'.J.- ■:\-''"' -J. Desai and Lieber 

 u' = ^Tn' = ^^^~^ + B+ C log^ r+ Dr^) cos 8 (1.39) 



v' = - ^ = (Ar"2- B- C- C log r- 3Dr2) sin 61 . (1.40) 



dr ^ 



We have four conditions on the flow to consider. 



(1.41) 



r = l 



= 

 r = l 



lim u' = - cos 



r->co 



1 im v' = + sin 6' 



r-»oo 



(1.42) 

 (1.43) 

 (1.44) 



Evidently all these conditions cannot be fulfilled. We would like to obtain those 

 solutions which satisfy at least three out of the four conditions. We have four 

 cases to consider: 



(i) v' I ^3 J ?^ : Applying the conditions of Eqs. (1.41), (1.43), and (1.44) to 

 Eqs. (1.39) and (1.40), we get 



A + B + D = 



B+ C(m) + D(co) = -1 



- B - C(co) - C - 3D (CO) = +1 . 



This gives 



Consequently, 



B=-l, A=+l, c=D=0 



0' = - I r - — I sin 



u' = - (1 - ^) cos(9 (1.45) 



v' = + ( 1 + — ] sin (9 . 



(ii) u' I ^^j ^ : Applying the conditions of Eqs. (1.42), (1.43), and (1.44) to 

 Eqs. (1.39) and (1.40), we get 



540 



