Abstract A two-dimensional numerical analysis of combined heat transfer (transient natural convection, surface thermal radiation and conduction) in an air filled square enclosure having heat-conducting solid walls of finite thickness and a local heat source in conditions of convective heat exchange with an environment has been carried out. The governing equations formulated in terms of the dimensionless stream function, vorticity and temperature have been numerically solved using the finite difference method. Particular efforts have been focused on the effects of five types of influential factors such as the Rayleigh number 10 4 ≤ Ra ≤ 10 6 , the internal surface emissivity 0 ≤ ɛ k 1,2 ≤ 1000, the ratio of solid wall thickness to cavity spacing 0.1 ≤ l / L ≤ 0.3 and the dimensionless time 0 ≤ τ ≤ 100 on the fluid flow and heat transfer. Comprehensive Nusselt numbers data are presented as functions of the governing parameters mentioned above.