Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source

Abstract

Abstract We derived a semianalytical solution for the time-dependent temperature distribution in a three-layered laterally infinite scattering and absorbing slab illuminated by an obliquely incident collimated beam of light. The light propagation was modeled by the low-order $$P_1$$ P 1 and $$P_3$$ P 3 approximations to the radiative transfer equation with closed form expressions for eigenvalues and eigenvectors, yielding a quickly computable solution, while the heat conduction was modeled by the Fourier equation. The solution was compared to a numerical solution using a Monte Carlo simulation for the light propagation and an FEM method for the heat conduction. The results showed that using the $$P_3$$ P 3 solution for the light propagation offers a large advantage in accuracy with only a moderate increase in calculation time compared to the $$P_1$$ P 1 solution. Also, while the $$P_3$$ P 3 solution is not a very good approximation for the spatially resolved absorbance itself, its application as a source term for the heat conduction equation does yield a very good approximation for the time-dependent temperature.