ONSET OF DOUBLE DIFFUSIVE REACTION-CONVECTION IN AN ANISOTROPIC POROUS LAYER WITH INTERNAL HEAT SOURCE

Abstract

The effect of internal heat source on the onset of double diffusive reaction-convection in an anisotropic porous layer subjected to chemical equilibrium on the boundaries is investigated analytically using both linear and weak nonlinear stability analyses. The linear analysis is based on the usual normal mode method. The Darcy model is employed for the momentum equation. The effects of internal Rayleigh number, Damkohler number, mechanical anisotropy parameter, thermal anisotropy parameter, Lewis number, and normalized porosity on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the effects of internal Rayleigh 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. A weak nonlinear analysis based on truncated representation of Fourier series is performed to find heat and mass transfer. Further, the transient behavior of the Nusselt number and Sherwood number is studied by solving the finite amplitude equations using the Runge-Kutta method.