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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| Format: | Article |
| Language: | English |
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EDIZIONI ETS
2017
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| Online Access: | http://eprints.utm.my/77386/1/WanZaidiOmar2017_ExactGraetzProblemSolution.pdf |
| _version_ | 1796862667964547072 |
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| author | Belhocine, Ali Omar, Wan Z. W. |
| author_facet | Belhocine, Ali Omar, Wan Z. W. |
| author_sort | Belhocine, Ali |
| collection | ePrints |
| 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. |
| first_indexed | 2024-03-05T20:15:06Z |
| format | Article |
| id | utm.eprints-77386 |
| institution | Universiti Teknologi Malaysia - ePrints |
| language | English |
| last_indexed | 2024-03-05T20:15:06Z |
| publishDate | 2017 |
| publisher | EDIZIONI ETS |
| record_format | dspace |
| spelling | utm.eprints-773862019-01-28T04:45:31Z http://eprints.utm.my/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/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 |
| spellingShingle | TJ Mechanical engineering and machinery Belhocine, Ali Omar, Wan Z. W. Exact Graetz problem solution by using hypergeometric function |
| title | 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_short | Exact Graetz problem solution by using hypergeometric function |
| title_sort | exact graetz problem solution by using hypergeometric function |
| topic | TJ Mechanical engineering and machinery |
| url | http://eprints.utm.my/77386/1/WanZaidiOmar2017_ExactGraetzProblemSolution.pdf |
| work_keys_str_mv | AT belhocineali exactgraetzproblemsolutionbyusinghypergeometricfunction AT omarwanzw exactgraetzproblemsolutionbyusinghypergeometricfunction |