F • CONVECTIVE HEAT TRANSFER IN GASES 

 function of u^ becomes 



r^ = 1 - exp 



1 - 



K 



^Cf/2 



(1 - u^) 



(11-7) 



in which K is the universal mixing-length constant. 



The next step in the evaluation of Eq. 11-5 is to place values on the 

 hmits M^iam and w^f This is done by following von Karman [24\, who 

 stipulated for the velocity profile: (1) a laminar sublayer between the 

 hmits ^ ?/* ^ 5 where y* = p \/t(0)/p y/n, whence u* = y*, where 



Fig. F,lla. Velocity and shear distributions for laminar and turbulent flow. 



u* = u/\/t(0)/p; and (2) a transition or buffer zone between the limits 

 5 ^ ?/* ^ 30 and following the law u* = 5[1 + In {y*/5)].^ Therefore, 



''ilslam 



Cf 



and 



w^t = 5(1 + In 6) 



Cf 



(11-8) 



(11-9) 



1 A more significant velocity profile that fits the flow all the way to the wall is 

 given by van Driest [26].) 



Jo 1 



in which ^ * = 26. Now 



so that for small y* 



+ Vl + 4fc2t/*2[l - exp i-y*/A*)]^ 

 IX l(du*/dy*)J 



A*2 



y*' 



Thus the ratio of the turbulent to the molecular momentum transport coefficient 

 starts out as y*K 



( 374 ) 



