The onset of double diffusive convection in a sparsely packed porous layer using a thermal non-equilibrium model

We examine the effect of local thermal non-equilibrium on double diffusive convection in a fluid-saturated sparsely packed porous layer heated from below and cooled from above, using both linear and nonlinear stability analyses. The Brinkman model is employed as the momentum equation. A two-field model that represents the fluid and solid phase temperature fields separately is used for the energy equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. It is found that a small inter-phase heat transfer coefficient has significant effect on the stability of the system. There is a competition between the processes of thermal and solute diffusion that causes the convection to set in through either oscillatory or finite amplitude mode rather than stationary. The effect of solute Rayleigh number, porosity modified conductivity ratio, Lewis number, ratio of diffusivities, Vadasz number and Darcy number on the stability of the system is investigated. The nonlinear theory based on the truncated representation of Fourier series method predicts the occurrence of subcritical instability in the form of finite amplitude motions. The effect of thermal non-equilibrium on heat and mass transfer is also brought out.