Numerical computation of thermal and electrical constriction resistance in finite tube

This study presents an analysis of the coupled electrical and thermal constriction phenomena. The finite element method is used to calculate constriction resistance (thermal and electrical) of a conducting semi-infinite cylinder subjected to heat and current spot at the same time. Three fundamental cases are presented successively. The first case deals with the transient thermal constriction in a semi-infinite heat flux tube. The second one deals with the steady state electrical constriction in the same geometry. The third and most important case presents the numerical computation of constriction resistance when the semi-infinite tube is the site of volumetric heat generation resulting from Joule effect (electrical conduction). The preliminary studies are conducted to validate the numerical computation by their comparison to available analytical solutions in the literature. The transient thermal constriction resistance and the steady state electrical constriction resistance are presented and analyzed for different constriction ratio and coupling parameter. All presented examples use a uniform spatial distribution of the electrical density and the heat flux dissipated by the spot.