Entropy generation for MHD pulsating stratified liquid flow between two permeable beds

In natural systems such as lakes, reservoirs, and the upper ocean layers, temperature-induced stratified fluid flows are frequently observed. Numerous studies have explored key aspects of these flows, including stability, mixing, and thermal transport. However, the heat transfer characteristics of stratified fluid flow between permeable beds remain unexplored. This study aims to address this gap by performing an entropy generation analysis of pulsating stratified fluid flow between two permeable beds, with key applications in geothermal energy extraction, environmental modelling, and biomedical engineering. Liquid is injected through the lower bed and extracted from the upper bed at an equal velocity. The governing flow equations are solved numerically using the fourth-order Runge–Kutta (RK-4) method in combination with the shooting method in Mathematica. Graphical results are presented to illustrate the influence of key parameters on velocity, temperature, Nusselt number, entropy generation, Bejan number, mass flux, and stress distribution. Our results indicated that a rise in the Reynolds number, pressure gradient, and stratification parameter boosts the fluid velocity, while a higher slip parameter tends to reduce it. The temperature distribution declines with the rise of magnetic field and Reynolds number. In contrast, it intensifies with elevated Brinkman number, pressure gradient, and stratification parameter.