Transport phenomena in a differentially heated lid-driven cavity: A study using multi-relaxation-time thermal lattice Boltzmann modeling

Physics of Fluids, Volume 32, Issue 9, September 2020. In this study, investigation of mixed convection phenomena in a lid driven square cavity with heated side walls is carried out. The left and right walls are maintained at different constant temperatures, while the upper and bottom walls are thermally insulated. The left wall temperature is higher than the cavity fluid temperature, and the right wall is maintained at the initial fluid temperature. Transport phenomena inside the cavity within a wide parametric range are investigated. The parameters include the Reynolds number (10 ≤ Re ≤ 1000), the Prandtl number (0.01 ≤ Pr ≤ 50), and the Richardson number (0.01 ≤ Ri ≤ 10). It was observed that the flow is induced in the cavity by a shear force resulting from the motion of the upper lid combined with the buoyancy force due to the temperature difference in the cavity. The effects of Re, Pr, and Ri within the cavity were observed simultaneously. The numerical simulations were carried out using the thermal lattice Boltzmann method with multi-relaxation time collision model. The present investigation generates a benchmark dataset for the average Nusselt number (Nuavg) with varying Re, Pr, and Ri within the laminar flow regime. Results show that heat transfer from the side wall is not affected significantly by change in Pr in low levels of Ri, but as Ri increases, average Nu increases significantly. It is also observed that the average value of Nu increases with Pr and Re at a particular value of Ri. However, at a given Ri, for Re above 500 and Pr over 10, the Nu value remains unaffected by change in Re and Pr, which defines the limiting heat transfer in the laminar regime.