Magneto–thermal convective flow in fluid–porous region with heat source/sink effects: analytical study

This study unveils a detailed analytical exploration of interfacial convective movement within a hybrid fluid–porous setup exposed to a vertical magnetic field, accompanied by either internal heating or cooling mechanisms. The porous area is represented through Darcy’s law, while the boundary conditions feature a rigid, adiabatic lower boundary and a free, isothermal upper boundary. To investigate varying thermal settings, three distinct temperature profiles are analyzed: linear (Model 1), parabolic (Model 2), and inverted parabolic (Model 3). Closed-form expressions for the thermal Marangoni number (Mn) are established, facilitating a systematic assessment of the effects of depth ratio, heat source intensity, and magnetic field strength. An extensive discussion elaborates on how different parameters influence the eigenvalue in relation to the depth ratio, providing a comprehensive examination of the interconnections at work. The results highlight the intricate and substantial interactions between magnetic fields, thermal gradients, and surface tension effects, all of which collaboratively shape the stability and dynamic behavior of the fluid interface in focus. By employing advanced mathematical modeling techniques and cutting-edge computational simulations, this research offers invaluable insights into the fundamental mechanisms driving convection in layered fluid systems, which exhibit considerable potential applications across a wide range of engineering and industrial endeavors. Moreover, it has been noted that the impact of heat sources or sinks within the fluid layer is significantly greater than their effects observed in the porous layer when analyzing the eigenvalue. These phenomena are crucial for areas such as microgravity crystal growth, geothermal energy extraction, cryogenic applications, multilayer thermal insulators, and liquid metal energy storage solutions. The analytical outcomes align closely with previous studies, confirming the validity of the developed model.