An analysis of an analogue solution applied to the heat conduction problem in a cartridge fuse

The general equation of heat conduction for a wire heated by an electric current and contained in an insulating cartridge filled with powder cannot be solved by analytical methods. In this paper, two approximate solutions are obtained; the first, obtained by an analytical method, assumes that radial heat loss from the wire is negligible; the second assumes that the parameters of the wire, filler, and cartridge remain constant at some average value, so that the equation can be solved by an analogue method. The analogue is described and the results obtained are checked against those calculated by assuming no radial heat loss, the circuit of the analogue being modified to eliminate the elements representing that loss. The magnitudes of the various errors associated with the analogue are determined as far as possible. The range of fusing current over which the analytical solution with no radial heat loss gives a good approximation to the correct temperature distribution is examined, and found to cover most of the region which is important in fuse operation. The temperature distributions obtained are used to determine the distribution of axial and radial losses along the length of a particular wire. From this the variation of losses with fusing current is obtained, and the range of current over which heat losses are negligible is determined.