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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Format: | Article |
Language: | English |
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Wiley
2013-01-01
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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. |
format | Article |
id | doaj-art-05c7549a3e78476e919bf5c0f536d2e8 |
institution | Kabale University |
issn | 1687-9643 1687-9651 |
language | English |
publishDate | 2013-01-01 |
publisher | Wiley |
record_format | Article |
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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