Nonhomogeneous Porosity and Thermal Diffusivity Effects on a Double-Diffusive Convection in Anisotropic Porous Media

Abstract

Abstract A model for double-diffusive convection in anisotropic and inhomogeneous porous media has been analysed. In particular, the effects of variable permeability, thermal diffusivity and variable gravity with respect to the vertical direction, have been studied. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using three dimensional simulation. Our results show that the linear theory produce a good predicts on the onset of instability in the basic steady state. It is known that as R c ${R_c}$ increases the onset of convection is more likely to be via oscillatory convection as opposed to steady convection, and the three dimensional simulation results show that as R c $Rc$ increases, the actual threshold moving toward the nonlinear stability threshold and the behaviour of the perturbation of the solutions becomes more oscillated.