Boundary conditions

Opaque and Diffuse Walls with Prescribed Temperature

In the article “Mathematical Formulation”, the boundary condition of the radiative transfer equation (RTE) for an opaque surface that emits and reflects diffusely was given (Modest, 2003):

(1)

In this equation I_w(r_w, s) is the radiation intensity leaving the boundary surface, I(r_w, s′) the radiation intensity in s′ direction arriving at that surface, I_b(r_w) = I_bw the blackbody radiation intensity at the temperature of the boundary surface, ε the surface emissivity, ρ the surface reflectivity, and n_f the outward unit vector normal to the surface, pointing from the surface to the medium. Equation (1) holds on a spectral basis. If the medium and the walls are grey, then the radiation ...