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

    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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