Model for thermal convection with uniform volumetric energy sources

A theoretical model is derived to predict both the heat fluxes at the upper and lower horizontal surfaces of an internally heated (IH) convection cell by extending the well-known [5] theory. The approach of [1] is generalized for a fluid heated internally and uniformly, confined between top and bottom plates of equal temperature. For each plate, a Nusselt number is defined and an analytical formula is given to predict its variations with the Rayleigh and Prandtl numbers. The turbulent flow produced in the upper half of the IH convection cell is very similar to that observed in standard Rayleigh-Benard (RB) convection. On the contrary, the lower plate is swept by the large scale flow that circulates through the entire cell. The corresponding boundary layer is therefore modelled by a laminar boundary layer of the Blasius type. These predictions are confirmed by previous experimental and numerical results.