Comparative Analysis of the Entropy of Radiative Heat Transfer and Heat Conduction

Abstract

Many thermodynamic texts incorrectly imply that the entropy flux of thermal radiation (TR) is the same as that for heat conduction, the heat flux divided by the local temperature (q/T). However, for blackbody radiation (BR) emission a 4/3 factor occurs. BR represents the maximum entropy for all radiation with the same emission temperature, as well as all radiation with the same energy radiance. However, using Planck’s formulas it is shown that BR emission has the lowest entropy-to-energy ratio, and thus the lowest entropy factor, for all radiation with the same emission temperature or radiation with an enclosed energy spectrum. In practice, analysis of radiative transfer includes incident, reflected and emitted fluxes. Case-specific integration, based on Planck’s entropy formula, can be used to determine the net radiative entropy flux. However, this net entropy flux can be put in the form n(q/T), where n is a coefficient unique to the radiative fluxes involved. This allows the net entropy flux to be easily calculated given the energy flux and the temperature of the opaque absorbing material. This entropy coefficient can vary greatly, taking on values less than unity, and values greater than unity. This implies that the misuse of the heat conduction entropy flux expression can vary from overestimating (n < 1) to underestimating (n > 1) the net radiative entropy flux. Graphical tools and simplified approximate expressions are presented that allow the entropy coefficient n to be quickly determined in certain general scenarios of radiative transfer encountered in practice.

Keywords

• entropy, second law, radiation, heat transfer, conduction, blackbody, graybody