Multi relaxation time Lattice Boltzmann analysis of lid-driven rectangular cavity subject to various obstacle configurations

We have simulated two-dimensional laminar heat transfer in a lid-driven rectangular enclosure encapsulating heated obstacle filled with a regular viscous fluid. A square and rectangular-shaped heated blockage with different eccentric configurations is used in the physical domain to study mass and heat transfer in flow and temperature fields. We have applied D2Q9 and D2Q5 models of the Multi-Relaxation Time Lattice Boltzmann method to compute and simulate our results. The effect of dimensionless parameters like Grashof number (Gr = 10(3), 10(4), 10(5), 10(6)), Richardson number (Ri = 0.01, 0.1, 1, 5, 10, 50, 100), Prandtl number (Pr = 0.71, 1, 7) and of different eccentric placements of heated obstacle is studied on mixed convection heat transfer. The assigned value of the Reynolds number is 1000. We have also studied the impact of different aspect ratios (AR = 2, 0.5, 5, 0.2) of the enclosure and the sizes of heated obstacles on fluid flow. We have also computed the local Nusselt number (Nu(local)) average Nusselt number ((Nu) over bar) along the cold wall of the enclosure.