Use of Contact Resistance Algorithm to Implement Jump Boundary Conditions for the Radiation Diffusion Approximation

Thermal conduction codes can be used as solvers for the diffusion approximation for radiation heat transfer. Energy fluxes and temperature distributions that result from thermal radiation in an optically-thick participating medium can be estimated. Allowing dependence on temperatures from either side of the interface, a contact resistance algorithm can be used to implement “jump” (or slip) boundary conditions appropriate for the diffusion approximation in solving the radiation transfer equation. For steady, pure radiation (no conduction) systems analytical expressions exist to specify the temperature in the radiating medium at the wall as a function of the wall temperature, wall emissivity, and extinction coefficient. Radiation and conduction solutions for gray, absorbing/emitting and conducting media bound by diffuse surfaces for the simple case of the steady planar layer are considered. Reference solutions are developed by detailed zone-methods solving the coupled differential forms of both the radiation and conduction heat transfer equations. From the reference solutions, empirical relations are developed for surface resistance as functions of the local wall and adjacent media temperatures, the wall emissivity, the absorptivity, and the thermal conductivity of the medium. Performance of the approximate solution is compared to the reference solutions.