Onset of double diffusive convection in a maxwell fluid saturated anisotropic porous layer with internal heat source

Abstract

The onset of double diffusive convection in a Maxwell fluid saturated anisotropic porous layer with internal heat source is studied using both linear and weak nonlinear stability analyses. The linear theory is being related to the normal mode method. The modified Darcy-Maxwell model is used for the momentum equation. The effects of various parameters on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the effects of the internal Rayleigh number, mechanical anisotropy parameter, and relaxation parameter have a destabilizing effect, while the thermal anisotropy parameter has a stabilizing effect on the stationary, oscillatory, and finite amplitude convection. A weak nonlinear stability analysis is based on truncated representation of Fourier series method and is employed to find the Nusselt number and Sherwood number. Further, the transient behavior of the Nusselt and Sherwood numbers is obtained by solving the finite amplitude equations using a numerical method. © 2013 by Begell House, Inc.