﻿940 Mr. A. H. Davis on the Cooling Power 



I desire to express my thanks to Dr. G. W. C. Kaye and 

 Dr. Ezer Griffiths for the kind and encouraging way in 

 which the facilities for the present work have been provided, 

 to Mr. W. G. Bickley, M.Sc, for critically reading a draft 

 of the theoretical part, and to my wife for assistance with 

 the numerous calculations involved in the reduction of the 

 experimental observations. 



May 1922. 



LXXX. The Cooling Power of a Stream of Viscous Fluid. 

 Bxj A. H. Davis, M.Sc.*' 



[From the National Physical Laboratory.] 



IN some previous papers f the author has studied the 

 phenomenon of convective cooling, both natural and 

 forced, from the point of view of similitude, and has shown 

 how excellently experimental data for gases agree with a 

 grouping of variables that Boussinesq J deduced by hydro- 

 dynamical reasoning for inviscid fluids. The most recent § 

 of this series of papers considered for natural convective 

 cooling the necessary modifications of Boussinesq's analysis 

 in dealing with the problems of viscous fluids, and the new 

 formula thus obtained was tested experimentally in certain 

 conditions and found to be satisfactory. 



The present note develops the theory of forced convection 

 in the same way, studying the effect of introducing a 

 viscosity term into Boussinesq's analysis for inviscid fluids. 



The problem concerns the cooling of a hot body immersed 

 in an infinite fluid stream maintained at a certain tempera- 

 ture, 6 degrees in excess of that of the fluid at infinite 

 distance to which all temperatures are referred. The fluid 

 stream is rectilinear, and moving with uniform velocity v m 

 at distances from the body sufficiently great. This velocity 

 is supposed to be sufficiently great for the natural convection 

 (gravity) currents set up by the hot body itself to be 

 negligible. We thus neglect the coefficient of expansion of 

 the liquid. 



Let p and v be respectively the density of the fluid and its 

 kinematical viscosity. At a given time t, and for an element 

 of the fluid at the point x, y, z, let t, u, v, w, P be the 



* Communicated by the Author. 



t Phil. Mag. xl. p. 691 ; xli. p. 899; xliii. p. 329. 



% Boussinesq, Comj'tes Mendus, cxxxii. p. 1382; cxxxiii. p. 257 (1901). 



§ See p. 920. 



