Antony A. Hill

Double-diffusive convection in a porous medium with a concentration based internal heat source

Linear and nonlinear stability analyses of double–diffusive convection in a fluid–saturated porous layer with a concentration based internal heat source are studied. Darcys law and the Boussinesq approximation are employed, with the equation of state taken to be linear with respect to temperature and concentration. Both the numerical and analytical analysis for the linear theory strongly suggest the presence of a critical value γc, where γ is essentially a measure of the internal heat source, for which no oscillatory convection occurs when γc ⩽ γ. This, in the present literature, appears to be an unobserved phenomenon. A nonlinear energy stability analysis demonstrates more comparable linear and nonlinear thresholds when the linear theory predicts the onset of fully stationary convection. However, irrespective of the γ value, the agreement of the thresholds does deteriorate as the solute Rayleigh number Rc increases.

Poiseuille flow in a fluid overlying a porous medium

This paper numerically investigates the instability of Poiseuille flow in a fluid overlying a porous medium saturated with the same fluid. A three-layer configuration is adopted. Namely, a Newtonian fluid overlying a Brinkman porous transition layer, which in turn overlies a layer of Darcy-type porous material. It is shown that there are two modes of instability corresponding to the fluid and porous layers, respectively. The key parameters which affect the stability characteristics of the system are the depth ratio between the porous and fluid layers and the transition layer depth.

Global stability for thermal convection in a fluid overlying a highly porous material

This paper investigates the instability thresholds and global nonlinear stability bounds for thermal convection in a fluid overlying a highly porous material. A two-layer approach is adopted, where the Darcy–Brinkman equation is employed to describe the fluid flow in the porous medium. An excellent agreement is found between the linear instability and unconditional nonlinear stability thresholds, demonstrating that the linear theory accurately emulates the physics of the onset of convection.

Convection due to the selective absorption of radiation in a porous medium

A model for convection due to the selective absorption of radiation in a fluid saturated porous medium is investigated. The model is based on a similar one introduced for a viscous fluid by Krishnamurti [x]. Employing this adapted model we show the growth rate for the linearised system is real. A linear instability analysis is performed. Global stability thresholds are also found using nonlinear energy theory. An excellent agreement is found between the linear instability and nonlinear stability Rayleigh numbers, so that the region of potential subcritical instabilities is very small, demonstrating that the linear theory accurately emulates the physics of the onset of convection.