Scale analysis of combined thermal radiation and convection heat transfer

Simple order-of-magnitude relationships predicting heat transfer in limiting cases of combined convection and radiation problems in boundary layer flows are found using the method of scale analysis. Key nondimensional groups are developed that help identify the fundamental interactions between thermal radiation and convection modes of heat transfer for two cases of laminar two-dimensional convection heat transfer from a semi-infinite vertical wall. The first case is that of heat transfer from a gray wall with a specified heat flux to a surrounding non-participating medium and considers both forced and natural convection effects. The second case is that of heat transfer from a black wall with a specified temperature to an optically thick, gray, nonscattering medium and considers forced, natural, and mixed convection effects. The scale analysis results are presented in terms of the local Nusselt number. They include closed form expressions for order-of-magnitude estimates of the heat transfer rate, and dimensionless parameters that indicate the dominant mode of heat transfer and correlate experimental data well. The scale analysis results are validated against both experimental data and theoretical results.