Imperfectly Impermeable Boundaries and Variable Viscosity Perspectives on the Stability of Natural Convection in a Vertical Porous Layer

Abstract

This study examines the simultaneous impact of temperature-dependent viscosity and Robin boundary conditions on velocity, focusing on analyzing the stability of buoyant parallel flow in a differentially heated vertical porous layer. The neutral stability condition and the instability thresholds are determined numerically for various values of governing parameters. The onset of instability of the base flow is accurately analyzed by introducing a non-negative parameter that measures the extent of departure of boundaries from impermeable to permeable. It is established that the base flow becomes unstable when this parameter exceeds a threshold value, which significantly depends on the variable viscosity parameter. This work demonstrates a clear bridge between impermeable and permeable boundaries in the context of a variable viscosity fluid.