330 Mr. A. H. Davis on Natural 



transfer from a hot body by the medium o£ a fluid moving 

 past the surface. Such cooling is said to be " natural " or 

 " free " when the fluid is still except for the streams set up 

 by the heat from the hot body itself. 



The theory involves the dilatability of the fluid, the hydro- 

 dynamical equations of motion, the Fourier equations of 

 heat-flow, and the appropriate boundary conditions. From 

 this point of view Boussinesq ** has studied both natural and 

 forced convection for similar bodies immersed in an infinite 

 inviscid fluid. His formulae may also be derived from the 

 principle of similitude by simple consideration of the 

 variables involved, and may be extended to viscous fluids by 

 the same means. The following formula is obtained for the 

 heat loss by natural convection from similar bodies similarly 

 immersed in viscous fluids. 



hl/ke = F(c 2 gl 5 adlP)f(cvlk), . . . . (1) 

 where 



h = heat-loss per second per unit area of the body, 



k = thermal conductivity of the fluid, 



c = capacity for heat of the fluid per unit volume, 



= temperature excess of the body, 



a = coefficient of density reduction of the fluid per 



degree rise of. temperature, 

 g = acceleration due to gravity, 

 Z = linear dimensions of the body. 



For a given kind of gas cv/k appears to be constant as 

 required by the kinetic theory, and the formula becomes 

 simpler 



h = (k0/l)¥(c*gl*a0/P) (2) 



The formula involves an assumption that a and g always 

 occur as a product, that is, that the expansion of the fluid is 

 negligible, except in so far as it alters the weight of unit 

 volume, and thus supplies the necessary driving force for 

 the convection currents. This restriction may impose limits 

 to the temperature excess for which the formula is applicable 

 for a given series of bodies. 



If only the temperature and size of the model are varied, 

 the gaseous constants (c, a, and k) and gravity (g) remaining 

 the same, the formula becomes 



h={0/l)F(0P) (3) 



* Boussinesq, Comptes Rendus, cxxxii. p. 1382 (1901). 



