onset of darcy-brinkman reaction-convection in ananisotropic porous layer

The linear and nonlinear stability analysis of double diffusive reaction-convection in a sparsely packedanisotropic 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 momentumequation. 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 normalizedporosity 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.