602 Dr. A. Russell on the Convection of Beat 



Thus j3 has extreme values when 



x=±la, y = mb, 

 and when 



x= — la and y = — mb y 



Hence we find that 



Substituting this value in (11) we get 



H=4-y/^ y/%Z+Ff0, (14) 



Hence the cooling of the cylinder by the stream of liquid is 

 independent of the direction in which the stream impinges 

 on it. For a given area of cross-section and a given tempe- 

 rature the cooling power increases with the eccentricity of 

 the ellipse, being a minimum for a cylinder having a circular 

 cross-section. It is not permissible to apply (14) when the 

 liquid is flowing parallel to the minor axis and b/a is a very 

 small quantity. In this case, the velocity of the liquid 

 round the pointed ends of the ellipse would be very high and 

 eddy currents would be formed. 



7. FlatBtrip. 



If the solid be a thin strip of metal placed so that its 

 length is perpendicular and its surface parallel to the direc- 

 tion of flow, we have by (11) 



so-kVb a 



— 0o U5) 



H =V 



where b is the breadth of the strip. This also follows from 

 (14). The convection of heat n per square centimetre of the 

 surface of the strip per degree of temperature per second is 

 given by 



^VW • • in 



If the strip be bent so as to form a hollow cylinder of 

 circumference b, we have, by (13) 



= 3-19\/ 



irl 



Ttt 



■kV 



approximately. 



OTT 



