Internal Temperatures of Relay Windings

1 As in Reference (1), it is assumed that there is no heat loss through the ends of the coil, so that the temperature gradient is wholly radial, and that the actually heterogeneous coil structure can be treated as homogeneous. Then if Q is the heat supplied per unit volume per unit time, and K is the thermal conductivity, the radial distribution of temperature is the solution to Poisson's equation: £ + i f + | = o , drr dr A (i) 1 C. L. Emmerich, Steady-State Internal Temperature Rise in Magnet Coil Windings, Journal of Applied Physics, 21, 75, 1950. 141 142 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 where r is the co-ordinate of a surface of temperature T. The general solution to equation (1) is given by the equation: T = A + B ] o g r (2)