Convective Cooling of Wires. 331 



In a previous paper * where this formula was studied, it 

 was shown that in general, both for forced and for free 

 convection, the hydrodynamie formulae are in very promising- 

 agreement with published data, except in the case of free 

 convection from hot thin wires. The present paper investi- 

 gates this apparent disagreement. 



(2) Convection loss from wires. 



Experimenters have almost invariably conducted wire 

 experiments at temperatures much higher than those used 

 with larger bodies, and this suggests two possible sources of 

 the apparent failure of the theoretical formula. Firstly, it 

 may be that in this extreme case it is no longer legitimate 

 to assume that "a" and "g" occur only as a product, the 

 mere volume changes of the air now having sensible effect. 

 Secondly, it may be now necessary to allow for the change 

 of the conductivity and specific heat of the fluid due to the 

 temperature rise caused by the hot wire. The present paper 

 shows the remarkable improvement which follows an attempt 

 to allow for this second effect, so that even for thin wires 

 the equation appears to be substantially correct. 



The formula may be put in a more convenient form for 

 our purpose. In (1) " h " refers to unit area, and if the 

 body is a long cylinder, "A" is obviouslv unaffected by the 

 length. It readily follows that for long cylinders (diameter 

 d) the heat loss H per unit length per degree temperature 

 elevation is given by 



K/k = F{c 2 gd s a6/k 2 ) (4) 



Writing v for k/c (since cvjk is constant for a given kind 

 of gas) and regarding u a " f and u g " as constant, we have 



R/k = ¥{0d 3 /v 2 ). (5) 



Consequently, if data for the natural convective cooling 

 of long cylinders be plotted on a graph with H/k as ordinate 

 and 0d 3 /v 2 as abscissa, the result should be a single curve 

 independent of the size of the cylinders, and also of their 

 temperature excess, if appropriate allowance be made for 

 the variation of k and v with temperature. Further, from 

 the method of its derivation, formula (5) would appear to 

 hold for all fluids for which cv\k is the same. For gases the 



* Davis, Phil. Mag. xl. p. 692 (1920). 



t The convection currents depend on the density change relative to 

 the density of the cold fluid, so that " a " must be regarded as applicable 

 to the cold gas, and independent of the temperature of the wire. 



