An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid

The main feature of the boundary layer flow problems of nanofluids or classical fluids is the inclusion of the boundary conditions at infinity. Such boundary conditions cause difficulties for any of the series methods when applied to solve such a kind of problems. In order to solve these difficultie...

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Main Authors: Abdelhalim Ebaid, Hassan A. El-Arabawy, Nader Y. Abd Elazem
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2013/865464
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author Abdelhalim Ebaid
Hassan A. El-Arabawy
Nader Y. Abd Elazem
author_facet Abdelhalim Ebaid
Hassan A. El-Arabawy
Nader Y. Abd Elazem
author_sort Abdelhalim Ebaid
collection DOAJ
description The main feature of the boundary layer flow problems of nanofluids or classical fluids is the inclusion of the boundary conditions at infinity. Such boundary conditions cause difficulties for any of the series methods when applied to solve such a kind of problems. In order to solve these difficulties, the authors usually resort to either Padé approximants or the commercial numerical codes. However, an intensive work is needed to perform the calculations using Padé technique. Due to the importance of the nanofluids flow as a growing field of research and the difficulties caused by using Padé approximants to solve such problems, a suggestion is proposed in this paper to map the semi-infinite domain into a finite one by the help of a transformation. Accordingly, the differential equations governing the fluid flow are transformed into singular differential equations with classical boundary conditions which can be directly solved by using the differential transformation method. The numerical results obtained by using the proposed technique are compared with the available exact solutions, where excellent accuracy is found. The main advantage of the present technique is the complete avoidance of using Padé approximants to treat the infinity boundary conditions.
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institution Kabale University
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series International Journal of Differential Equations
spelling doaj-art-05c7549a3e78476e919bf5c0f536d2e82025-02-03T01:09:46ZengWileyInternational Journal of Differential Equations1687-96431687-96512013-01-01201310.1155/2013/865464865464An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a NanofluidAbdelhalim Ebaid0Hassan A. El-Arabawy1Nader Y. Abd Elazem2Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaThe main feature of the boundary layer flow problems of nanofluids or classical fluids is the inclusion of the boundary conditions at infinity. Such boundary conditions cause difficulties for any of the series methods when applied to solve such a kind of problems. In order to solve these difficulties, the authors usually resort to either Padé approximants or the commercial numerical codes. However, an intensive work is needed to perform the calculations using Padé technique. Due to the importance of the nanofluids flow as a growing field of research and the difficulties caused by using Padé approximants to solve such problems, a suggestion is proposed in this paper to map the semi-infinite domain into a finite one by the help of a transformation. Accordingly, the differential equations governing the fluid flow are transformed into singular differential equations with classical boundary conditions which can be directly solved by using the differential transformation method. The numerical results obtained by using the proposed technique are compared with the available exact solutions, where excellent accuracy is found. The main advantage of the present technique is the complete avoidance of using Padé approximants to treat the infinity boundary conditions.http://dx.doi.org/10.1155/2013/865464
spellingShingle Abdelhalim Ebaid
Hassan A. El-Arabawy
Nader Y. Abd Elazem
An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid
International Journal of Differential Equations
title An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid
title_full An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid
title_fullStr An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid
title_full_unstemmed An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid
title_short An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid
title_sort improvement of the differential transformation method and its application for boundary layer flow of a nanofluid
url http://dx.doi.org/10.1155/2013/865464
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