Formulas for calculating temperature distribution in transformer cores and other electric apparatus of rectangular cross section

THIS paper comprises solution of a very general problem in the mathematical theory of heat; application of it to effect formulas for the temperature distribution T, the maximum temperature Tm, and the average temperature Ta in transformer cores; and indication of its use with reference to other electric apparatus of rectangular cross section and of such general shape that the temperature distribution is essentially two dimensional. As theory indicates and experiment confirms that this condition is often fulfilled in practice, these formulas ought to be of considerable interest to designers of such equipment. For, commonly, the maximum electric loading of an electric device is determined by the permissible maximum or hot-spot temperature in it. Hence knowledge of this maximum temperature and of the temperature distribution in general is desired by the designer faced with making up new designs, improving operating performance of existing designs, or deciding upon maximum, yet safe, overload limits for apparatus already in service.