EFFECTS OF NON-UNIFORM SALINITY GRADIENTS ON THE ONSET OF DOUBLE DIFFUSIVE MAGNETO – MARANGONI CONVECTION IN A COMPOSITE LAYER

Abstract

The onset of double diffusive magneto Marangoni convection in a two-layer system comprising an incompressible two component, electrically conducting fluid saturated porous layer over which lies a layer of the same fluid in the presence a vertical magnetic field has been studied analytically with respect to uniform and non-uniform salinity gradients. The upper boundary of the fluid layer is free and the lower boundary of the porous layer is rigid and both the boundaries are insulating to heat and mass. At the interface the velocity, shear stress, normal stress, heat, heat flux, mass and mass flux are assumed to be continuous conducive for Darcy-Brinkman model. The resulting Eigen value problem is solved by regular perturbation technique. The critical Rayleigh number, which is the criterion for stability of the system, are obtained for uniform and non-uniform salinity gradients. The effects of different physical parameters on the onset of double diffusive magneto-convection are investigated for all the gradients in detail.