Geometrical effects in a Joule heating problem from miniature soldering

The soldering of small, delicate electronic devices by means of a blade thermode (a small, thin, rectangular or -shaped soldering iron) requires the lower side of the thermode to have a uniform temperature distribution. This is not easily obtained: during start-up the corners tend to be too hot, and too cold in the stationary phase. In the present study the various aspects that determine the heat flow and the temperature distribution are analysed, both for the dynamic and the stationary cases. For a temperature-independent (linear) material, approximate solutions are obtained for the dynamic problem. For the stationary problem, an exact solution is utilized that includes temperature-dependent (nonlinear) material. Practical design rules based on these solutions are proposed. The analysis compares very well with a numerical finite-element simulation.