Stability of stationary plane-parallel flow of viscoplastic fluid between two differentially heated vertical plates

Abstract

Stability of a stationary plane-parallel convective flow of viscoplastic fluid between two differentially heated vertical rigid plates is studied. It has been found that, as in the case of Newtonian fluid, depending on the Prandtl number value, the hydrodynamic monotonic perturbations (vortices at the boundary of counter-flows) or oscillatory thermal perturbations (thermal waves) are responsible for the onset of instability. Stability maps in the Grashof number–Prandtl number plane are obtained for different values of the yield stress. It has been shown that for large Prandtl number values typical for viscoplastic fluids the oscillatory thermal perturbations are most dangerous. Two-dimensional non-linear regimes of convection are studied numerically by the finite difference method.