()06 Dr. A. Russell on the Convection of Heat 



When the last term can be neglected this becomes 



H=13-51R,y/' w J-0 o .(22) 



Similarly when a — 31 we get 



V 7r V y ,V o (2n + 1) 3/J 



= 13-05 R^/^J' d», (23) 



and when a = 6/, 



H = 12'86Ry^ Vi o (24) 



If the temperature o£ the liquid entering the tube be zero 

 and the temperature of the liquid leaving it be practically 

 zero, except at points very close to the tube, we may deduce 

 a formula from Boussinesq's formula (15) for a strip as 

 follows : 



= 12-57^^0 (25) 



This result is in good agreement with the preceding three 

 formulae. 



11. Turbulent Flow. \ 



It must be carefully noticed that in the above problem we 

 have supposed that the particles of water flow in straight 

 lines parallel to the axis of the tube. It is known, however, 

 that in practice, when the velocity exceeds a certain critical 

 value, the flow becomes turbulent and the eddy currents 

 cause the particles of liquid to flow in sinuous paths. The 

 theory of the convection of heat in this case has been studied 

 by Osborne Reynolds *. He states that it is due to two 

 causes. 1. The natural internal diffusion when at rest. 

 2. The eddies caused by visible motion which mix the fluid 



* Proc. of the Lit. and Phil. Soc. of Manchester, vol. xiv. p. 9 (1874). 



IT 



Wl a 



7T 



