Triple diffusive Marangoni convection in a fluid-porous structure: Effects of a vertical magnetic field and temperature profiles

Abstract

In this study, the triple diffusive Marangoni convection (TDMC) problem when a steady heat source is present in both layers and a vertical uniform magnetic field in a fluid-porous structure is investigated in closed form. The horizontally infinite fluid-porous structure, which is horizontally surrounded by adiabatic boundaries and subjected to basic uniform and non-uniform temperature profiles. For all three temperature profiles (TP), linear, parabolic and inverted parabolic, the eigenvalues, the thermal Marangoni numbers (TMNs) are determined in closed form for lower rigid and upper free boundaries with surface tension, depending on both temperature and concentrations. The effects of relevant parameters on the eigenvalues, hence on TDMC, against depth ratio are attempted for all TPs. It is noticed that, the inverted parabolic TP on TDMC in a composite layer is the most stable of all the three TPs, the linear TP is the most unstable one and the parabolic TP is the moderate one. The relevant physical parameters considered in the study are effective for porous layer dominant fluid-porous structures.

Keywords

• Heat source/sink
• Triple diffusive convection
• Magnetic field
• Modified internal Rayleigh numbers
• Depth ratio