Heat transfer in specularly reflecting tubes

Heat exchange inside a specularly reflecting tube is analysed. Expressions are obtained for heat transfer between cross-sections, between incremental wall annuli, between finite wall annuli, and combinations of the above. The expressions are related to the angle factor for opposed discs, but are infinite summations; they are easily evaluated, requiring some 20 emissivity terms. The basic disc-to-disc expression also represents the fraction of radiation leaving a disc that is still propagating at some distance along the tube, including reflection. Special case results are obtained for the radiant loss from double and single ended holes. For the practical application considered, it was found that conduction and radiation could be treated separately, permitting evaluation of a radiation loss factor for a specularly reflecting tube between two heat reservoirs