The equation of phonon radiative transfer (EPRT) was first proposed to be used a decade ago to provide the theoretical basis for thermal conductivity prediction of thin dielectric films. Heat conduction by phonons is similar to that of photons and can be analyzed as a radiative transfer  problem. To the extent that the EPRT is solved, it is exactly the same as the equation of radiative transfer (ERT); and, exact solutions for gray medium under radiative equilibrium between black walls at specified temperatures have been extensively studied . Although, several approximate methods of solution to the ERT are indeed available and are valid in solving the EPRT for single thin films, as the complexity of the film increases better numerical modeling techniques are much needed. In this regard, past studies have involved the finite-difference method for determination of temperature and to an extent the flux distributions, in order to predict the thermal conductivity of thin dielectric films. However, very little or no information and data is provided for the heat flux distributions. Due to the radiative equilibrium assumption imposed on thin films, it is known that the heat flux must be constant through the film. However, it is interesting to note that although the temperature distribution can be accurately obtained for a large range of film thicknesses with a very coarse mesh, the same appears to be not true for the flux distribution. In this paper we examine in detail and present numerical results using the method of exponential kernel approximation and finite-differences, as well as introduce for the first time the solution by use of finite-elements (which has not been done to date). This paper also reports deficiencies regarding the heat flux computation which have not been reported earlier.
|Original language||English (US)|
|State||Published - Dec 1 2002|
|Event||40th AIAA Aerospace Sciences Meeting and Exhibit 2002 - Reno, NV, United States|
Duration: Jan 14 2002 → Jan 17 2002
|Other||40th AIAA Aerospace Sciences Meeting and Exhibit 2002|
|Period||1/14/02 → 1/17/02|