600 . Dr. A. Russell on the Convection of Heat 



current of air flowing uniformly. He states * " aeris partes 

 aequales aequalibus temporibus calefactae sunt Sf calorem con- 

 ceperunt calori ferri proportionalem" 



A. C. Mitchell f has shown that Newton's law is very 

 approximately true up to a difference of temperature between 

 the solid and the air of 200° C, and P. Compan % has proved 

 it true for temperatures up to 300° C. 



In several practical applications the assumption of Newton's 

 law for the convection of heat by fluids leads to results which 

 are found to be in close accordance with experiment. For 

 instance, in the theory of the Irwin § hot-wire oscillograph, 

 the assumption is made that the convection of heat from the 

 heated metal strips which are immersed in convection- 

 currents of oil is proportional to the difference of tem- 

 perature between the metal and the oil. The very satis- 

 factory results obtained in practice prove that the assumption 

 is approximately correct. It will be seen from § 11 below 

 that, even in the case of the turbulent motion of water 

 through a pipe, Newton's law is very approximately true. 

 Jt is not applicable, however, to natural free convection 

 from a heated body in a gas or a liquid. In this case || 

 Lorenz's law (see above) is applicable. 



In the case of the circular cylinder we find, from the 

 values of /3 X and /3 given above, that 



A - & = K 

 and hence 



If we denote the surface of unit length of the cylinder 

 by S, so that S = 2-rra, the expression for the rate 

 at which heat is lost by the cylinder per unit length is 

 generally assumed by engineers to be equal to AS#, where h 

 is independent of the radius of the cylinder. We see from 

 (12) that the value of h for the perfect liquid is given by 



h= W-^- ^ 



Thus h varies inversely as the square root of the radius of 



* "Scala Graduuni Caloris," Phil. Trans, p. 828, April 1701. The 

 paper is not signed. In Neivtoni Opera Horsleii, vol. iv. p. 403 (1782), 

 the title is given as "Tabula Quantitatum et Graduum Caloris." 



t Roy. Soc. Edin. Trans, xl. 1, p. 39 (1899). J L. c. ante. 



§ Journ. Inst, of Elect. Enjrin. vol. xxxix. p. 617 (1907). 



i| P. Compan, I. c. ante ; H. Ebeling-, Ann. der Physik. xxvii. 2, p. 391 



