Effect of viscous dissipation on thermal convection in bidispersive porous media with vertical throughflow: Global stability analysis

Abstract

This article investigates the onset of convection in a bidispersive porous medium, considering the impact of viscous dissipation and throughflow using both linear and nonlinear theories. The flow is modeled using the Oberbeck–Boussinesq approximation and Darcy's law, with local thermal equilibrium between the fluid and solid phases. The temperature field depends solely on the vertical coordinate in the basic solution. The study employs a two-pronged approach to analyze the system's stability, utilizing the normal mode technique for linear analysis and the energy method for nonlinear analysis. The article confirms the validity of the principle of exchange of stabilities. The numerical solution of the eigenvalue problem for both linear and nonlinear theories is obtained using the bvp4c routine. The research explores the influence of various physical parameters on the system's stability. Viscous dissipation's effect on convection onset is noticeable only with significant throughflow. In the absence of viscous dissipation, the throughflow direction does not affect the system's stability. The effective permeability ratio stabilizes the system with upward throughflow and exhibits opposite behavior with downward throughflow. The sub-critical region remains unchanged for the Gebhart number range but increases with higher moment transfer coefficient and effective permeability ratio. Additionally, an analytical expression is derived for the small Peclet number regime of the Rayleigh number using asymptotic analysis.