A Method for Studying a Coupled System of Differential Equations

2005 ◽  
Vol 41 (6) ◽  
pp. 887-894 ◽  
Author(s):  
Yu. T. Sil’chenko
Keyword(s):  
Differential Equations ◽  
Coupled System ◽  
System Of Differential Equations

Flow in Straight Ducts of Arbitrary Cross Section

1979 ◽  
Vol 46 (2) ◽  
pp. 263-268 ◽  
Author(s):  
P. W. Duck
Keyword(s):  
Fourier Series ◽  
Conformal Mapping ◽  
Differential Equations ◽  
Cross Section ◽  
Coupled System ◽  
Arbitrary Cross Section ◽  
Numerical Results ◽  
Steady Flows ◽  
System Of Differential Equations ◽  
Oscillatory Flows

A method is presented for treating flows in straight ducts. The method involves the conformal mapping of the cross section on to a semicircle, and then solving the problem using Fourier series. For oscillatory flows (to which most of the paper is devoted) the method results in an infinite, coupled system of differential equations, although reliable numerical results may be obtained by truncation. For steady flows, however, the method yields a solution involving integrals of the Jacobian of the transformation.

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