594: Dr. A. Uussell on the Convection of Heat 



expect that the loss of heat per square centimetre of the 

 surface of a wire would be greater the smaller the diameter 

 of the wire. This is in agreement with the experiments of 

 Cardani *, Ayrton and Kilgour f, Sala J, and Kennelly §. 



We also show later on that in certain cases the fusing- 

 current of wires when immersed in a stream of liquid varies 

 as the T25th power of the radius of the wire. This agrees 

 with experimental results obtained by Schwartz and James || 

 for wires in air. 



The further assumptions are made that the thermal con- 

 ductivity of the liquid is very small and that the variation in 

 its density does not appreciably alter the shape of the 

 trajectories of the liquid particles in the immediate neigh- 

 bourhood of the solid from the shape they have during 

 isothermal flow. The former assumption is true in most 

 practical cases, and the latter is permissible when the 

 velocity of the current is appreciable and no eddies are 

 formed. 



It is interesting to remember that in Hele-Shaw'slI method 

 of reproducing the stream-lines of a perfect fluid flowing past 

 an obstacle in two dimensions, a thin film of viscous liquid, 

 glycerine for example, is employed, and results of high 

 accuracy are obtained. Even for a thick film, the shape of 

 the lines does not alter much from the ideal case, and hence 

 the assumption that the stream-lines coincide with the stream- 

 lines of a perfect fluid is not a serious one. 



The surface of the solid being cooled by the current is 

 supposed to be isothermal, and the liquid in immediate 

 contact with it at any instant is supposed to have the same 

 temperature as the solid. These two assumptions are quite 

 legitimate. 



4. Flow in Two Dimensions. 



Making the above assumptions we shall now obtain the 

 differential equation which determines the temperature at 

 any point of the liquid, once the steady state has been 

 established. 



Let us suppose that the velocity of the liquid at a great 

 distance from the solid being cooled is V. In our problem 



* Nuov. Cim. xxx. p. 33 (1891). 

 t Phil. Trans, clxxxiii. part i. p. 371 (1892). 

 % Nuov. Cim. iv. p. 81 (1890;. § L. c. ante. 



j| Jom-n. Inst. Elect, Engin. xxxv. p. 364 (1905). 

 f Brit. Assoc' Kep'ort,' .1898. In this report Sir G. G. Stokes gives a 

 theoretical proof of the method. , 



