Analytical solutions of the one-dimensional advection–dispersion solute transport equation subject to time-dependent boundary conditions
► We extend the Duhamel theorem to the case of advective–dispersive solute transport. ► Analytical formulas relate exact solutions to time-independent auxiliary solutions. ► Explicit analytical expressions are developed for selected particular cases. ► Results are compared with other specific soluti...
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| Published in | Chemical engineering journal (Lausanne, Switzerland : 1996) Vol. 221; pp. 487 - 491 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.04.2013
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1385-8947 1873-3212 |
| DOI | 10.1016/j.cej.2013.01.095 |
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| Abstract | ► We extend the Duhamel theorem to the case of advective–dispersive solute transport. ► Analytical formulas relate exact solutions to time-independent auxiliary solutions. ► Explicit analytical expressions are developed for selected particular cases. ► Results are compared with other specific solutions from the literature.
Analytical solutions of the advection–dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective–dispersive transport subject to transient (time-dependent) boundary conditions. Generalized analytical formulas are established which relate the exact solutions to corresponding time-independent auxiliary solutions. Explicit analytical expressions were developed for the instantaneous pulse problem formulated from the generalized Dirac delta function for situations with first-type or third-type inlet boundary conditions of both finite and semi-infinite domains. The developed generalized equations were evaluated computationally against other specific solutions available from the literature. Results showed the consistency of our expressions. |
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| AbstractList | Analytical solutions of the advection–dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective–dispersive transport subject to transient (time-dependent) boundary conditions. Generalized analytical formulas are established which relate the exact solutions to corresponding time-independent auxiliary solutions. Explicit analytical expressions were developed for the instantaneous pulse problem formulated from the generalized Dirac delta function for situations with first-type or third-type inlet boundary conditions of both finite and semi-infinite domains. The developed generalized equations were evaluated computationally against other specific solutions available from the literature. Results showed the consistency of our expressions. ► We extend the Duhamel theorem to the case of advective–dispersive solute transport. ► Analytical formulas relate exact solutions to time-independent auxiliary solutions. ► Explicit analytical expressions are developed for selected particular cases. ► Results are compared with other specific solutions from the literature. Analytical solutions of the advection–dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective–dispersive transport subject to transient (time-dependent) boundary conditions. Generalized analytical formulas are established which relate the exact solutions to corresponding time-independent auxiliary solutions. Explicit analytical expressions were developed for the instantaneous pulse problem formulated from the generalized Dirac delta function for situations with first-type or third-type inlet boundary conditions of both finite and semi-infinite domains. The developed generalized equations were evaluated computationally against other specific solutions available from the literature. Results showed the consistency of our expressions. |
| Author | van Genuchten, M.Th Pérez Guerrero, J.S. Pontedeiro, E.M. Skaggs, T.H. |
| Author_xml | – sequence: 1 givenname: J.S. surname: Pérez Guerrero fullname: Pérez Guerrero, J.S. organization: Radioactive Waste Division, Brazilian Nuclear Energy Commission, DIREJ/DRS/CNEN, Rio de Janeiro, Brazil – sequence: 2 givenname: E.M. surname: Pontedeiro fullname: Pontedeiro, E.M. organization: Department of Nuclear Engineering, POLI&COPPE, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, Brazil – sequence: 3 givenname: M.Th surname: van Genuchten fullname: van Genuchten, M.Th organization: Department of Mechanical Engineering, COPPE/LTTC, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, Brazil – sequence: 4 givenname: T.H. surname: Skaggs fullname: Skaggs, T.H. email: Todd.Skaggs@ars.usda.gov organization: US Salinity Laboratory, USDA-ARS, Riverside, CA, USA |
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| Snippet | ► We extend the Duhamel theorem to the case of advective–dispersive solute transport. ► Analytical formulas relate exact solutions to time-independent... Analytical solutions of the advection–dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this... Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this... |
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| SubjectTerms | Advection–dispersion equation Analytical solution chemical engineering Duhamel theorem equations Solute transport solutes |
| Title | Analytical solutions of the one-dimensional advection–dispersion solute transport equation subject to time-dependent boundary conditions |
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