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Exact Graetz problem solution by using hypergeometric function

This paper proposes an exact solution of the classical Graetz problem in terms of an infinite series represented by a nonlinear partial differential equation considering two space variables, two boundary conditions and one initial condition. The mathematical derivation is based on the method of sepa...

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Main Authors: Belhocine, Ali, Omar, Wan Z. W.
Format: Article
Language:English
Published: EDIZIONI ETS 2017
Subjects:
TJ Mechanical engineering and machinery
Online Access:http://eprints.utm.my/id/eprint/77386/1/WanZaidiOmar2017_ExactGraetzProblemSolution.pdf
http://eprints.utm.my/id/eprint/77386/
http://dx.doi.org/10.18280/ijht.350216
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spelling my.utm.773862019-01-28T04:45:31Z http://eprints.utm.my/id/eprint/77386/ Exact Graetz problem solution by using hypergeometric function Belhocine, Ali Omar, Wan Z. W. TJ Mechanical engineering and machinery This paper proposes an exact solution of the classical Graetz problem in terms of an infinite series represented by a nonlinear partial differential equation considering two space variables, two boundary conditions and one initial condition. The mathematical derivation is based on the method of separation of variables whose several stages were illustrated to reach the solution of the Graetz problem.A MATLAB code was used to compute the eigenvalues of the differential equation as well as the coefficient series. In addition, the analytical solution was compared to the numerical values obtained previously by Shah and London. It is important to note that the analytical solution is in good agreement with published numerical data. EDIZIONI ETS 2017-06 Article PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/77386/1/WanZaidiOmar2017_ExactGraetzProblemSolution.pdf Belhocine, Ali and Omar, Wan Z. W. (2017) Exact Graetz problem solution by using hypergeometric function. International Journal Of Heat And Technology, 35 (2). pp. 347-353. ISSN 0392-8764 http://dx.doi.org/10.18280/ijht.350216 DOI:10.18280/ijht.350216
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic TJ Mechanical engineering and machinery
spellingShingle TJ Mechanical engineering and machinery
Belhocine, Ali
Omar, Wan Z. W.
Exact Graetz problem solution by using hypergeometric function
description This paper proposes an exact solution of the classical Graetz problem in terms of an infinite series represented by a nonlinear partial differential equation considering two space variables, two boundary conditions and one initial condition. The mathematical derivation is based on the method of separation of variables whose several stages were illustrated to reach the solution of the Graetz problem.A MATLAB code was used to compute the eigenvalues of the differential equation as well as the coefficient series. In addition, the analytical solution was compared to the numerical values obtained previously by Shah and London. It is important to note that the analytical solution is in good agreement with published numerical data.
format Article
author Belhocine, Ali
Omar, Wan Z. W.
author_facet Belhocine, Ali
Omar, Wan Z. W.
author_sort Belhocine, Ali
title Exact Graetz problem solution by using hypergeometric function
title_short Exact Graetz problem solution by using hypergeometric function
title_full Exact Graetz problem solution by using hypergeometric function
title_fullStr Exact Graetz problem solution by using hypergeometric function
title_full_unstemmed Exact Graetz problem solution by using hypergeometric function
title_sort exact graetz problem solution by using hypergeometric function
publisher EDIZIONI ETS
publishDate 2017
url http://eprints.utm.my/id/eprint/77386/1/WanZaidiOmar2017_ExactGraetzProblemSolution.pdf
http://eprints.utm.my/id/eprint/77386/
http://dx.doi.org/10.18280/ijht.350216
_version_ 1643657554299977728
score 13.211869

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