Throughflow and variable gravity outlooks on bidispersive porous convection with relatively large macropores

Abstract

This study explores the combined effects of variable gravity and a uniform vertical throughflow on linear instability and nonlinear stability of thermal convection in a bidispersive porous medium (BDPM) characterized by relatively large macropores with single temperature field. The fluid flow in micropores and macropores is modelled using Darcy's and Brinkman's theories, respectively. The analysis encompasses three depth-dependent gravity laws: linear, quadratic, and exponential. The principle of exchange of stabilities is established. The numerically computed critical thresholds of linear instability and nonlinear stability are found to be different indicating the manifestation of subcritical instability and also the direction of throughflow dictates the stability of base flow. In particular, the upflow is found to be more stabilizing than downflow, highlighting the dominant influence of gravity variation over throughflow in determining the system's stability. Under a constant gravitational field, however, the linear instability threshold coincides precisely with the global nonlinear stability boundary in the absence of throughflow. Moreover, with throughflow, subcritical instability arises and the stability of the system remains unaffected by the direction of the throughflow.