from a Body cooled by a Stream of Fluid. 603 



Hence the average convection per square centimetre of 

 effective surface is considerably increased. 



8. Cylindrical Tube. 



Let the length of the tube be b, its temperature O and the 

 velocity of the liquid flowing through it V. 



In this case, when the steady state is attained, Poisson's 

 equation (1) gives us 



~dr 2 r ~dr c) t c 2 ~~ k ~§x 



As the mathematical formulae are complex we shall simplify 

 the work by neglecting the conduction of heat in the direc- 

 tion of the flow, in which case 



ve i-do_saV-dd 



It is easy to show that the equation * 



?/= - ■■ S~ r sin ~ — - — cos v — . (1/) 



J f o 2n + l 2a a v ' 



makes y, O from x= — l/2 to -f 1/2, from 1/2 to a — 1/2, — O 

 from a — 1/2 to a + 1/2, from a + 1/2 to a + 31/2, and so on 

 periodically. 



Let us now consider an infinitely long tube. Take the 

 origin at the centre of a portion of it of length I which is 

 maintained at temperature O . Let the contiguous portions 

 be of length a — I and be kept at zero temperature, and let 

 the portions beyond these be of length I and be at tempera- 

 ture — O , and so on. Then by taking a\l sufficiently great 

 we can ensure that the liquid entering the hot portion of the 

 tube is practically at zero temperature. 



Writing equation (16) in the form 



yd , IS*, (2n + l)m 2 do , m 



Br* r B~r ~ (2n + l)(7r/a)^' * * * { * } 



Russell, ' Alternating Currents/ vol. ii. p. 388. 



