Approximate Analytical Solutions for Marangoni Mixed Convection Boundary Layer

Abstract

The paper deals with a steady coupled dissipative layer, called Marangoni mixed convection boundary layer, which can be formed along the interface of two immiscible fluids, in surface driven flows. The mixed convection boundary layer is generated besides the Marangoni convection effects induced flow over the surface due to an imposed temperature gradient, there are also buoyancy effects due to gravity and external pressure gradient effects. We shall use a model proposed by Chamkha wherein the Marangoni coupling condition has been included into the boundary conditions at the interface. The similarity equations are first determined, and the approximate analytical solutions are obtained by an efficient transformation, asymptotic expansion and Pade´ approximant technique. The features of the flow and temperature fields as well as the interface velocity and heat transfer at the interface are discussed for some values of the governing parameters. The associated fluid mechanics was analyzed in detail.