LINEAR AND NONLINEAR ANALYSIS FOR THERMAL CONVECTION IN AN INTERNALLY HEATED FLUID-SATURATED ANISOTROPIC POROUS MEDIUM WITH THROUGHFLOW AND THE VARIABLE GRAVITY FIELD

The purpose of this paper is to investigate the impact of throughflow and variable gravity force on the stability of an internally heated anisotropic porous medium. Four types of gravity field variations with depth and three cases of internal heat sources are considered for investigation. The normal mode technique and energy method are used for linear and nonlinear analysis, respectively. Here, the effect of three types of internal heating, four types of variable gravity forces, throughflow, and anisotropic parameters on the critical Rayleigh number is explored numerically using the Galerkin method. This study suggests that throughflow in an upward or downward direction increases the stability of the system. However, the size of the convection cell decreases due to increasing upward throughflow. Moreover, a comparison between the results obtained from linear analysis and nonlinear are shown, and thus the possibility of subcritical regions of instability is indicated in this investigation.