Combined Effects of Magnetic Field and Heat Source on Double-Diffusive Marangoni Convection in Fluid-Porous Structure

The problem of double-diffusive Marangoni convection (DDMC) in a fluid-porous structure, which is horizontally infinite, is investigated in the presence of constant heat source/sink in both the layers as well as a uniform vertical magnetic field. This composite layer is enclosed by adiabatic and isothermal boundaries. The system of ordinary differential equations is solved in closed form for the thermal Marangoni number (tMn), which is an eigenvalue, for adiabatic-adiabatic and adiabatic-isothermal boundary combinations. In-depth comparisons between the various parameters and depth ratio are made. It is noted that the thermal Marangoni number for the adiabatic-adiabatic thermal boundary condition is higher than that for the adiabatic-isothermal boundary condition as examined in detail. As a result, the fluid-porous structure is stable and can be employed in situations where convection needs to be controlled in the case of an adiabatic-adiabatic thermal boundary condition.