Studies on the Motion of Viscous Flows— III 



we obtain, after some algebraic manipulation, the following governing equations 

 for (2„ and 5^: 



2 1-2 2r \ r2/ 1 2 \ r^ / ^ 2 3t (2.3) 



fl. ^ 7 fl, - - CI, . - 1 + - a, + - 1 - - Ut^ . Re 1 - - - = Re 



V 2 3t 



(2.4) 

 1 ^ n2 (n+ 1) Re / 1 \ (n- 1 ) Re / i \ 



n r n ^2 n 2r \ j- ^ J "^ 2r \ r2/ "" * 



Re /, 1 \ ^, Re /, 1 \ ^, ^ ^^n 



n = 2, 3, 4, . . . ; 

 Q" 1 <<). 1 o Re /, 1 \,o Re /, l\cD. r. ^*i 



2 •■ 2 r2 2 2r V r^j ' 2 \ r^ I' 



3Re / 1 \ ^ Re / 1 \ ^, ^®2 



+ 1 + — S, + — 1 - — S: = Re 



2r \ r2/ 3 2 \ v^ ) ' 3t (2.7) 



n r n ^2 n 2r V v^ ""^ 2 V r2/ "-1 



(n+ 1) Re / 1 \ Re / i \ ^® 



2r \ r2 / ""^1 2 \ r2 / ■ """i 3t 



n =: 3, 4, . . 



From Eq. (1,60) we have 



1 ^^1 



Vi(r,0,t) 



oi 



- nA„(r,t) nB„(r,t) 



/ - sinna + cosni! 



i—j r r 



30, 



(2.8) 



- A;(r,t) - ^ [A;(r,t) cosn^ + B;(r,t) sinn^] (1.63a) 



n= 1 



557 



