Forchheimer–Bénard Instability of the Non-Newtonian Fluid

¹ Energy Laboratory, Physics Department, Faculty of Sciences, Abdelmalek Essaadi University, Tétouan, Morocco.
² Advanced Materials, Structures and Civil Engineering Laboratory, National School of Applied Sciences at Tetouan, Abdelmalek Essaadi University, Tetouan, Morocco.

^* Corresponding author: elfakiri.hanae-etu@uae.ac.ma

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.