﻿of a Stream of Viscous Fluid. 943 



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

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

 communicates to the interior of the fluid, is given by 



<*£+•*! + *5> • • • (10 > 



Introducing the new variables, we have 



*-(*-.w(f.g+«tg +*g> • • (id 



At corresponding points of the surfaces /(f, 77, f) = 

 limiting the bodies considered, the direction cosines l u m 1? n l 

 have the same values, and at corresponding times t l = const. 



the derivatives sr-75 ^at corresponding points have also 



ofay, 



the same values. Consequently, at corresponding times the 

 trinomial coefficient is a function of the shape and orientation 

 of the bodies only. 



Thus, for a family of similar bodies similarly orientated, 

 having linear dimensions L given by 



Locv/r^, i.e. ?? x L/i> = const., . . . (12) 



the heat loss per unit area at corresponding tim es from 

 corresponding points is given by 



hozkv 0/v; (13) 



and this will also be true if " A" be the mean heat loss taken 

 at the given instant over the whole surface of the solid. 

 So for bodies of this shape and orientation we have 



h = (kvJ/v)f{v„Llv; vjt/v}, . . . (U) 



which may be written 



AL 

 kO 



{V L ^-| o»> 



When the conditions have become steady — that is, inde- 

 pendent of time t, — the formula reduces to 



g-FftSf). ..... (16 



And, further, if the conditions do not settle down to complete 

 steadiness, but settle down to periodic fluctuations, then these 

 fluctuations will be similar in form for corresponding cases, 

 and the average value of the heat loss will still be given 

 by (16). 



