Numerical analysis of natural convection and surface thermal radiation in a cubical cavity having heat-conducting solid walls of finite thickness with a heat source located at the bottom of the cavity in conditions of convective heat exchange with an environment has been carried out. Mathematical study has been based on a numerical solution of the three-dimensional Boussinesq equations in the dimensionless variables such as vector potential functions, vorticity vector and temperature by finite difference method. Main attention was paid to the effects of the Rayleigh number 10(3) <= Ra <= 10(5), an emissivity of internal surfaces of the solid walls 0 <= epsilon < 1, a thermal conductivity ratio 1 <= k(1,2) <= 15 and a dimensionless time 0 <= tau <= 100 on the velocity and temperature fields. The effect scales of key parameters on the average Nusselt numbers have been determined. (C) 2014 Elsevier Ltd. All rights reserved.