The temperature distribution in a flat conductive disk heated by a direct current

The problem of the steady-state temperature distribution in a flat conductive disk that is heated by a direct current was investigated. An analytical solution was obtained and limiting cases corresponding to different mechanisms of heat transfer were examined. It was determined that the peak value of the temperature and its distribution in such a disk are strongly governed by the ratio of the heat transfer coefficient to the coefficient of heat conductivity. High values of this ratio correspond to a highly non-uniform distribution of temperature (a hot spot). Low values correspond to a smooth decrease in temperature from the center to the boundaries of the conductor.