Onset of Darcy-Brinkman Reaction-Convection in an Anisotropic Porous Layer

Abstract

The linear and nonlinear stability analysis of double diffusive reaction-convection in a sparsely packed anisotropic porous layer subjected to chemical equilibrium on the boundaries is investigated analytically. The linear analysis is based on the usual normal mode method and the nonlinear theory on the truncated representation of Fourier series method. The Darcy-Brinkman model is employed for the momentum equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. The effect of Darcy number, Damkohler number, anisotropy parameters, Lewis number, and normalized porosity on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the effect of Darcy number and mechanical anisotropy parameter have destabilizing effect, while the thermal anisotropy parameter has stabilizing effect on the stationary, oscillatory and finite amplitude convection. The Damkohler number has destabilizing effect in the case of stationary mode, with stabilizing effect in the case of oscillatory and finite amplitude modes. Further, the transient behavior of the Nusselt and Sherwood numbers are investigated by solving the nonlinear system of ordinary differential equations numerically using the Runge-Kutta method.

The Onset of Convection in a Two-Layered Porous Medium with Anisotropic Permeability

“…This was sufficient to achieve qualitative new flow patterns with a tilted plane of motion or tilted lateral cell walls. Other earlier papers considering onset of convection in anisotropic porous media are: Trew and McKibbin (1994), Rees and Storesletten (1995) and Rees et al (2006), to mention a few, while recent research has gravitated towards determining how the combination of anisotropy with other effects modifies onset criteria; see Hill and Morad (2014) Gaikwad and Dhanraj (2016) and Raghunatha et al (2018).…”

Effect of Horizontal Magnetic Field and Horizontal Rotation on Thermosolutal Stability of a Dusty Couple-Stress Fluid through a Porous Medium: a Brinkman Model

“…Mahajan and Sharma (2012) studied the asymptotic stability and also determine the stability bounds for both equilibrium and arbitrary flows of a couple-stress fluid in a Brinkman flow. Recently, the linear and nonlinear stability analysis of double-diffusive reaction convection in an anisotropic DarcyBrinkman porous layer is performed by Gaikwad and Dhanraj (2016).…”