A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution
This paper discusses a possible generalization of the transport model describing the chlorine concentration decay in pipes. The proposed generalized model is governed by a second-order fractional partial differential equation. The exact solution of the generalized model is obtained via the Laplace t...
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| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2021-05-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/2376 |
| _version_ | 1818730321879760896 |
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| author | Yussri M. Mahrous |
| author_facet | Yussri M. Mahrous |
| author_sort | Yussri M. Mahrous |
| collection | DOAJ |
| description | This paper discusses a possible generalization of the transport model describing the chlorine concentration decay in pipes. The proposed generalized model is governed by a second-order fractional partial differential equation. The exact solution of the generalized model is obtained via the Laplace transform method and the method of residues. The exact solution reduces to the corresponding published one as the fractional order α tends to one. Analytical expression for the dimensionless cup-mixing average concentration is deduced. Influences of various parameters on the behavior of the dimensionless cup-mixing average concentration are discussed. It is shown that the physical interpretation of the dimensionless cup-mixing average concentration in view of the fractional calculus is completely different than its interpretation in the classical calculus. |
| first_indexed | 2024-12-17T22:59:56Z |
| format | Article |
| id | doaj.art-444012e54bae4f988c691f4c47a67e58 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-17T22:59:56Z |
| publishDate | 2021-05-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-444012e54bae4f988c691f4c47a67e582022-12-21T21:29:26ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392021-05-01194604618542A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact SolutionYussri M. Mahrous0University of TabukThis paper discusses a possible generalization of the transport model describing the chlorine concentration decay in pipes. The proposed generalized model is governed by a second-order fractional partial differential equation. The exact solution of the generalized model is obtained via the Laplace transform method and the method of residues. The exact solution reduces to the corresponding published one as the fractional order α tends to one. Analytical expression for the dimensionless cup-mixing average concentration is deduced. Influences of various parameters on the behavior of the dimensionless cup-mixing average concentration are discussed. It is shown that the physical interpretation of the dimensionless cup-mixing average concentration in view of the fractional calculus is completely different than its interpretation in the classical calculus.http://etamaths.com/index.php/ijaa/article/view/2376 |
| spellingShingle | Yussri M. Mahrous A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution International Journal of Analysis and Applications |
| title | A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution |
| title_full | A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution |
| title_fullStr | A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution |
| title_full_unstemmed | A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution |
| title_short | A Possible Generalized Model of the Chlorine Concentration Decay in Pipes: Exact Solution |
| title_sort | possible generalized model of the chlorine concentration decay in pipes exact solution |
| url | http://etamaths.com/index.php/ijaa/article/view/2376 |
| work_keys_str_mv | AT yussrimmahrous apossiblegeneralizedmodelofthechlorineconcentrationdecayinpipesexactsolution AT yussrimmahrous possiblegeneralizedmodelofthechlorineconcentrationdecayinpipesexactsolution |