Forchheimer–Bénard Instability of the Non-Newtonian Fluid

Abstract

The present paper examines the effect of vertical throughflow on the onset of convective instability in a horizontal porous layer filled with a non-Newtonian power-law fluid (PL). The permeable boundary layers are exposed to two different uniform constant temperature conditions, The Oberbeck-Boussinesq hypothesis is considered with the Darcy-Forchheimer model. A fourth-order eigenvalue problem is stemmed from the performance of the linear stability analysis, and the critical values are obtained using the shooting method combined with the Runge-Kutta method. The non-Newtonian Darcy-Rayleigh number ( R ), the Péclet number ( P e ), the Forchheimer number ( G ), and the power-law index ( n ) are the parameters whose value play a crucial role in the onset of instability. The finding shows more stabilizing effects arise in pseudoplastic fluid than dilatant one at Peclet number P e << 1 where the inverse behaviour takes place at large Peclet number even with the existence of the drag number or without it.