Effects of specular reflection on radiative heat transfer in an absorbing,emitting, and anisotropically-scattering medium

The effect of specular reflection in a one-dimensional, absorbing, emitting, and anisotropically-scattering medium is analyzed. The mathematical formulation is shown to involve the function F_n(x)= ∝¹_o(e^-x/μ/1 - ?₁?^-2e_2L/μ)υ^n-2 dμ, which can be readily evaluated as a fast-coverging, infinite series of exponential integral functions. Numerical solutions to the resulting integral equations are generated by the method of point allocation.Physically, the radiative energy within a participating medium bounded by specularly reflective surfaces is observed to experience more multiple reflection than the corresponding diffuse reflection case. This leads to some differences between the two cases in the heat transfer and temperature profile results. These differences, however, are generally quite minor for the considered one-dimensional planar system.