Desai and Lieber 



BOUNDARY CONDITIONS ON THE ITERATIONS 

 At the Cylinder Wall ( r = 1) 

 First Iteration — 





(1.77) 



Vj(l,5,t) = I - — ) = -2 sine for al 1 t > . q ygs 



r=l 



Second Iteration — 



u,(l,e,t)=^^^j = ° f-^^^ ' (1.79) 



r= 1 



v,(l,0,t) = ^- — j =0 for all t . ^^3Q) 



r= 1 



Higher Iterations ( n > 3) — 



u„(l,e,t)=^J^j =0 for all t ^^3^) 



r= 1 



^n(l-^-t)= ^-^; =0 for all t . ^^82) 



r= 1 



At Physically Infinite Distance ( r = h*) 



We first note that according to Eq. (1.16) the actual flow field is such that it 

 can be regarded as uniform beyond a certain distance h*. The potential base 

 flow also becomes uniform with increasing distance, and during the discussion 

 on a physically infinite distance it was shown, with reference to Table 1, that 

 h* = 50 may be taken as the corresponding physically infinite distance. Now 

 u = Uq + Uj + Uj + • • • and V = vq + Vj + Vj + • • • . Hence if u^ and Vn, n > 1 

 all become zero at some distance hf evaluated in the sense of a physically in- 

 finite distance, the flow beyond h* will be given by uq, and the condition of 

 uniform flow will be satisfied by u because it is satisfied by uq. The distance 

 h\ must be found so that the solutions u^,, n > 1 do not change significantly if 

 the condition of their vanishing is applied at any other distance greater than h*; 

 i.e., h* is to be the physically infinite distance for the iterative solutions. We 

 note that this distance h\ must be the same for all iterations, because higher 



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