Internal Temperatures of Relay Windings 



By R. L. PEEK, JR. 



{Manuscript Received Aug. i8, igso) 



The steady state temperature distribution of a relay winding depends upon 

 the power supplied and upon the rates of heat removal at the inner and outer 

 surfaces. This is analyzed in terms of a more general form of the temperature 

 distribution relation discussed by Emmerich {Journal of Applied Fhysics)K 

 This analysis is used to determine empirical constants for the rates of heat 

 removal at the surfaces. Illustrative data are given for a stepping magnet. 



Introduction 



EMMERICH^ has developed an expression for the steady state tem- 

 perature distribution in a magnet coil when the heat flow is wholly 

 radial, and the temperatures of the inner and outer surfaces are the same. 

 A more general problem arises in the case of relays and other electromagnets 

 used in telephone switching apparatus. In these cases, the coil is mounted 

 on an iron core. Heat is withdrawn from the coil partly by conduction 

 through this metal path, and partly by radiation from the outer surface. 

 In consequence of this, the temperatures of the inner and outer surfaces 

 are in general different. 



In the relay and switching magnet problem, primary interest attaches 

 to the rate at which heat is withdrawn through these two paths, as their 

 combined effect determines the maximum temperature attained within 

 the coil. The analysis outlined below has been employed to determine the 

 division of heat between these two paths, and for the evaluation of em- 

 pirical constants of heat removal. These constants are used in estimating 

 the relation between the temperature of the winding and the power sup- 

 plied to it. 



Theory 



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 solu- 

 tion to Poisson's equation: 



dr' ^ r dr ^ K 



1 C. L. Emmerich, Steady-State Internal Temperature Rise in Magnet Coil Wind- 

 ings, Journal of Applied Physics, 21, 75, 1950. 



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