290 Passage of Heat beticeen Metal Surfaces and Liquids. 



Or, if ds = the surface, and dli the heat transmitted, that 

 dR = k.ds.v m (T Q -t)(l + <zTo)(i + f3t), 



^vvhere m has a value little less than unity, and varies from 0'825 to 

 0*855 in these experiments. 



It is also shown that these results are in accordance with Professor 

 Osborne Reynold's theory of the convection of heat from a hot 

 surface to cold water flowing over it, this theory being that the 

 motion of heat from the surface of the pipe follows the same laws as 

 the motion of momentum, so that from Professor Reynold's equation 

 for the loss of pressure in a pipe,* we may write down for the slope 

 of temperature in the pipe : — 



dx~ A D ' (2rf-» W (i ° l) 



where P = (1+0-0336T+0-000221T 2 )" 1 ' 



D — weight of unit volume of water, 



w — velocity of water along the axis of the pipe, 



r = radius of pipe, 



JB and A constants depending on the nature of the pipe ; 



and where k' will depend on the viscosity of the water at the 

 bounding surface, through which the heat is transmitted by 

 .conductivity. 



The experiments show that k' may be written : — 



k' = &(l + aT )(l + /30 



where a = 0-004, y3 = O'Ol ; 



■so that for a pipe of length L, we have from equation (1) 



^log^4 1 (2r) 3 -» 

 • " P*- w (l + «T )(l+/3^) 



Experiments have been made on three pipes of diameters 1'39, 

 1*07, and 0'736 cm., and lengths 47, 46, and 44*5 cm., respectively, 

 at velocities varying from 28 to 394 cm. per second, and with ranges 

 of temperature of from 30° to 3°. 



The values of k are very consistent for all the experiments made, 

 the extreme variations differing by not more than 4 per cent, for any 

 one pipe. 



The above case is for heat transmitted from the metal surface to 

 the water. When the flow of heat is from the water to the surface, 



(i) 



(2) 



