46 PRINCIPLES OF ELECTRICAL DESIGN 



as the degrees Centigrade rise in temperature when the loss in 

 watts is equal to the cooling surface in square inches; and A is 

 the actual cooling surface expressed in square inches. The area 

 of this cooling surface will be reckoned as the sum of the outside 

 and inside perimeters multiplied by the length of the coil, plus 

 the area of both ends of the coil. The temperature rise is 

 found to differ very little whether the coil is surrounded entirely 

 by air, or provided with an iron core, and for this reason the 

 writer prefers to consider the total external area of the coil as 

 the cooling surface. 1 



The heating coefficient k is not a constant, even for a given size 

 and shape of magnet. It is a function of the difference of 

 temperature between the coil surface and the surrounding 

 medium; it also depends upon the material of the spools or 

 bobbins, on the insulating varnish and wrappings (if any), and 

 other details of construction. Assuming a surface temperature 

 rise of about 40 C. and open type coils that is to say, coils 

 with ends and outside surface exposed to the air finished with 

 a coat or two of varnish over the cotton-covered wire, the coeffi- 

 cient k might lie between 160 and 200, with an average value of 

 180. With a temperature rise of only 20C. the average value 

 of k should be taken as 190. 



In the case of iron-clad coils such as those found in many 

 designs of lifting magnets and magnetic clutches, the final 

 internal temperature will depend largely on the shape and thick- 

 ness of the surrounding iron, and on the total radiating surface; 

 but, for approximate calculations, the same coefficient may be 

 used as for the open coils, bearing in mind that, in all cases, 

 the temperature rise T of formula (30) is that of the outside layer 

 of wire, and the area A is that of the total external surface of the 

 copper coil. 



12. Intermittent Heating. Without attempting to discuss 

 exhaustively the effects of intermittent service, the two extreme 

 cases may be considered : (a) the apparatus is alternately carrying 

 the full current, and carrying no current, during short periods of 

 time extending over many hours, so that the total cooling surface 

 is the factor of importance; and (6), the apparatus is in use at 



1 This is the recommendation of MR. G. A. LISTER in his excellent paper 

 published in the British Journal Inst. E. E., vol. 38, p. 402, to which the 

 reader is referred if he wishes to pursue further the subject of magnet- 

 coil heating. 



