Analytical Solutions of ADE with Temporal Coefficients for Continuous Source in Infinite and Semi-Infinite Media
Publication: Journal of Hydrologic Engineering
Volume 23, Issue 3
Abstract
In the present technical note, two aspects commonly used to obtain the analytical solution of advection–diffusion equation (ADE) with time-dependent coefficients describing solute transport due to a continuous source in infinite and semi-infinite porous media, respectively, have been addressed. One is regarding describing a continuous source in an infinite medium and the other is in the context of the analytical solution of the ADE with time-dependent coefficients in a semi-infinite medium. Primarily, this note establishes that in an infinite medium, the correct concentration attenuation pattern from a continuous or instantaneous source may be obtained through the solution of the ADE only if the pollutant’s source is defined by a nonhomogeneous term of the ADE in the form of the Dirac delta function, whereas the solution of the ADE with a first-order decay term when the continuous source is expressed by means of an initial condition in the form of the Heaviside function does not exhibit the expected attenuation pattern. In the second part, it is shown that the analytical solutions of the ADE with temporally dependent coefficients in a semi-infinite medium may be obtained, contrary to it being held in the literature that it could not be obtained.
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Acknowledgments
The first author acknowledges his gratitude to University Grants Commission, Government of India, for financial and academic assistance in the form of a Senior Research Fellowship. The authors are very much grateful to the reviewers for their valuable comments and suggestions that enhanced the merit of the paper.
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Published In
Journal of Hydrologic Engineering
Volume 23 • Issue 3 • March 2018
Copyright
©2017 American Society of Civil Engineers.
History
Received: Oct 27, 2016
Accepted: Jul 7, 2017
Published online: Dec 21, 2017
Published in print: Mar 1, 2018
Discussion open until: May 21, 2018
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