The effect of wall slip on the stability of the Rayleigh–Bénard Poiseuille flow of viscoplastic fluids

Abstract

This work investigates the effect of wall slip on the stability of the Bingham Rayleigh–Bénard Poiseuille flow. The steady state of the Bingham plane Poiseuille flow is characterized by an unyielded region of 2 y b width and two sheared regions close to the walls with both no-slip and slip conditions at the walls. A linear stability analysis of this flow with slip conditions is proposed in this paper. The slip boundary conditions case leads to flow destabilization compared with the results obtained in the no-slip case. Critical conditions are modified by varying C f , the friction number. For C f < O ( 1 ) , critical Rayleigh values Ra c tend to that obtained with a free–free case ( C f tends to zero). For 10 < C f < 30 , Ra c values decrease and reach a minimum in this zone. The value of C f , for which Ra c is minimal, varies slowly with the Bingham number B. For C f > 30 the flow is stabilized, i.e. Ra c values increase and finally tend to that of the no-slip case when C f > 1000 . Furthermore, for 1 < C f < 10 4 , asymmetric modes were obtained. They are due to the slip boundary conditions at the walls.