The study of effects of surface tension, magnetic field and non-uniform salinity gradients on the onset of double diffusive convection in composite system

Abstract

The effects of surface tension, magnetic field and basic non - uniform salinity gradients on the onset of double diffusive convection is studied analytically in composite system comprising an incompressible, two component, electrically conducting fluid lying above a saturated porous layer of the same fluid in the presence of vertical magnetic field imposed. The governing partial differential equations are solved by the method of regular perturbation. The upper boundary of the fluid layer is free and the lower boundary of the porous layer is rigid, insulated to heat and mass. The fluid flow in porous layer is governed by the Darcy-Brinkman equation. The critical Rayleigh number which exhibits the stability of the system is accomplished for piece wise linear salting below, desalting above and step function salinity gradients. We have figured out that by increasing Darcy number, due to the presence of magnetic field the convection is accelerated in all the three non uniform salinity gradients considered.