INTERNAL TEMPERATURES OF RELAY WINDINGS 147 



conducting and radiating paths by which heat is removed, it is difficult to 

 estabUsh a relationship of the type shown in Fig. 3 by analysis of the paths 

 of heat removal. For given mounting conditions, however, this relationship 

 can be determined empirically by the procedure outlined above and used to 

 estimate the heat removal from a given coil mounted under conditions for 

 which such measurements have been made. 



The rate of heat removal is thus measured by the slopes of the heat flow 

 vs. temperature curves, which may be designated ki and ^2. Thus ki is the 

 time rate of heat flow to the core per square centimeter of surface per °C 

 difference between the inner coil surface and the ambient temperatures, 

 while ^2 is the corresponding coefficient for the cover surface. For the case 

 shown in Fig. 3, ki = 0.0045 watts per cm^ per °C, and ^2 = 0.0020 watts 

 per cm^ per °C. This observed value of ^2 is characteristic of the cover sur- 

 faces of coils mounted as in telephone apparatus, where the heat removal is 

 primarily by radiation to surfaces at or near the ambient temperature. 

 While the value of h observed for this case is representative of that applying 

 to inner coil surfaces, the values of h for such surfaces vary widely, and are 

 particularly sensitive to variations in the clearance between the metallic 

 core and the interior surface of the coil. 



Prediction of Coil Temperatures 

 If values for the heat removal coefficients are known, the distribution of 

 temperature within the coil for a given steady state power input may be 

 determined from equation (4). The power input and the coil volume deter- 

 mine the rate of heat supply per unit volume Q. The rate of heat flow to the 

 core per unit length of coil is therefore tt (/^ - rl) Q. The core area per unit 

 length through which this heat passes is 2 irri. So from the empirical linear 

 relation between the heat removed and the surface and ambient tempera- 

 tures : 



r, - To = '^^^j^, (8a) 



where To is the known ambient temperature. Similarly, for the cover 

 surface : 



Zk2r2 

 By substituting these expressions for Ti and T2 for T in equation (4), 

 with r taken as n in one case and r2 in the other, there is obtained an ex- 

 pression for / which reduces to the following equation: 



2 2 

 ri rp , ^2 - ri 



n _ ki h 2K (Q) 



^ J^ I 1 . 1 1 !?' 



