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

Abstract

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.

Mass-balance and locality versus accuracy with the new boundary and interface-conjugate approaches in advection-diffusion lattice Boltzmann method

“…Other utility is that the method builds recursively the steady-state ADE with the non-uniform, global-mass conserving sources; the ADE is closed by an impermeable Neumann boundary or periodic interface, and its symbolic solutions are available 37,94 for benchmarking purpose. 38 The flow and the associated heat transport are often modeled with the so-called (multiple-relaxation-time thermal) MRT-TLBM, e.g., in a very recent work 78 using the BB and ABB straight-wall rules. However, the MRT-TLBM operates the d2q9 flow collision with only two distinctive relaxation rates: the symmetric one for the fluid viscosity and the anti-symmetric one for the second-order BB accuracy using the exact Poiseuille flow solution, 20,22 whereas the energy conservation equation is modeled with the d2q5 isotropic MRT-ADE.…”