146 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 



from equation (4), using the values already found for r' , T and — . These 



A 



core and cover temperatures are included in Table I. 



It is of some interest to examine the observed values of apparent con- 

 ductivity K. As the temperature differences for the two lower input meas- 

 urements are small, the results for the other two cases are more accurate. 

 The latter give a value for K of approximately 0.8 X 10~^ calories per °C 

 per sec. per cm. In this form wound coil using No. 29 wire, the volume 

 occupied by the insulation is approximately 36 per cent. As the conductivity 

 of the copper is very large compared with that of the insulation, the con- 

 ductivity of the latter may be estimated as of the order of K multiplied by 

 the fraction of the volume occupied by the insulation. This gives an indicated 

 conductivity for the insulation of the order of 3 X 10~^ calories per °C per 

 sec. per cm. which is about the same as that of dry paper. 



0.4 



30 40 



50 60 70 80 90 100 110 120 130 140 



temperature in degrees centigrade 



Fig. 3 — Rates of heat removal from coil of 197 switch magnet. 



For engineering purposes the results of major interest are those for the 

 quantities of heat leaving the core and the cover. The results in Table I 

 show that the heat flow is about equally divided between these two paths. 

 As the core radius is about half the cover radius, the rate of heat flow to 

 the core per unit area of surface is about twice that leaving unit area of the 

 cover surface. 



The rates of heat removal per unit area through the inner and cover 

 surfaces are shown plotted against the corresponding temperatures in Fig. 

 3. It will be seen that the relation between the rate of heat removal per unit 

 area and temperature is approximately linear, and intersects the tempera- 

 ture axis at 38°C (100°F), which was the ambient temperature in these 

 tests. 



It follows that for engineering purposes the rate of heat removal per unit 

 area through either the inner or cover surface may be taken as proportional 

 to the difference between the surface and ambient temperatures. A similar 

 linear approximation has been found to apply for other relay and switch 

 coils when mounted under conditions representative of telephone apparatus. 

 Because of the multiplicity of mounting conditions and the complexity of 



