Effective Thermal Conductivity for Combined Radiation and Free Convection in an Optically Thick Heated Fluid Layer

The effective thermal conductivity for radiative heat transfer within an optically thick fluid layer undergoing high Rayleigh number convection is derived. This result is combined with available “pure” free-convection heat-transfer correlations to obtain closed-form analytical descriptions of the gross properties of a radiating fluid layer heated internally or from below. These simple solutions compare favorably with recent work in which the governing energy equation incorporating both turbulent heat transport and thermal radiation is solved numerically.