NUMERICAL STUDY OF BENARD CONVECTION WITH TEMPERATURE-DEPENDENT VISCOSITY IN A POROUS CAVITY VIA LATTICE BOLTZMANN METHOD

In this paper, the heat transfer characteristics of a two-dimensional steady Benard convection flow with a temperature-dependent viscosity are studied numerically by the lattice Boltzmann method (LBM). The double-distribution model for LBM is proposed, one is to simulate incompressible flow in porous media and the other is to solve the volume averaged energy equation. The method is validated by comparing the numerical results with those existing literature. The effect of viscosity dependent on temperature is investigated. The average Nusselt numbers for the cases of exponential form of viscosity-temperature and effective Rayleigh number based on average temperature (T-ref = 0.5(T-h + T-c)) are compared. A new formula of reference temperature (T-ref = T-c + f(b)(T-h -T-c)) is proposed and the numerical results show that the average Nusselt numbers predicted by this method have higher precision than those obtained by average temperature.