Radiative heat transfer in a heat generating and turbulently convecting fluid layer

Abstract

The coupled problem of radiative transport and turbulent natural convection in a volumetrically heated, horizontal gray fluid medium, bounded from above by a rigid, isothermal wall and below by a rigid, adiabatic wall, is investigated analytically. An approximate method based upon the boundary layer approach is employed to obtain the dependence of heat transfer at the upper wall on the principal parameters of the problem, which, for moderate Prandtl number, are the Rayleigh number, Ra, the optical thickness, κL, and the conduction-radiation coupling parameter, N. Also obtained in this study is the behavior of the thermal boundary layer at the upper wall. At large κL, the contribution of thermal radiation to heat transfer in the layer is found to be negligible for N > 10, moderate for N ∼ 1, and overwhelming for N < 0.1. However, at small kL, thermal radiation is found to be important only for N < 0.01. While a higher level of turbulence results in a thinner boundary layer, a larger effect of radiation is found to result in a thicker one. Thus, in the presence of strong thermal radiation, a much larger value of Ra is required for the boundary layer approach to remain valid. Under severe radiation conditions, no boundary layer flow regime is found to exist even at very high Rayleigh numbers. Accordingly, the ranges of applicability of the present results are determined and the approximate method justified. In particular, the validity of the present analysis is tested in three limiting cases, i.e. those of κL /ar ∞, N /a ∞, and Ra /ar ∞, and is further confirmed by comparison with the numerical solution.