Relations for local radiative heat transfer between rectangular boundaries of an absorbing-emitting medium

An analytical solution was obtained by Siegel (1991, 1992) for local boundary heat fluxes by a radiating medium at uniform temperature in a 2D rectangular region. It is shown here that, after local fluxes from the medium to the walls have been evaluated, it is very easy to compute local fluxes arriving from the adjacent and opposite walls. This extends the previous analysis and provides convenient relations to include radiation from a black boundary, each side of the rectangle being at a different uniform temperature. The final expressions are helpful in performing spectral calculations that must be made for many spectral bands.