and hence, 



from a Body cooled by a Stream of Fluid. 609 



If the rod were of pure copper 



p = 1*56 x 10" 6 , and a = 0"004. 

 If, in addition, 

 a = 0"25 cm, V = 25 cm./sec. and C = 1600 amperes, 

 we readily find from (29) that is ll°-3 C. 



15. The Effect on the Convection of Heat from a Cylinder 

 of putting a Covering round it *. 



Let a be the radius of the cylinder which we suppose to 

 be maintained at a constant temperature #,, and let b be the 

 outer radius of the insulating covering. We shall suppose 

 that k { , the thermal conductivity of the insulating covering, 

 is large compared with the conductivity k of the cooling 

 liquid, so that we can suppose the outer surface of this cover- 

 ing to be isothermal. 



The equation to the steady flow of heat across the insulating 



covering is 



7s6 

 ^k 1 27rr^-= constant = H, 



*-*-£*** (30) 



where 6 Q is the temperature of the outer surface of the 

 covering. By (12), we find that 



n H sJtt H . b /Q1 v 



^ = 8V^vT + ^ log ^- ' • • (31) 



Let us now consider how the temperature $i of the wire 

 varies with the thickness b — a of the insulating covering 

 when H remains constant. We have 



Hence if a be less than 7r 3 ^ 1 2 /(645o-^V), we see that when 

 the thickness of the covering is very small 'dOij'db is negative, 

 and thus putting on a thin layer of insulating material will 

 have the effect of lowering the temperature of the wire. 

 When 6 = 7r 3 & 1 2 /(64s<7&V) the temperature of the wire has its 

 minimum value min which is given by 



XT r- m^ftlc i 



^-£{1 + 10*87^} • • .(32) 



* Cf. L. Roy, Soc. Int. Elect, Bull. p. 69 (1910). 

 Phil Mag. S. 6. Yol. 20. No. 118. Oct. 1910. 2 S 



