from a Body cooled by a Stream of Fluid. 597 



Hence, substituting these values in (5), we get 



^""cVW + W' • ' ' ' w 



which is a much simpler equation than (5) as the coefficient 

 of the right-hand side is a constant quantity. 



Our assumptions allow us to simplify this equation still 

 further. Since the liquid is a very bad conductor of heat, 

 6 alters very rapidly with a but very slowly with /5. The 

 term d 2 0/B/3 2 is also negligibly small compared with B 2 #/c)« 2 . 

 We thus obtain the equation 



M - 1 ?!? m 



d/3~cVB* 2 ' K J 



the solution of: which has been put into various forms by 

 Fourier and others. 



5. Circular Cylinder. 

 We shall now consider the problem of the cooling of a 

 circular cylinder immersed in a stream of liquid with its axis 

 horizontal and at right angles to the direction of flow. 



Fig. 2 



* ^K 



n/ 





U5"/\j 



o 





45°\yA 



5/. 



ream lin*& ctj Fluid (fowi/yg past cylinder-. 

 M> & A °re ^e tWo aity&ular equipo/eKtfia/ curves. 



Let us take the origin of co-ordinates on the axis of the 

 cylinder, and let us suppose that the liquid is flowing with 



