The onset of Lapwood–Brinkman convection using a thermal non-equilibrium model

The stability of a horizontal fluid saturated sparsely packed porous layer heated from below and cooled form above when the solid and fluid phases are not in local thermal equilibrium is examined analytically. The Lapwood–Brinkman model is used for the momentum equation and a two-field model is used for energy equation each representing the solid and fluid phases separately. Although the inertia term is included in the general formulation, it does not affect the stability condition since the basic state is motionless. The linear stability theory is employed to obtain the condition for the onset of convection. The effect of thermal non-equilibrium on the onset of convection is discussed. It is shown that the results of Darcy model for the non-equilibrium case can be recovered in the limit as Darcy number Da → 0. Asymptotic analysis for both small and large values of the inter phase heat transfer coefficient H is also presented. An excellent agreement is found between the exact solutions and asymptotic solutions when H is very small.