Nonhomogeneous porosity and thermal diffusivity effects on stability and instability of double-diffusive convection in a porous medium layer: Brinkman Model

A model for double-diffusive convection in anisotropic and inhomogeneous porous media has been analysed. In particular, the effect of variable permeability and thermal diffusivity has been studied using the Brinkman model. Moreover, we analyse the effect of slip boundary conditions on the stability of the model. Due to numerous applications in micro-electro-mechanical-systems (MEMS) and other microfluidic devices, such a study is essential to have. Both linear instability analysis and nonlinear stability analysis are employed. We accurately analyse when stability and instability will commence and determine the critical Rayleigh number as a function of the slip coefficient