698 Mr. A. H. Davis on 



2. Convection from a Body in a Stream of Fluid. 



Formula. 



Convection from a body in a stream of fluid moving with 

 velocity v (natural convection being negligible) has been 

 determined by Boussinesq, 



h= (kd/l)¥(lvc/k), • (9) 



and Rayleigh has shown the derivation from the principle 

 of similitude. 



Since from the kinetic theory of gases, as mentioned 

 above, cv/k is constant, (9) becomes /< = (/■#//) F(/r/i>), and 

 r lvlv) is the well-known variable in experiments on fluid 

 resistance and flow. This raises the possibility of a useful 

 relation between the thermal and dynamic effects of a 

 fluid stream. It is important apart from this, however ; 

 for if heat-loss is affected bj change from stream-line 

 motion to turbulence, it is satisfactory to find the 'equation 

 for heat-loss contains the variable {Ivjv) which determines 

 turbulence. 



A formula given by Russell * for stream-line flow past a 

 cylinder at right angles to the stream is readily seen to be 

 equivalent to (9), where F(lvc/k)a:(lvc/k)V 2 . Although 

 such special approximate forms of the function F calculated 

 for stream-line flow might cease to hold when turbulence 

 set in, the formula (9) would still be satisfactory. One 

 recalls that in dealing with purely hydrodynamic problems 

 of the flow of viscous fluids in cylindrical pipes, Stanton & 

 Pannell f investigated the resistance to flow from the stand- 

 point of similitude. Their results show that although the 

 relation analogous to (9) has a special form for stream-line 

 motion, which apparently alters when turbulence sets in, 

 the general relation holds even for turbulent motion, and is 

 continuous through the transition region. 



Examination of Formula. 



Experimental work on the heat-losses from bodies in 

 a stream of air has been carried out chiefly on thin wires, 

 but some data are available for larger cylinders. Let us 

 consider these two cases. 



* Russell, Phil. Mag. xx. p. 591 (1910). 



t Stanton & Pannell, Phil. Trans, ccxiv. p. 199 (1914). 



