460 Mr. A. Griffiths on Diffusive Convection. 



the other tube. In both cases the maximum value (since SL 



is small) equals— r-j- approximately; i. e. the maximum value 



is double the velocity produced when the tubes are of equal 

 bore. 



It can be shown by algebraical transformations that the 

 correcting factor equals 



1 + 



(¥+*■) 



It is unity when r equals infinity or zero. Its maximum 



value occurs when r= jr- (i.e. when the diameters of the 



tubes are in the same proportion as their lengths) and is 



1 -f j j I approximately ; it is seen that the maximum 



value is practically identical with the value in the case of 

 tubes of equal bore. 



Fig. 4. 

 • 



Section VI. 

 Probable effect of Viscosity on the Convective Flow. 



The internal friction of the moving liquid will diminish, to 

 some extent, the velocity. It is obvious that the liquid in the 

 interior portion of a tube will travel at a faster rate than 

 that near the walls, and there is little 

 doubt that the surfaces of equal density 

 will not be horizontal planes. In all 

 probability therefore the diffusion will 

 take place radially as well as axially. 

 It is also possible that the stream-lines 

 will no longer be vertical ; but super- 

 imposed on the vertical motion there 

 may be slight eddies. 



The author has not attempted the 

 general problem, and in what follows 

 only the ideal case is considered, in 

 which both diffusion and motion take lc R >1 

 place in a vertical direction, i. e. their 10 



radial components are neglected. 



Let 00' represent the axis of the tube of radius E. 



By considering the space between two concentric cylinders 



r> 



