Title

Orthogonal cubic spline collocation method for the nonlinear parabolic equation arising in non-Newtonian fluid flow

Authors

Authors

F. T. Akyildiz;K. Vajravelu

Comments

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Abbreviated Journal Title

Appl. Math. Comput.

Keywords

orthogonal cubic splines; collocation method; nonlinear parabolic; equations; non-Newtonian fluid flow; Mathematics, Applied

Abstract

Using the orthogonal cubic spline collocation method, solution for the nonlinear parabolic equation arising in magnetohydrodynamic unsteady Poiseuille flow of the generalized Newtonian fluid (Carreau rheological model) is obtained. Also, using the Lyapunov functional, a bound for the maximum norm of the semi-discrete solution is derived. Moreover, optimal error estimates are established for the semi-discrete solution. Numerical results thus obtained are presented graphically and the salient features of the solution are discussed, for various values of the parameters. The results obtained reveal many interesting behaviors that warrant further study on the parabolic equations related to non-Newtonian fluid phenomena. Furthermore the analysis can be used to study the mathematical models that involve the flow of viscous fluids with shear rate-dependent properties: For example, models dealing with polymer processing, tribology and lubrication, and food processing. (c) 2006 Elsevier Inc. All rights reserved.

Journal Title

Applied Mathematics and Computation

Volume

189

Issue/Number

1

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

462

Last Page

471

WOS Identifier

WOS:000247328400047

ISSN

0096-3003

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