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

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 2yb2yb 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 CfCf, the friction number. For Cf30Cf>30 the flow is stabilized, i.e. RacRac values increase and finally tend to that of the no-slip case when Cf>1000Cf>1000. Furthermore, for 1

► Effect of wall slip on the linear stability of the Bingham Rayleigh–Bénard Poiseuille (RBP) flow. ► Slip boundary conditions destabilize the RBP flow compared with the no-slip case. ► Criticality depends on the Bingham number B   and on the friction number CfCf. ► Asymmetric modes are obtained for 1