Study On The Application Of Equivalence Principle In Heat Conduction Problems Of Three Dimensional Anisotropic Media

Recent years, with the rapid development of high speed integratedcircuit, many researchers have been dedicated to the heat transfer study onanisotropic media for practical uses by using numerical computationalmethods, but unfortunately there still are not enough researches on threedimensional anisotropic medium.This article presents the concept of equivalence principle to do thethermal analysis in three-dimensional IC`s design. Analytical solution toanisotropic model is given in an explicit way and the domain mappingtechnique is applied to derive the analytical solution to the problem. Basedon the heat conduction governing equation, a volume integral equation ispresented here of which the Green function for the equation is used toderive the integral solution by the establishment of equivalence heatconduction source model with the given three kinds of heat conductionboundary conditions. Concrete analytical solutions to the matrix elementsare presented in this paper, and the temperature distribution can beobtained by using the MoM codes. The idea of equivalence heat sourceborrowed from classical electromagnetic equivalence principle may enableit possible to do the electromagnetic analysis and electro-thermal analysistogether with the previous scattering codes by sharing the same meshedstructures, and this is also the meaning of this paper`s study. Some effortsof three-dimensional Green function technique are researched in this papertoo, but regarding its complexity of the singularity of Green function, theresearch work stuck in trouble. In the end of the paper, the validity of the proposed scheme is demonstrated by numerical examples where the resultsare compared with analytical solution, and the work done in this paper laysfoundation to do further research in the next stage.