Marangoni convection in superposed fluid and anisotropic porous layers with throughflow

Abstract

Marangoni convective flow of fluid layer overlying a porous layer with anisotropic permeability and thermal diffusivity is addressed. Flow analysis has been carried out in presence of throughflow. Beavers-Joseph's slip condition is applied to the fluid-porous layer interface. The boundaries are known to be rigid, but permeable, and insulated to fluctuations in temperature. The problem of own value resulting from the stability analysis is solved through regular perturbation technique. Flow pattern with the influence of pertinent parameters namely the throughflow parameter, mechanical, thermal anisotropy parameters Prandtl number and depth ratio is investigated. Expression of critical Marangoni number is computed and analyzed. It is found that the depth of the relative layers, the direction of throughflow and mechanical and thermal anisotropy parameters deeply affect system stability. Reducing the parameter of mechanical anisotropy and increasing the parameter of thermal anisotropy contributes to process stabilization. In addition, the probability of regulating surface driven convection is discussed in detail through the appropriate choice of physical parameters.