from a Body cooled l>y a Stream of Fluid. 593 



obtains an approximate solution for the case of a heated strip 

 cooling in air. When the strip is protected from draughts 

 he proves that the heat convected from it varies as 3/4 where 

 is the difference of temperature between the strip and the 

 air before it is heated by the strip. L. G-raetz * finds the 

 mathematical equation for thermal conduction in a liquid 

 flowing through a cylindrical tube, and obtains a solution 

 in terms of Bessel's functions. Harold Wilson t gives a 

 solution of this problem, taking the viscosity of the liquid 

 into account ; but unfortunately his solution is only applicable 

 to a very special case. 



Boussinesq was the first to state clearly the laws for the 

 cooling of a heated body by a stream of liquid when the flow 

 is not turbulent. In 1901 % he published the formula for 

 the cooling of a strip by a liquid flowing past it in a direction 

 at right angles to its length and parallel to its breadth. Four 

 years afterwards (I. c. ante) the same author published the 

 solution of the problem of the convection of heat from a 

 horizontal cylindrical rod of elliptical cross-section immersed 

 in a liquid flowing in a direction at right angles to the axis 

 of the rod. He also gave the solution for the similar problem 

 of the convection of heat from an ellipsoidal shaped body. 



3. The Assumptions made. 



In order to simplify the mathematical work the following- 

 assumptions are made. The liquid is supposed to be 

 athermanous, that is, opaque to heat rays. It is also sup- 

 posed to have no viscosity. The liquid therefore slips past 

 the surface of the solid. In addition it is supposed to be 

 incompressible. Hence we should only expect the solutions 

 to give roughly approximate values when applied to the 

 problem of spheres and cylinders being cooled by currents of 

 air. It is instructive to notice, however, that Boussinesq's 

 result, that the convection of heat by a stream of liquid from 

 a sphere or a cylinder maintained at a constant temperature 

 varies as the difference of temperature between the solid and 

 the liquid and as the square root of the velocity of the current, 

 is in good agreement with the results obtained by P. Corn- 

 pan § from experiments with spheres in draughts of air, and 

 also with Kennelly's || results for the cooling of cylindrical 

 wires. Boussinesq's theoretical results also would lead us to 



* Ann. der Physik, xviii. p. 79 (1883). 



t Carab. Phil. Soc. Proceedings, xii. p. 406 (1904). 



\ Comptes Rendus, cxxxiii. p. 257. 



$ Ann. de Chim. et Phys. xxvi. p. 488 (1902). 



|| Amer. Inst. Elect. Engin. Proc. July 1909. 



Phil M«g. Ser. 6. Vol. 20. No. 118. Oct. 1910. 2 R 



