Natural Convection in a Porous Cavity with a Varying-Amplitude Wavy Wall Under a Partially Applied Magnetic Field: A Finite Element Study

This study investigates natural convection within a square porous cavity subjected to a partially applied horizontal magnetic field along a section of the left vertical wall. The top and bottom horizontal walls are thermally insulated. The left wall is maintained at a high temperature, while the opposing right wall, characterized by a varying-amplitude wavy surface, is kept at a lower temperature. The Brinkman–Forchheimer-extended Darcy model is employed to simulate the fluid flow within the porous medium. The governing equations are numerically solved using the Galerkin finite element method, and the accuracy of the approach is validated through comparison with previous study. The effects of key parameters including the magnetic field length, Hartmann number, Rayleigh number, Darcy number, and the wall wave damping effect are analyzed in terms of streamlines, isotherms, and average Nusselt number. The results demonstrate that the magnetic field suppresses convective flow and reduces heat transfer, highlighting its potential for controlling thermal transport and fluid motion within porous enclosures. Furthermore, increasing the damping effect of wall waves reduces heat transfer by simplifying convective patterns.