Correlations for the transport characteristics of Radiative Rayleigh-Bénard convection in optically thick media

Due to stable chemical properties and large latent heat of phase change, molten salt has been widely used as energy storage material, especially in the technology of solar power. For example, the salt is heated to the molten state by the sunlight in concentrated solar power and the natural convection plays an important role in this process. Accounting to the high working temperature, it is obvious that thermal radiation shows extraordinary effects on the molten salt flow and heat transport. In this paper, we focus on the influence of thermal radiation on the classical Rayleigh-Bénard (RB) convection, a paradigmatic representation of thermal convection in which the fluid is heated from below and cooled from above. The theoretical derivation has been conducted by modifying the Grossmann-Lohse theory. Because of the particularity of thermal radiation transfer in the form of electromagnetic waves, the optically thick limit approximation, i.e., Rosseland diffusion approximation has been used. Based on the turbulent dissipation theory and the relative contribution of bulk and boundary layers to dissipation, four main regimes can be obtained and one of them has been investigated in this paper. One can easily find that, although thermal radiation stabilizes flow, it can significantly enhance the heat transfer efficiency. Besides, by comparing the results between DNS and theoretical analysis, the summarized scaling law can effectively predict the Nu of radiative Rayleigh-Bénard convection, and the deviation is about 9%.