A numerical study of two-dimensional transient natural convection in a rectangular enclosure having finite thickness heat-conducting walls with a heat source of constant heat transfer rate located on the inner side of the left wall in conditions of convection-radiation heat exchange with an environment on one of the external boundaries has been performed. Mathematical simulation has been carried out in terms of the dimensionless variables such as stream function - vorticity -temperature. Stream function, vorticity and energy equations have been solved by finite difference numerical method. The relevant governing parameters were: the Grashof number from 10(6) to 10(8), the Prandtl number, Pr = 0.7 and the conductivity ratio. Detailed results including streamlines and temperature profiles have been obtained. (C) 2010 Elsevier Ltd. All rights reserved.