Abstract
Three complex variable circle theorems for studying the two-dimensional Stokes flows interior to a circular cylinder are presented. These theorems are formulated in terms of the complex velocities of the fundamental singularities in an unbounded incompressible viscous fluid. Illustrative examples are given to demonstrate their usefulness.
Highlights
The solutions of fluid mechanical problems involving fundamental singularities in the presence of rigid boundaries are of considerable interest in practice
Our object is to study Stokes flow interior to a circular cylinder in the light of the complex variable theory and to establish a number of complex variable circle theorems for slow viscous fluid motion within a circular cylinder in terms of the complex velocities of the fundamental singularities found in Chowdhury and Sen [11]; these theorems correspond to the complex variable circle theorems for potential flow [12, 13] in an inviscid fluid within the same cylinder
In the case of twodimensional slow flow theory there is a complex variable circle theorem [1] for the solutions of Stokes flows due to singularities outside a circular cylinder which corresponds to Milne-Thomson’s circle theorem [2, 3] for potential flow outside the same cylinder, in the inviscid flow theory
Summary
The solutions of fluid mechanical problems involving fundamental singularities in the presence of rigid boundaries are of considerable interest in practice. Sen [5] has pointed out a method to solve some problems of slow viscous fluid flow within a circular cylinder with the aid of his circle theorems for the flows outside a circular boundary. Our object is to study Stokes flow interior to a circular cylinder in the light of the complex variable theory and to establish a number of complex variable circle theorems for slow viscous fluid motion within a circular cylinder in terms of the complex velocities of the fundamental singularities found in Chowdhury and Sen [11]; these theorems correspond to the complex variable circle theorems for potential flow [12, 13] in an inviscid fluid within the same cylinder.
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