Surface radiation influence on the regimes of conjugate natural convection in an enclosure with local energy source

A numerical analysis of the unsteady regimes of the natural convection and thermal radiation in a square enclosure with heat-conducting walls has been carried out in the presence of a heat source of finite sizes located in the base zone under the conditions of convective exchange with the ambient medium. The mathematical model formulated in the dimensionless variables “stream function — vorticity — temperature” has been implemented numerically by a finite difference method. The influence of the reduced emissivity of internal surfaces of bounding walls on the local characteristics (the streamlines and temperature fields) and on the integral complex (the mean Nusselt number on typical boundaries) has been analyzed in detail for 0 ≤ ? < 1, the location of the heat source 0.1 ≤ l/L ≤ 0.4, and its length 0.2 ≤ l _hs /L ≤ 0.6 for Ra = 10⁶, Pr = 0.7. The approximation relations have been derived for the mean convective and radiation Nusselt numbers depending on the reduced emissivity of the internal surfaces of bounding walls and the energy source location relative to vertical walls.