Heat transfer of heat-releasing fluid in the top portion of a closed volume

The method of analytic estimates is used to determine the characteristics of steady-state free-convection heat transfer of a fluid with internal heat sources in the top part of a closed volume with different conditions of heat removal on the top horizontal boundary at the Prandtl number value on the order of unity. It is demonstrated that, in the case of adiabatic condition on the top boundary of the volume, the maximal heat flux $q_{\mathrm{max}}$ attained in the region of intersection of the top horizontal and vertical boundaries depends only on the maximal temperature in the volume $T_{\mathrm{max}}$ and on the thermal characteristics of the fluid. The correction to the bulk temperature (outside of the boundary layers) $\delta T_b\sim z^{1/4}$, which is a function of the vertical coordinate $z$, significantly prevails over perturbations in the horizontal section. When the turbulent Rayleigh-Benard (RB) convection arises, the heat removal through the top boundary is defined only by the energy release in the RB-layer. Given a fixed power of heat release $\mathcal{Q}$, the RB-layer thickness increases by the linear law $h=q/\mathcal{Q}$ with increasing heat flux q through the top horizontal boundary.