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Numerical Study of the Effect of Viscous Heat Dissipation and Compression Work on Microscale Rayleigh–Bénard Convection Based on a Coupled Thermal Lattice Boltzmann Method

In the present work, an improved double-distribution-function thermal lattice Boltzmann method (LBM) is developed for analyzing the effect of viscous heat dissipation and compression work on microscale Rayleigh–Benard convection. In the proposed method a temperature change is introduced into the LB momentum equation in the form of a momentum source to realize the coupling between the momentum and the energy fields; two sets of evolution equations are established, one for the mass and momentum conservation and the other for the total energy that incorporates viscous heat dissipation and compression work. Numerical results show that the effect of viscous heat dissipation and compression work on the temperature distribution, flow distribution, and average Nusselt number at some Rayleigh numbers and aspect ratios is significant.