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2013 An Improvement of the Differential Transformation Method and Its Application for Boundary Layer Flow of a Nanofluid
Abdelhalim Ebaid, Hassan A. El-Arabawy, Nader Y. Abd Elazem
Int. J. Differ. Equ. 2013: 1-8 (2013). DOI: 10.1155/2013/865464


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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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." Int. J. Differ. Equ. 2013 1 - 8, 2013.


Received: 4 April 2013; Accepted: 22 April 2013; Published: 2013
First available in Project Euclid: 20 January 2017

zbMATH: 06172139
MathSciNet: MR3055166
Digital Object Identifier: 10.1155/2013/865464

Rights: Copyright © 2013 Hindawi


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