The onset of Darcy-Brinkman convection in a porous medium layer with vertical throughflow and variable gravity field effects

In this study, the influence of constant throughflow and varying downward gravity field on the onset of Darcy-Brinkman convection in a porous medium layer is examined numerically. We considered two cases of gravity field variations: (a) linear and (b) parabolic. A higher-order Galerkin-weighted residual technique and QZ procedure are used to get the numerical solution for the entire Darcy numbers amid Da = 0 (Horton-Rogers-Lapwood convection) and Da -> infinity (Rayleigh Benard Convection). It is obtained that the throughflow, the downward gravity field and the Darcy number are to holdup the beginning of convection. It is also obtained that the system is more stable for linear variation of gravity field in comparison to the parabolic variation.