Solution of Two-Dimensional Stokes Flow With Elliptical Coordinates and Its Application to Permeability of Porous Media-Reference-Cited by-同舟云学术

Solution of Two-Dimensional Stokes Flow With Elliptical Coordinates and Its Application to Permeability of Porous Media

Published:2021-04-22 Issue:6 Volume:88 Page:
ISSN:0021-8936
Container-title:Journal of Applied Mechanics
language:en
Short-container-title:

Author:

Hellou Mustapha¹,Lominé Franck¹,Bourbatache Mohamed Khaled¹,Hajjam Mohamed²

Affiliation:

1. Civil Engineering and Mechanical Engineering Laboratory-EA3913, University of Rennes, INSA Rennes, Rennes F-35000, France

2. Department of Mechanical and Systems Engineering Complexes, Institut Pprime, UPR CNRS 3346, University of Poitiers, F-86000, Poitiers, France

Abstract

Abstract In this paper, analytical developments of the biharmonic equation representing two-dimensional Stokes flow are performed with elliptical coordinates. It is found that the streamfunction is expressed with series expansions based on Gegenbauer polynomials of first and second kinds with order one Cn1 and Dn1 for n natural integer number. Application to an elliptical fiber enclosed in an elliptical boundary with uniform flow is made. It is found that a particular solution responsible of the drag must be added to the general solution. Following this, the flow through rectangular arrays of elliptical fibers is studied, and the permeability of this medium is determined as a function of porosity.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Link

http://asmedigitalcollection.asme.org/appliedmechanics/article-pdf/88/6/061009/6686740/jam_88_6_061009.pdf

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