Effects of heat source/sink on Darcian-Benard-Magneto-Marangoni convective instability in a composite layer subjected to nonuniform temperature gradients

Abstract

The problem of Bènard-Magneto-Marangoni convection in a composite layer which is infinite along x and y directions is considered for the Darcian case in the presence of constant heat source/sink in both the layers. This composite layer is subjected to uniform and nonuniform temperature gradients. The eigenvalue, thermal Marangoni number is obtained in closed form with the lower surface rigid and upper surface free with surface tension effects for the velocity and isothermal temperature boundary combinations. The influence of porous parameter, magnetic field and nonuniform temperature gradients on the Eigen value problem are discussed. It is experiential that the effect of heat source/sink in the fluid layer is dominant on the eigenvalue over the same in the porous layer. The important parameters like Chandrasekhar number, modified internal Rayleigh number and thermal ratio which control Bènard-Magneto-Marangoni convection are discussed in detail.