Galerkin-Legendre spectral method for the velocity and thermal boundary layers over a non-linearly stretching sheet

Journal article

Authors / Editors

Siginer, Dennis

Research Areas

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Publication Details

Author list: Akyildiz FT, Siginer DA

Publisher: Elsevier

Place: OXFORD

Publication year: 2010

Journal: Nonlinear Analysis: Real World Applications (1468-1218)

Journal acronym: NONLINEAR ANAL-REAL

Volume number: 11

Issue number: 2

Start page: 735

End page: 741

Number of pages: 7

ISSN: 1468-1218

eISSN: 1878-5719

Languages: English-Great Britain (EN-GB)

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Abstract

Analytical solutions for the velocity and temperature fields in a viscous fluid flowing over a nonlinearly stretching sheet are obtained via Galerkin-Legendre spectral method. The application of spectral methods to this problem is novel as well as the concept of the non-uniqueness of the solution and the efficient algorithms developed in this paper. The governing partial differential equations are converted into a nonlinear ordinary differential equation for the velocity field f and a variable coefficient linear ordinary differential equation for the temperature field theta by a similarity transformation in the semi-infinite physical domain. A coordinate transformation is introduced to map the physical state space into a bounded computational domain. It is shown that Galerkin-Legendre spectral method is the most efficient among spectral methods that lead to the analytical solution of the governing set of nonlinear differential equations in the computational domain. Computationally efficient algorithms are constructed for the velocity gradient and temperature profile computations and two distinct solutions of the field equations are presented. (C) 2009 Elsevier Ltd. All rights reserved.

Keywords

Galerkin-Legendre spectral method, Nonlinear third order differential equations, Similarity transforms

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