Studies on the Motion of Viscous Flows—Ill 



C^(l,t) = , D^(l,t) = n = 1, 2, ... 

 C;(l,t) = , D;(l,t) = n = 0, 1, 2, ... ; 

 En(l't) = , F„(l,t) = n = 1, 2, ... 

 E;(l,t) = , F;(l,t) =0 n = 0, 1, 2, ... . 

 The conditions of Eqs. (1.67a), (1.67b), and (1.67c) imply that at r = l we have 



Bu "^^ '-'i ^^1 



— - = , : = , — - = 2 cos 



'dd de^ Br 



Bv, 



B2v, 



(1.67b) 



(1.67c) 



+ 2 sin 



Bu, B^u 



= , = 



dd B^2 



Bu, 



B2u, 



^ 



Buj 



T7 

 'd7 



Bv^ 



,B0 



BV3 



= 



B2v„ 



B2V3 

 3612 



. 



(1.68) 



We also have 



and 



Bu. 



Bv, 



= 



= 2 cos^ 



(1.69) 



All partial derivatives with respect to time are zero at the wall. The results of 

 Eqs. (1.68) are a consequence of the periodicity condition. If we apply the con- 

 ditions of Eqs. (1.66), (1.68), and (1.69) to Eqs. (1.47), (1.48), (1.51), (1.52), 

 (1.55), and (1.56), we get r = 1 the following equations: 



1 dPi 



2 Br 



32, 



Re 3r2 



6 cos 

 Re 



(1.70a) 



-4 sin2^ 



Re 



(1.70b) 



1 ^^ 



2 3r 



32u, 



Re Br2 



(1.70c) 



547 



