A note on the thermistor problem in two space dimensions

We consider two coupled nonlinear p.d.e’s describing heat and current flow in a thermistor. For certain boundary conditions these equations may be reduced to one nonlinear o.d.e. and Laplace’s equation, as noted in [1]. We give a geometrical interpretation of this reduction in two space dimensions in terms of a conformal map from the thermistor onto a rectangle.