C. S. K., Kumar, M. D., and Weera, W. (2022). Nonlinear Boussinesq and Rosseland approximations on 3D flow in an interruption of ternary nanoparticles with various shapes of densities and conductivity properties. AIMS Mathematics. 7(10), 18416-18449.
RamReddy, C., Naveen, P., and Srinivasacharya, D. (2019). Influence of nonlinear Boussinesq approximation on natural convective flow of a power-law fluid along an inclined plate under convective thermal boundary condition. Nonlinear Engineering. 8, 94-106.
Srinivasacharya, D., RamReddy, C., and Naveen, P. (2018). Effects of nonlinear Boussinesq approximation and double dispersion on a micropolar fluid flow under convective thermal condition. Heat Transfer. 48(1), 414-434.
Wang X., Ye Y., Zuo H. and Li Y. (2024). Neurobiological effects and mechanisms of magnetic fields: a review from 2000 to 2023. BMC Public Health. 24:3094.
Roshani, H., Jalili, P., Jalili, B., and Ganji, D. D. (2024). Impact of various heat sources on the transient heat transfer rate in a 3D cylinder consisting of parts with different thermal conductivity coefficients. International Journal of Thermofluids. 23, 100799.
Idowu, A. S., and Olabode, J. O. (2021). Dynamics of heat generating upper-connected maxwell fluid in a porous medium over melting stretching sheet with stratification. Journal of Applied Sciences, Information and Computing. 2(1), 12-23.
Olabode, J. O., Idowu, A. S., Akolade, M. T., and Titiloye, E. O. (2021). Unsteady flow analysis of Maxwell fluid with temperature dependent variable properties and quadratic thermo-solutal convection influence. Partial Differential Equations in Applied Mathematics. 4, 100078.
Iranian, D. Sudarmozhi, K., Khan, I., and Mohamed, A. (2023). Significance of heat generation and impact of suction/injection on Maxwell fluid over a horizontal plate by the influence of radiation. International Journal of Thermofluids. 20, 100396.
Daramola, D. A., Ajibade, A. O., and Lawal, H. A. (2023). Role of suction/injection on mixed convection flow in a vertical microchannel filled with porous material. FUDMA Journal of Sciences. 7(3), 293-303.
Jha, B. K., and Oni, M. (2020). Nonlinear mixed convection flow in an inclined channel with time-periodic boundary condition. International Journal of Engineering Physics. 6, 21-33.
Isede, H. A., Adeniyan, A., and Oladosu, O. O. (2023). Entropy optimization and heat transfer analysis of MHD heat generating fluid flow through an anisotropic porous parallel wall channel: An analytic solution. International Journal of Mathematical Sciences and Optimization: Theory and Applications. 9(1), 81-103.
Nwaigwe, C., Weli, A., and Mebarek-Oudina, F. (2023). Modelling the impacts of shape and volume fraction of nanoparticles on water based nanofluid flow with variable thermophysical properties. International Journal of Mathematical Sciences and Optimization: Theory and Applications. 8(2), 94-108.
Isede, H. A., Adeniyan, A., and Ogbonna, N. (2023). Lie-group analysis of flow and heat transfer of a dissipating fluid past stretching/shrinking surfaces with variable viscosity and nonuniform heat flux. International Journal of Mathematical Sciences and Optimization: Theory and Applications. 9(1), 59-80.
Jha, B. K., Aina, B., and Ajiya, A. T. (2015). Role of suction/injection on MHD natural convection flow in a vertical microchannel. International Journal of Energy and Technology. 7(2), 30-39.
Yale, I. D., and Musa, M. (2022). Unsteady MHD Couette flow in a vertical porous channel with effect of thermal radiation and variable temperature. Global Journal of Engineering and Technology Advances. 10(3), 85-94.
Anyanwu, E. O., and Raymond, D. (2023). Effects of Hartmann number on unsteady MHD flow in a porous medium bounded by parallel plate. Asian Journal of Pure and Applied Mathematics. 5(1), 396-41.
Ajibade, A. O., Umar, A. M., and Tafida, M. K. (2021). An analytical study on effect of viscous dissipation and suction/injection on a steady MHD natural convection Couette flow of heat generating/absorbing fluid. Advances in Mechanical Engineering. 13(5), 1-12.
Usman, H., Dogondaji, A. M. and Sammani, A. (2023). Effect of suction/injection on unsteady MHD natural convective radiative flow of heat mass transfer in a plumb frequency. Saudi Journal of Engineering and Technology. 8(7), 171-180.
Oni, M. O., and Rilwanu, U. (2023). Role of suction/injection on electromagnetohydrodynamic natural convection flow in a porous microchannel with electro osmotic effect. International Journal of Applied Mechanics and Engineering. 28(4), 94-113.
Ajibade, A. O., and Bolaji, S. (2020). Steady natural convection MHD flow in a vertical channel with induced magnetics field and variable fluid properties. Journal of Mathematical Science Series. 47(1), 176-192.
Jha, B. K. and Samaila, G. (2022). Nonlinear approach for natural convection and mass transfer in a vertical channel. doi:10.1002/htj.223443.
Raju, S. R., Reddy, G. J., Rao, J. A., and Rashidi, M. M. (2016). Thermo diffusion and diffusion thermo effects on an unsteady heat and mass transfer MHD natural convection Couette flow using FEM. Journal of Computational Design and Engineering, 3, 349-362.
Amouzadeh, F., Tondro, M., Asadi, Z., and Ganji, D. D. (2021). Suction and injection effect on MHD fluid flow within a vertical annulus for electrical wire cooling. Case Studies in Thermal Engineering, 27; 101241.
Chitra, M., and Suhasini, M. (2017). Effect of suction/injection on unsteady MHD oscillatory flow through a vertical channel filled with porous medium. Research Journal of Science and Technology, 9(4), 498-504.
Jha, B. K., and Malgwi, P. B. (2022). Hydromagnetic free convection flow in a vertical microporous channel with hall current and ion slip effect. Journal of the Egyptian Mathematical Society, 30(21), 2-26.
Yao, S. W. Ahmad, M. Mustafa, I., Ahmad, I., Asjad, M. I., and Nazar, M. (2022). Suction effect on MHD flow of Brinkman-type fluid with heat absorption and first-order chemical reaction. frontiers in energy research. 10:963583.
Chutia, M. (2022). Numerical solution of MHD channel flow in a porous medium with uniform suction and injection in the presence of an inclined magnetic field. Journal of Applied Mathematics and Computational Mechanics. 21(2), 5-13.
Palai, D. P., Chaudhuri, S., and Das, B. (2025). Effects of uniform injection and suction on the flow of a rivlin-ericksen fluid of grade three through porous parallel plates: A semi-analytical study. Journal of Heat and Mass Transfer Research. 12(1), 45-60.
Chakradhar, K. Nandagopal, K. Prashanthi, V. Parandhama, A. Somaiah, T. Thrinath, B. V., Tarakaramu, N., Rasool, G., and Abduvalieva, D. (2025). MHD effect on peristaltic motion of williamson fluid via porous channel with suction and injection. Partial Differential Equations in Applied Mathematics. 13, 101103.
Hamrelaine, S., Mebarek-Oudina, F., and Sari, M. R. (2019). Analysis of MHD jefrey hamel flow with suction/injection by homotopy analysis method. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences. 58(2), 173-186.
Sarki, M. N., Hamza, M. S., and Tanko, A. (2025). Impact of chemical reaction, sore effects on nonlinear free convection mass transfer in Couette flow within a vertical channel. International Journal of Innovative Mathematics, Statistics and Energy Policies. 13(2), 100-113.
Sajjan, K., Shah, N. A., Ahammad, N. A., Raju, C. S. K., Kumar, M. D., and Weera, W. (2022). Nonlinear Boussinesq and Rosseland approximations on 3D flow in an interruption of ternary nanoparticles with various shapes of densities and conductivity properties. AIMS Mathematics. 7(10), 18416-18449.
RamReddy, C., Naveen, P., and Srinivasacharya, D. (2019). Influence of nonlinear Boussinesq approximation on natural convective flow of a power-law fluid along an inclined plate under convective thermal boundary condition. Nonlinear Engineering. 8, 94-106.
Srinivasacharya, D., RamReddy, C., and Naveen, P. (2018). Effects of nonlinear Boussinesq approximation and double dispersion on a micropolar fluid flow under convective thermal condition. Heat Transfer. 48(1), 414-434.
Wang X., Ye Y., Zuo H. and Li Y. (2024). Neurobiological effects and mechanisms of magnetic fields: a review from 2000 to 2023. BMC Public Health. 24:3094.
Roshani, H., Jalili, P., Jalili, B., and Ganji, D. D. (2024). Impact of various heat sources on the transient heat transfer rate in a 3D cylinder consisting of parts with different thermal conductivity coefficients. International Journal of Thermofluids. 23, 100799.
Idowu, A. S., and Olabode, J. O. (2021). Dynamics of heat generating upper-connected maxwell fluid in a porous medium over melting stretching sheet with stratification. Journal of Applied Sciences, Information and Computing. 2(1), 12-23.
Olabode, J. O., Idowu, A. S., Akolade, M. T., and Titiloye, E. O. (2021). Unsteady flow analysis of Maxwell fluid with temperature dependent variable properties and quadratic thermo-solutal convection influence. Partial Differential Equations in Applied Mathematics. 4, 100078.
Iranian, D. Sudarmozhi, K., Khan, I., and Mohamed, A. (2023). Significance of heat generation and impact of suction/injection on Maxwell fluid over a horizontal plate by the influence of radiation. International Journal of Thermofluids. 20, 100396.
Daramola, D. A., Ajibade, A. O., and Lawal, H. A. (2023). Role of suction/injection on mixed convection flow in a vertical microchannel filled with porous material. FUDMA Journal of Sciences. 7(3), 293-303.
Jha, B. K., and Oni, M. (2020). Nonlinear mixed convection flow in an inclined channel with time-periodic boundary condition. International Journal of Engineering Physics. 6, 21-33.
Isede, H. A., Adeniyan, A., and Oladosu, O. O. (2023). Entropy optimization and heat transfer analysis of MHD heat generating fluid flow through an anisotropic porous parallel wall channel: An analytic solution. International Journal of Mathematical Sciences and Optimization: Theory and Applications. 9(1), 81-103.
Nwaigwe, C., Weli, A., and Mebarek-Oudina, F. (2023). Modelling the impacts of shape and volume fraction of nanoparticles on water based nanofluid flow with variable thermophysical properties. International Journal of Mathematical Sciences and Optimization: Theory and Applications. 8(2), 94-108.
Isede, H. A., Adeniyan, A., and Ogbonna, N. (2023). Lie-group analysis of flow and heat transfer of a dissipating fluid past stretching/shrinking surfaces with variable viscosity and nonuniform heat flux. International Journal of Mathematical Sciences and Optimization: Theory and Applications. 9(1), 59-80.
Published
2026-01-30
How to Cite
Tafida, M., Yahuza , M., & Yusha’u, I. (2026). MHD Natural Convection Couette Flow in a Vertical Channel: Effects of Nonlinear Boussinesq Approximation and Suction/Injection. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(4), 69 - 82. Retrieved from https://ijmso.unilag.edu.ng/article/view/2916
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