Local Thermal Non-equilibrium Analysis of the Instability in a Vertical Porous Slab with Permeable Sidewalls

The role of a second diffusing component on the Gill-Rees stability problem

The stability of natural convection in a vertical porous layer using a local thermal nonequilibrium model was first studied by Rees (Transp Porous Med 87:459-464, 2011) following the proof of Gill (J Fluid Mech 35:545-547, 1969), called the Gill-Rees stability problem. The aim of the present study is to investigate the implication of an additional solute concentration field on the Gill-Rees problem. The stability eigenvalue problem is solved numerically and some novel results not observed in the studies of double-diffusive natural convection in vertical porous (local thermal equilibrium case) and non-porous layers are disclosed. The possibility of natural convection parallel flow in the basic state becoming unstable due to the addition of an extra diffusing component is established. In some cases, the neutral stability curves of stationary and travelling-wave modes are connected to form a loop within which the flow is unstable indicating the requirement of two thermal Darcy-Rayleigh numbers to specify the stability/instability criteria. Moreover, the change in the mode of instability is recognized in some parametric space. The results for the extreme cases of the scaled interphase heat transfer coefficient are discussed.

Optimal Stability Thresholds in Rotating Fully Anisotropic Porous Medium with LTNE

Abstract

The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved.

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