The minimal set of parameters for exact dynamic thermal models

A thermal model is presented that follows from the heat conduction equation and is exact under the conditions that the mass density, the specific heat and the thermal conductivity in the set-up do not depend on temperature and that the individual thermal contact areas of the models have uniform temperature distribution. The network models allow for the determination of both: the transient temperatures at specified thermal contacts and the associated heat flows at the contact areas. Compared to previous models, the network of the reduced compact model consists of one-port impedance links between external terminals and one reference node, which is explicitly added. When m is the number of thermal device contact areas and p the number of heat sources, the model is characterized by (m + p +1) (m + p ) / 2 one-port impedances with its associated R, C, L elements. A methodology is investigated for the determination of the network parameters, which poses in many cases a highly ill conditioned problem, which may render the results useless. Alternative methods are suggested.