Transient couple heat transfer in an absorbing rectangular medium with one semitransparent diffuse boundary

This paper studies 2-D transient coupled radiative and conductive heat transfer in an absorbing non-scattering rectangular medium. The medium have one diffuse semitransparent boundary, and the other three boundaries are black. The reflectivity of the diffuse semitransparent boundary is determined by integrating the reflected energy over the whole hemispherical space according to the Fresnel's reflective law and Snell's refractive law based on assuming each bit of the rough surface to be optically smooth.