Couple Stress Fluid Flow in A Doubly Connected Region Bounded by Elliptic Cylinders
DOI:
https://doi.org/10.26713/cma.v14i4.2576Keywords:
Couple-stress fluid, Confocal ellipses, Doubly connected region, Conformal mapping, Frobenius methodAbstract
A doubly connected region formed by confocal elliptic cylinders is considered. The cylinder walls are assumed to be impermeable, and rigid and fully developed flow of couple-stress fluid between the cylinders is considered. Conformal mapping of the form \(z = c\big(\zeta+\frac{\lambda}{\zeta}\big)\) is applied \(x\)-\(y\) plane to \(\xi\)-\(\eta\) plane to transform elliptical cylinders into concentric circular cylinders. The governing equations are solved analytically in \(\xi\)-\(\eta\) plane using the Frobenius method. The solution obtained is numerically evaluated and graphically depicted.
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