Electrical conductance between conductors with dissimilar temperature-dependent material properties

The method of Greenwood and Williamson is extended to give a general solution for the coupled nonlinear problem of steady-state electrical and thermal conduction across an interface between two conductors of dissimilar materials, for both of which the electrical resistivity and thermal conductivity are functions of temperature. The method presented is sufficiently general to cover all combinations of conductor geometry, material properties and boundary values provided that (i) the current enters and leaves the conductor through two equipotential isothermal surfaces, (ii) the remaining boundaries of the conductor are thermally and electrically insulated and (iii) the interface(s) between different materials would be equipotential surfaces in the corresponding linear problem. Under these restrictions, the problem can be decomposed into the solution of a pair of nonlinear algebraic equations involving the boundary values and the material properties, followed by a linear mapping of the resulting one-dimensional solution into the actual conductor geometry. Examples are given involving single and multiple contact areas between dissimilar half spaces.