Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow

Abstract

The vertical throughflow effect is investigated on the onset of porous convection by considering a cubic density-temperature relationship and using the Forchheimer-Darcy model. The stability eigenvalue problem is explained numerically using the Galerkin technique. Contrary to the linear density-temperature relationship, the direction of throughflow alters the onset of convection. The throughflow dependent Péclet number is found to stabilize the fluid motion against convection and the upflow is found to be either stabilizing or destabilizing than the downflow depending on the values of thermal condition parameters λ1 and λ2. A destabilizing effect on the onset is observed with increasing λ1 and λ2. The Darcy number Da and the Forchheimer drag co-efficient, cb instability characteristics have been investigated and depicted graphically.