Numerical simulation of turbulent natural convection in a rectangular enclosure having finite thickness walls

Turbulent natural convection in a rectangular enclosure having finite thickness heat-conducting walls at local heating at the bottom of the cavity provided that convective-radiative heat exchange with an environment on one of the external borders has been numerically studied. Mathematical simulation has been carried out in terms of the dimensionless Reynolds averaged Navier-Stokes (RANS) equations in stream function-vorticity formulations. The formulation comprises the standard two equation k-ε turbulence model with wall functions, along with the Boussinesq approximation, for the flow and heat transfer. The special attention was paid to the effects of the Grashof number 108 ⩽ Gr < 1010, the transient factor 0 < τ < 1000 and the thermal conductivity ratio k2,1 = 5.7 × 10−4, 6.8 × 10−5 both on local and on integral problem parameters. Detailed results including stream lines, temperature profiles and correlation for the average Nusselt number in terms of Grashof number have been obtained.