Numerical study of turbulent natural convection in a cube having finite thickness heat-conducting walls

Three-dimensional transient natural convection in a cubic enclosure having finite thickness solid walls subject to opposing and horizontal temperature gradient has been investigated by a finite volume method. The turbulent flow considered into the volume is described mathematically by the 3D Reynolds averaged Navier–Stokes equations using the standard k–ε model with wall functions, including the energy equation. The velocity and temperature distributions were calculated at fixed Prandtl number, Pr = 0.7 and different values of the Rayleigh number, thermal conductivity ratio and dimensionless time. Three-dimensional velocity and temperature fields, temperature profiles at middle cross-sections and average Nusselt numbers have been presented. It has been found that an insertion of the third coordinate for the conjugate problem leads to a decrease in the average Nusselt number by 5.8 % in conditions of a stationary heat transfer mode.