Heat Transfer Enhancement in Magnetohydrodynamic Darcy–Brinkman Flow Through Anisotropic Porous Media With Viscous Dissipation Effects at the Entry

Abstract The hydrodynamic and thermal behavior of flow through a rectangular channel filled with fluid-saturated anisotropic porous media is investigated numerically. The flow is governed by the Darcy–Brinkman model, incorporating hydrodynamic and thermal anisotropy. The finite volume method (FVM) is implemented to solve these coupled partial differential equations. The permeability tensor is characterized by the principal permeabilities and their orientation angle with respect to the axial direction. This study examines the impact of magnetic field, anisotropy, and viscous dissipation on velocity profiles, skin friction, and heat transfer, focusing on the local Nusselt number. Interestingly, introducing anisotropy enhances heat transfer under specific conditions compared to the isotropic case. Additionally, increasing the Hartmann number further modifies flow behavior, leading to enhanced heat transfer in the axial direction. The clear fluid compatible model demonstrates improved heat transfer efficiency over the other two models. Anisotropy can significantly enhance heat transfer efficiency, achieving an improvement of over 42% compared to the isotropic case. However, under certain conditions, it can also reduce the efficiency of the heat transfer process by nearly 39%. A correlation has been developed to describe the dependence of the local Nusselt number on various parameters. Sensitivity analysis identified the most influential parameters affecting the local Nusselt number, while uncertainty analysis confirmed the robustness and reliability of the developed correlation for practical heat transfer applications. Present results are validated with published experimental and numerical data. The insights gained from this study are vital for optimizing the design of thermal systems utilizing anisotropic porous materials.