STABILITY ANALYSIS FOR ROTATING DOUBLE-DIFFUSIVE CONVECTION IN THE PRESENCE OF VARIABLE GRAVITY AND REACTION EFFECTS: DARCY MODEL

Abstract

The linear instability and nonlinear stability theories are performed to investigated the variable gravity, rotation and reaction effects on the thermosolutal convection in a porous medium of Darcy type. Two statuses are analyzed, the layer is heated from below and simultaneously salted from above or below. Three different types of gravity variation functions are presented: linear, parabolic, and exponential. The associated system of equations with the corresponding boundary conditions for both theories are calculated by using the $D^2$ Chebyshev tau method. The effect of various parameters on the Rayleigh number is shown graphically. Furthermore, the results reveal that employing the effects of gravity variation, rotation and reaction has a pronounced in determining the convection instability threshold.