Onset of Darcy-Brinkman convection in a Maxwell fluid saturated anisotropic porous layer

Abstract

In the present study, the onset of Darcy-Brinkman double diffusive convection in a Maxwell fluid-saturated anisotropic porous layer is studied analytically using stability analysis. The linear stability analysis is based on normal technique. The modified Darcy-Brinkmam Maxwell model is used for the momentum equation. The Rayleigh number for stationary, oscillatory and finite amplitude convection is obtained analytically. The effect of the stress relaxation parameter, solute Rayleigh number, Darcy number, Darcy-Prandtl number, Lewis number, mechanical and thermal anisotropy parameters, and normal porosity parameter on the stationary, oscillatory and finite amplitude convection is shown graphically. The nonlinear theory is based on the truncated representation of the Fourier series method and is used to find the heat and mass transfer. The transient behavior of the Nusselt and Sherwood numbers is obtained by solving the finite amplitude equations using the Runge-Kutta method.