On creeping flow over a cylinder rotating in presence of translating plane boundary
type: Item
instance of: scholarly article
title: On creeping flow over a cylinder rotating in presence of translating plane boundary
zbMATH Open document ID: 0976.76097
DOI: 10.1007/BF01190016
published in: Acta Mechanica
publication date: 2002-01-02T00:00:00Z
review text: The creeping flow over a cylinder rotating in the presence of translating plane boundary has been analysed by using conformal mappings. The problem reduces to the solution of biharmonic equation with conditions for fluid velocity posed on the two lines bounding the domain. A closed-form mapping function is obtained which transforms the original infinite domain of solution onto an annulus. The solution of the problem, represented by two Goursat functions, is derived in a general form, consisting of Laurent series supplemented by proper logarithmic terms. The system of linear equations for the unknown coefficients of these functions is obtained by requiring that the boundary conditions are satisfied on both circles bounding the annulus, and then a pseudospectral method is applied for the determination of coefficients. The author shows that all the coefficients of Goursat functions -- except seven -- vanish, so that the functions represent an exact solution in the annular domain. As the mapping function is exact, the solution is also exact in the original infinite domain. Finally, the author presents streamline patterns corresponding to four characteristic sets of boundary conditions.
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 76M40
Mathematics Subject Classification ID: 76B10
zbMATH DE Number: 1491326
zbMATH Keywords: conformal mapping
zbMATH Keywords: rotating cylinder
zbMATH Keywords: creeping flow
zbMATH Keywords: translating plane boundary
zbMATH Keywords: biharmonic equation
zbMATH Keywords: annulus
zbMATH Keywords: Goursat functions
zbMATH Keywords: Laurent series
zbMATH Keywords: logarithmic terms
zbMATH Keywords: pseudospectral method
zbMATH Keywords: exact solution
author: Maria E. Klonowska
reviewed by: R. Usha
MaRDI profile type: Publication
cites work: Q5552673
cites work: A contribution to the hydrodynamics of lubrication
cites work: On a method of computing the Stokes flow in plane multiply connected domains
full work available at URL: https://doi.org/10.1007/bf01190016
OpenAlex ID: W2060984424
description: scientific article; zbMATH DE number 1491326