Heat Conduction as Eigenvalue Problem

The time dependent solution of the heat conduction equation is represented by expandingTin terms of eigenfunctions and eigenvalues (= inverse time constants). Once these are known, the time evolution ofTcan be computed readily for arbitrary heat sources. A method is presented for computing eigenfunctions and eigenvalues for a multilayer structure, where all layers have the same lateral extension and differ vertically in thickness and material parameters. Those structures are encountered in modeling IC packages and multichip modules in power electronic applications. Examples will be given for the temperature evolution calculated for the time dependent heat distribution in power converter applications. However, computation time and storage demands will be high if high spatial and temporal resolution for the temperature field is needed. Using effective time constants and functions the numerical effort can be reduced considerably