The modified differential transform method for investigating nano boundary‐layers over stretching surfaces

The modified differential transform method for investigating nano boundary‐layers over... Purpose – The purpose of this paper is to investigate the nano boundary‐layer flows over stretching surfaces with Navier boundary condition. This problem is mapped into the ordinary differential equation by presented similarity transformation. The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method. The authors consider two types of flows: viscous flows over a two‐dimensional stretching surface; and viscous flows over an axisymmetric stretching surface. Design/methodology/approach – The governing equation is solved analytically by applying a newly developed method, namely the differential transform method (DTM)‐Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials. Findings – Graphical results are presented to investigate influence of the slip parameter and the suction parameter on the normal velocity and on the lateral velocity. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. It is predicted that the DTM‐Padé can have wide application in engineering problems especially for boundary‐layer problems. Originality/value – The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method, namely the DTM‐Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

The modified differential transform method for investigating nano boundary‐layers over stretching surfaces

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Publisher
Emerald Publishing
Copyright
Copyright © 2011 Emerald Group Publishing Limited. All rights reserved.
ISSN
0961-5539
DOI
10.1108/09615531111162837
Publisher site
See Article on Publisher Site

Abstract

Purpose – The purpose of this paper is to investigate the nano boundary‐layer flows over stretching surfaces with Navier boundary condition. This problem is mapped into the ordinary differential equation by presented similarity transformation. The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method. The authors consider two types of flows: viscous flows over a two‐dimensional stretching surface; and viscous flows over an axisymmetric stretching surface. Design/methodology/approach – The governing equation is solved analytically by applying a newly developed method, namely the differential transform method (DTM)‐Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials. Findings – Graphical results are presented to investigate influence of the slip parameter and the suction parameter on the normal velocity and on the lateral velocity. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. It is predicted that the DTM‐Padé can have wide application in engineering problems especially for boundary‐layer problems. Originality/value – The resulting nonlinear ordinary differential equation is solved analytically by applying a newly developed method, namely the DTM‐Padé technique that is a combination of the DTM and the Padé approximation. The analytic solutions of the nonlinear ordinary differential equation are constructed in the ratio of two polynomials.

Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Sep 20, 2011

Keywords: Differential transform method (DTM); Nanofluids; Padé approximants; Stretching sheet; Navier boundary condition; Flow; Boundary layers

References

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