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Analytical and numerical solutions of a generalized hyperbolic non‐Newtonian fluid flow
Author(s) -
Pakdemirli M.,
Sarı P.,
Solmaz B.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701028
Subject(s) - herschel–bulkley fluid , power law fluid , generalized newtonian fluid , flow (mathematics) , mechanics , non newtonian fluid , newtonian fluid , shear stress , mathematics , drilling fluid , fluid dynamics , physics , classical mechanics , mathematical analysis , rheology , drilling , thermodynamics , engineering , shear rate , mechanical engineering
Generalized hyperbolic non‐Newtonian fluid model first proposed by Al‐Zahrani [1] is considered. The model was successfully applied to some drilling fluids with better performance in relating shear stress and velocity gradient compared to power‐law and Hershel‐Bulkley model. Special flow geometries namely pipe flow, parallel plate flow and flow between two rotating cylinders are treated. For the first two cases, analytical solutions of velocity profiles in the form of integrals are presented. For the flow between two rotating cylinders, the differential equation is solved by Runge‐Kutta method combined with shooting. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)