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-epsilon 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 10(8) <= Gr < 10(10) the transient factor 0 < tau < 1000 and the thermal conductivity ratio k(2,1) = 5.7 x 10(-4), 6.8 x 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. (C) 2009 Elsevier Ltd. All rights reserved.