from a Body cooled by a Stream of Fluid. 599 



The flux of heat emitted per unit length of the cylinder 



per second ia 5} — Z;(^-— ) "ds 2 , where (=r— ) is the thermal 



\oVo V O*i/o 



gradient at the surface of the cylinder where a. — 0. By 



means of (3) this may be written in the form % — k(^- ) 0/3. 

 But from (9) we have 



where we have written ?? 2 for cVot t /(2k% 2 '). 



Hence the total flux H of heat per second from unit length 

 of the cylinder is given by 



H = - i^ -- P" f °/'(/9 + r) 3/3 B*; 



' Ji3 J 



«4*/^Yf {f(^ + ^)-f(fi l + r)}'dv- (10) 



7f 



«. 



Now f(@ l -f rf) is zero from 77 almost equal to nothing up 

 to 7] equal to infinity; and f(/3 + r) 2 ) is O from rj equal to 

 zero up to 77 equal to VA~A), and practically vanishes for 

 all greater values of 77. Hence 



fckTC v ^-&> 



v 



** y/0i-M„ .... (11 



where 5 is the specific heat, and a is the density of the 

 liquid. 



This result, which is true for two-dimensional flow round 

 a solid of any shape immersed in a stream of liquid, agrees 

 with that given by Boussinesq. It shows that the loss of 

 heat from the solid is proportional to the difference of 

 temperature between the solid and the liquid. Newton's 

 law is thus verified when the cooling fluid is a liquid. It 

 will be remembered that Newton enunciated his law with 

 reference to the convection and not the radiation of heat. 

 He considered the case of a block of iron being cooled in a 



