Stability analysis of bidispersive porous convection with maximum density and variable viscosity effects

Abstract

This study investigates the onset of penetrative convection in a bidispersive porous medium, incorporating variable viscosity effects and quadratic density-temperature. The fluid behavior is modeled using Darcy theory for micropores and Brinkman theory for macropores. Both linear and nonlinear stability analyses are conducted to examine small-amplitude disturbances and larger perturbations, respectively. It is observed that the nonlinear stability thresholds and linear instability thresholds are extremely close to each other in the presence of quadratic density variation (maximum density variation); however, in its absence (purely linear density variation), the thresholds coincide. The effects of linear, quadratic, and exponential variations of viscosity with temperature are addressed on the stability characteristics of the system. The non-dimensionalization process has yielded two distinct Rayleigh numbers: one corresponding to the linear variation of density and the other to the quadratic variation. Critical Rayleigh numbers, specific to each type of density variation, have been determined for given physical parameters. It has been noted that both quadratic and linear variations in density provide highly accurate predictions of instability, depending on the parameters associated with bidispersive porous media. The analysis shows that when variable viscosity and the density maximum characteristic are combined, they accelerate the onset of bidispersive porous convection significantly faster compared to when each of these factors is considered in isolation.