The Role of Viscous Dissipation and Gravity Variations on the Onset of Convection in a Porous Layer With Throughflow and a Magnetic Field

This study explores the interplay between a magnetic field, viscous dissipation, and varying gravity profiles on the initiation of thermal convection in a porous medium with throughflow. Four gravity variation profiles?linear, parabolic, cubic, and exponential?are examined to determine their effects on the system's stability, using linear stability analysis with the normal mode technique, the Eigen function computed via a single-term Galerkin approximation, supported by computational tool Mathematica. Results demonstrate that exponential gravity variations provide the highest stability due to their rapidly increasing gravitational force, followed by linear, parabolic, and cubic profiles. Throughflow is found to enhance stability by reducing thermal gradients, while magnetic fields contribute to stabilization through Lorentz forces that oppose fluid motion. However, increasing viscous dissipation diminishes the stabilizing effects of both throughflow and magnetic fields. This study highlights the intricate interplay between these parameters and their collective role in determining the stability of the system, offering insights applicable to geophysical and engineering contexts involving porous media.