﻿Connective Cooling in Fluids. 925 



Also, let ns put the equation of the solid in the form 



Thus, if the coefficient (0 gac/kv)^ changes, this amounts to 

 considering, instead of the actual solid, similar bodies having 

 linear dimensions inversely proportional to this coefficient. 

 Then the direction-cosines l,m,n, of the normal will remain 

 the same at corresponding points, and the boundary con- 

 ditions become 



At the surface U = V = W = and T = l, ) 



At the distance Vf + ^ + f 2 infinite (II, U, V, W, T) = 0.j ' ' 



The system of equations (8) and (10) determine (U, V, W, 

 T, II) as the functions of f'^f, and substituting in the 

 integrals for the eight new variables their equivalents as 

 given by (7), we have five relations of the form 



t (u, v, w) P 1 ) 



0' (fyaPVP' ( ^ Va 2 ^ Y" 8 \ = definite functions of 



/0gac\ m (0gac\' z /0gac\^ s 



\ kv ) x ; \ kv J v> \ kv ) z - ) 



The flux of heat furnished in unit time by unit area of 

 such a body, equal to that which the contiguous liquid layer 

 communicates to the interior of the fluid, is given by 



7 /vBt £t Bt\ 



V cU' dy ^z J 



Introducing the new variables, we have then 



h=Jc(0 gac/kv) >l*d(l || + m |^ + n ||). . (12) 



At corresponding points of the surfaces /(f, /7, f) = 

 limiting the bodies considered, the direction-cosines l,m,'n 



and the derivatives _ , . t- have the same values respec- 



tively ; so the trinomial coefficient is a function of the shape 

 and orientation of the bodies only. 



Thus the result may be stated in the following form. 

 For a family of similar bodies similarly oriented, and having 

 linear dimensions L given by 



Loc (6 "gac/kv)- 1 / 3 , i.e. (L z 0gac/kv) = const., 



(10) 



I ■ (11) 



