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Slow Steady Flow of an Idealized Elastico‐Viscous Incompressible Fluid of Oldroyd Type Through a Straight Tube with an Arbitrary Cross‐section
Author(s) -
Ramacharyulu N. Ch. Pattabhi
Publication year - 1967
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19670470603
Subject(s) - mechanics , tube (container) , compressibility , viscous liquid , perpendicular , physics , cross section (physics) , flow (mathematics) , perturbation (astronomy) , pressure gradient , steady state (chemistry) , constant (computer programming) , classical mechanics , geometry , mathematics , materials science , chemistry , quantum mechanics , computer science , composite material , programming language
In this paper, slow steady flow of an idealized elastico‐viscous liquid through a straight tube is discussed. Perturbation technique is employed to linearize the equations of motion and state. We observe that the flow, under the influence of a constant pressure gradient down the axis of the tube, is a rectilinear flow over which a secondary flow is superposed in planes perpendicular to the length of the tube. The basic equations derived are solved with the function theoretic method. The solution for any arbitrary cross‐section of the tube is obtained. The case of a tube with an elliptic‐limacon cross‐section is given as an example.