Linear and Weakly Nonlinear Stability Analyses of Two-Dimensional, Steady Brinkman–Bénard Convection Using Local Thermal Non-equilibrium Model

Abstract

Effect of local thermal non-equilibrium (LTNE) on onset of Brinkman–Benard convection and on heat transport is investigated. Rigid–rigid and free–free, isothermal boundaries are considered for investigation. The assumption of LTNE leads to an ‘advanced onset’ situation compared to that predicted by the local thermal equilibrium (LTE) assumption. This results in the ‘enhanced heat transport’ situation in the problem. Asymptotic analysis for small and large values of inter-phase heat transfer coefficient is also carried out on critical Rayleigh number, critical wave number and Nusselt number. In respect of boundary influences on onset and heat transport, it is found that classical results hold even under the LTNE assumption. The other parameters’ influences on onset and heat transport are qualitatively similar in LTNE and LTE cases.