Semi-analytical solution of equation for phonon radiative transport pertinent to thin films

Thermal energy transfer in thin films is governed by the phonon transport, and the Fourier heating law fails to predict correct temperature rise because of the assumption of infinite speed of the heat wave. The equation of phonon radiative transport predicts accurately thermal characteristics of the thin film when subjected to a thermal disturbance. Because the numerical solution of the transient equation phonon transport is very expensive in terms of computational efforts and run time, the analytical solution of the equation becomes fruitful. In the present study, a semi-analytical solution of transient equation for phonon radiative transport across the thin film is presented. In the analysis, the governing transport equation is transformed into two-dimensional linear mixed Fredholm-Volterratype integral equation, and the solution is obtained through Liouville-Neumann series. The results obtained from the semi-analytical solution are comparedtothatofthe numerical predictions, and findings revealed that both results are in good agreement. The semi-analytical solution reduces the computational run time by 30 fold shorter. Reducing the film thickness increases the temperature jump at the high-temperature edge of the film, which is more pronounced during the early heating period.