Publication

Abstract : Thermally driven convection in magnetized porous media is important in geothermal systems, thermal energy storage, and packed-bed reactors. Motivated by the need to understand and control heat transport in such systems, this study investigates the influence of internal heat modulation on convective instability in a porous layer saturated with an incompressible fluid under a uniform vertical magnetic field. Unlike earlier studies based mainly on Darcy’s law and linear theory, the present work employs the Brinkman extension to incorporate viscous shear effects and combines linear and weakly nonlinear analyses to examine both the onset and finite-amplitude evolution of convection. Linear stability analysis using the normal mode method is performed to determine the critical Rayleigh number as a function of governing physical parameters. To explore post-critical behavior, a weakly nonlinear analysis is carried out through the derivation of a Ginzburg–Landau equation on a slow time scale. The resulting finite-amplitude solutions are used to quantify heat transport via the Nusselt number. The results reveal that internal heating, magnetic field strength, and Brinkman effects delay the onset of stationary convection, thereby stabilizing the system. Thermal and magnetic Prandtl numbers exert opposite influences on heat-transfer efficiency. Furthermore, convective heat transport increases by approximately 23.24% when the internal heating parameter is raised by 75%. Streamlines, isotherms, and magnetic field lines illustrate the underlying flow and thermal structures. These findings provide insight into the coupled effects of magnetic damping, porous resistance, and internal heating, with applications to geothermal energy extraction, nuclear reactor cooling, and industrial filtration systems.