Variable viscosity effects on convective instability in superposed fluid and porous layers

Abstract

The variable viscosity effects on the stability characteristics of the motionless fluid in superposed fluid and porous layers bounded by conducting rigid boundaries are investigated. It is found that the stability characteristics in terms of the critical Rayleigh number Rmc, the critical wave number amc, and the critical flow patterns, are profoundly influenced by the viscosity variation, which is represented by γ=ln(νmax/νmin), where ν is the kinematic viscosity of the fluid. The intrinsic features of the critical flow are mainly determined by both the values of γ and ζ, the depth ratio of the fluid layer depth to the porous layer depth. Three critical flow patterns are identified on the basis of varying γ and ζ. The transition between any two of these three flow patterns is a bimodal instability. The present results may provide valuable information for understanding the convective motion of the melt during the solidification process of alloys.