The radiative transfer relations are rather complex integral equations, so it is useful to consider approximate techniques that might be incorporated more conveniently into computer design programs. One approximate technique is the two-flux method. It has the form of simultaneous differential equations and is relatively easy to solve for layers that are not optically dense. For dense layers a radiative diffusion method can be used that has the form of a single differential equation. The approximate solutions were compared with numerical solutions of the radiative transfer equations.
Radiative penetration is reduced in the dense substrate, and heat conduction is more dominating.
The coating has two spectral absorption bands. Both external boundaries are being cooled by convection. The three sets of curves are for various levels of radiation flux incident on the hot side. Temperature distributions by the two-flux and diffusion method are in excellent agreement with the numerical solutions. J. Heat Mass Trans.