Flow regime shift and temperature model of the radiation-induced convection system under surface cooling

The natural convection flow in the translucent fluid layer subjected to solar radiation heating plays a crucial role in the daytime heat and mass transfer in water bodies and solar energy collection. In a radiation-induced convection system under surface cooling, there are two possible flow regimes: the triple-layer and single-layer regimes. The flow regimes have a great influence on the mixing of fluid. The fluid is thermally stratified in the triple-layer regime, which should be avoided in the volumetric solar collector. In this paper, the transition condition of the flow regime shift between the triple-layer regime and the well-mixed single-layer regime is deduced since the thicknesses of the top and bottom mixing layers can be predicted through energy conservation analysis. Furthermore, a scaling analysis is conducted to obtain the scaling laws for the temperature differences across the thermal boundary layers regarding the control parameters, i.e., the Rayleigh number Ra, the Prandtl number Pr, the non-dimensional surface cooling heat flux ϕ, and the non-dimensional fluid depth H. A series of direct numerical simulations with the parameters in the range of 107 ≤ Ra ≤ 1010, 0.7 ≤ Pr ≤ 70, 0 ≤ ϕ ≤ 0.7, and 0.5 ≤ H ≤ 3 are carried out to quantify the prefactor of scaling laws and also to validate the transition condition of the flow regime-shift. Then, a one-dimensional model can be developed to predict the temperature profile over the fluid depth with arbitrarily specified parameters. Thanks to the advantage of rapid and accurate prediction, this temperature model has a potential application for the design of the volumetric solar collector.