Couple Stress Fluid Flow in A Doubly Connected Region Bounded by Elliptic Cylinders

Indira Ramarao; S. Pramod; S. Jagadeesha; K. R. Rashmi; K. R. Sreegowrav

doi:10.26713/cma.v14i4.2576

Authors

Indira Ramarao Department of Mathematics, Nitte Meenakshi Institute of Technology, Bengaluru, India https://orcid.org/0000-0001-8801-2927 (unauthenticated)
S. Pramod Department of Mathematics, Nitte Meenakshi Institute of Technology, Bengaluru, India https://orcid.org/0000-0002-0075-3497 (unauthenticated)
S. Jagadeesha Department of Mathematics, Nitte Meenakshi Institute of Technology, Bengaluru, India https://orcid.org/0000-0002-1294-6253 (unauthenticated)
K. R. Rashmi Department of Mathematics, Nitte Meenakshi Institute of Technology, Bengaluru, India https://orcid.org/0000-0003-4997-4714 (unauthenticated)
K. R. Sreegowrav Department of Mathematics, School of Applied Science, Reva University, Bengaluru, India https://orcid.org/0000-0003-2069-8402 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v14i4.2576

Keywords:

Couple-stress fluid, Confocal ellipses, Doubly connected region, Conformal mapping, Frobenius method

Abstract

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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