SERIES SOLTIONS OF TWO SIMULTANEOUS VECTOR 
DIFFERENTIAL EQUATIONS ORIGINATED FROM CLASSICAL STOKES 
FLOW PROBLEM 
Rajeh Eid
Supervisor:Hasan Taseli
January 1994, 98 Pages


Abstract: In this study, the infinite system of simultaneous ordinary differential equations with variable coefficients 

which is recently derived by Taželi and Demiralp to solve Stokes flow problem past an arbitrary axisymmetric 

body is considered. The complete series solutions of the truncated system are obtained for an arbitrary truncation 

order N.Each series solution together with logarithmic terms is shown to be convergent in the entire physical 

interval of interest. 

                 By constructing the solutions of the sytem of equations, the corresponding hydrodynamical problem 

formulated in terms of the stream function has been solved. As a numerical application, the drag on a prolate 

spheroid has been computed and compared with the exact result. Highly accurate numerical results have been 

achieved depending on the  ratio of the spheroid. 
                 Although the method is slowly convergent for spheroids having a small  ratio, results are very 

encouraging. It seems that the work provides a stable and efficient method, in a systematic manner to determine 

axisymmetric Stokes flow past an arbitrary body, the boundary shape of which is  analytic, especially, whenever 

certain numerical difficulties appearing in the algorithm have been cured. 

 Key words: Stokes Flow, Vector Differential Equations, Series Solutions, Drag.