Simulation of mixed convection in inclined rectangular cavity by means of Lattice Boltzmann Methods and GPTBC boundary condition

Laminar mixed convective heat transfer in two-dimensional rectangular inclined driven cavity is studied numerically by means of a double population Thermal Lattice Boltzmann Method coupled with the counter-slip internal energy density boundary condition (General Purpose Thermal Boundary Condition GPTBC1, 2). The bottom wall is maintained at lower temperature than the top moving lid, side walls are adiabatic. Simulations are performed for Pr = 0.7 and Re = 200 and for three value of the Richardson number Ri = 0.1, 1, 10 encompassing the dominating forced convection, mixed convection, and dominating natural convection flow regimes; the effects of the inclination angle equal to 0°, 30°, 60°, 90° on fluid flow and heat transfer are studied in case of positive and negative moving lid velocity. The results are presented as velocity and temperature profiles, stream function contours and isotherms. As expected, results show that heat transfer rate is increased on increasing inclination angle, but this effect is significant for higher Richardson numbers, when buoyancy forces dominate the problem; for horizontal cavity, average Nusselt number decreases on increasing Richardson number because of the stratified field configuration. For dominating free convection regime (high Richardson number and high tilting angle) fluid velocity near top and bottom wall becomes grater than moving lid velocity. It is concluded that Lattice Boltzmann Method together with the GPBC can be effectively used to simulate mixed convection heat transfer problems.