On the entropy of radiative heat transfer in engineering thermodynamics

The objective of this paper is to improve the understanding and also to simplify the calculation of the entropy transferred by thermal radiation (TR). Many thermodynamic texts incorrectly imply that the entropy flux of TR is the same as that for heat conduction, the heat flux divided by the local temperature (q/T). Also, fundamental equations, such as those derived from the Clausius inequality, express the entropy flux of TR in a q/T type form. However, for blackbody radiation (BR) emission a 4/3 factor is present and in this paper it is shown that the entropy flux of non-blackbody radiation (NBR) emission is even farther removed from q/T. The misuse of the heat conduction entropy flux equation for TR emission causes the irreversibility of a device to be underestimated whether the surface of the device is hot or cold relative to its surroundings. Further, it is shown that the reversible form of the Clausius expression applies when TR is involved yet the expression for irreversible processes does not apply. Finally, simple approximate expressions for the entropy of gray radiation (GR) are presented, as the exclusive use of numerical integration is laborious.