Joulean Heating of an Infinite Rectangular Rod With Orthotropic Thermal Properties

Abstract

The formal solution previously obtained for the transient thermal response of an infinite rectangular rod, with orthotropic thermal conductivity and linear boundary conditions, to Joulean heating under a constant current condition is extended to include the constant voltage case under certain restrictive conditions. The solution is a rapidly converging doubly infinite series whose leading term is an accurate approximation for the thermal response. Graphical aids are presented which allow the designer of such apparatus as solenoids and various coils to quickly obtain estimates of the temperature distribution, the heat flow from the boundaries, the thermal time constant, and the location of the peak temperature. It is found that in certain cases the theory for constant current case predicts no steady-state condition. This condition is unrealistic because it requires an infinite voltage to provide the constant current. The theory predicts that the constant voltage case is always bounded.