Transient radiative heat transfer through thin films using Laguerre-Galerkin method

Heat transfer through a semiconductor or dielectric thin film is investigated by using the single relaxation time approximation to the Boltzmann equation. The radiance is expanded in terms of the Laguerre polynomial with time as argument, and the ensuing time-independent equation is solved with the aid of the Galerkin technique. Films of different thicknesses, ranging from 0.01 to 10 mean free paths, have been considered. The results, calculated for different time, ranging from 0.01 to 10 relaxation times, are presented in the forms of the following quantities (in dimensionless units): the temperature (normalized dimensionless internal energy), the heat flux, and the irradiance. Differences between the results obtained by this approach and those found by solving partial differential equations of heat conduction (Fourier's Law and Cattaneo's equation) are noted.