Mathematical Solution of Two Dimensional Advection-Diffusion Equations

Khaled Sadek Mohamed Essa; Sawsan Ibrahim Mohamed El Saied

doi:doi:10.11648/j.jcebe.20190301.12

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Mathematical Solution of Two Dimensional Advection-Diffusion Equations

Khaled Sadek Mohamed Essa, Sawsan Ibrahim Mohamed El Saied

Published in Journal of Chemical, Environmental and Biological Engineering (Volume 3, Issue 1)

Received: 8 April 2019 Accepted: 17 May 2019 Published: 12 June 2019

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Abstract

The Laplace conversion technique was applied to the Advection-Diffusion Equations (ADE) in two dimensions to obtain crosswind integrated normalized concentration, consider wind speed and the vertical eddy diffusivity 'K_z' are constant. Data set used from atmospheric diffusion experiments conducted in the northern part of Copenhagen, Denmark was observed for hexafluoride traceability (SF6). A comparison was made between current results, previous work results and data. One finds that the present and previous work crosswind integrated normalized concentration results are agreement well with observed data (one to one) and others lie inside the factor of two and four.

Published in	Journal of Chemical, Environmental and Biological Engineering (Volume 3, Issue 1)
DOI	10.11648/j.jcebe.20190301.12
Page(s)	8-12
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Laplace Transforms Technique, Wind Speed, Copenhagen, Denmark, Advection-Diffusion Equations, Eddy Diffusivity

References

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[3]	Khaled S. M Essa and S. E. M. Elsaid (2015) Solving the advection diffusion equation in three dimensions in neutral case. Pyrex Journal of Ecology and the Natural Environment Vol 1 (1) pp. 001-006.
[4]	Gantulga Tsedendorjand Hiroshi Isshiki (2017) Numerical Solution of Two-Dimensional Advection–Diffusion Equation Using Generalized Integral Representation Method. International Journal of Computational MethodsVol. 14, No. 01.
[5]	Khaled Sadek Mohamed Essa, Sawsan Ibrahim Mohamed El Saied, Ayman Marrouf (2018) Analytical Solution of Time Dependent Diffusion Equation in Stable Case. American Journal of Environmental Science and Engineering; 2 (2): 32-36.
[6]	Chatterjee, A. and Singh, M. K. (2018) Two-dimensional advection -dispersion equation with depth-dependent variable source concentration. Pollution, 4 (1): 1-8.
[7]	Amruta Daga, V. H. (2013) Analytical solution of advection diffusion equation in homogeneous medium. International journal of science, spirituality, business and technology (ijssbt), vol. 2, no. 1, 2277-7261.
[8]	Perez.ُُ J. S. Guerrer. A. Pimentel. L. C. G. Skaggs. T. H. Van. Genuchten. M. Th. (2009). Analytical solution of the advection–diffusion transport equation using a change-of-variable and integral transform technique. International Journal of Heat and Mass Transfer 52, 3297–3304.
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[10]	Gryning. S. E. and Lyck. (1984) Atmospheric dispersion from elevated sources in an urban area: Comparison between tracer experiments and model calculations. J. Climate Appl. Meteor. 23, pp. 651-660.
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[13]	Tizianotirabassi, Davidson. Morerira. M. Marco. Tullio. Vilhena. Camilla. Pinto. Dam. Acosta. (2010) Comparison between non- Gaussian puff model and a model based on a time – dependent solution of advection equation. Journal of Environment, protection, and 1; 172-178.

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APA Style

Khaled Sadek Mohamed Essa, Sawsan Ibrahim Mohamed El Saied. (2019). Mathematical Solution of Two Dimensional Advection-Diffusion Equations. Journal of Chemical, Environmental and Biological Engineering, 3(1), 8-12. https://doi.org/10.11648/j.jcebe.20190301.12

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ACS Style

Khaled Sadek Mohamed Essa; Sawsan Ibrahim Mohamed El Saied. Mathematical Solution of Two Dimensional Advection-Diffusion Equations. J. Chem. Environ. Biol. Eng. 2019, 3(1), 8-12. doi: 10.11648/j.jcebe.20190301.12

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AMA Style

Khaled Sadek Mohamed Essa, Sawsan Ibrahim Mohamed El Saied. Mathematical Solution of Two Dimensional Advection-Diffusion Equations. J Chem Environ Biol Eng. 2019;3(1):8-12. doi: 10.11648/j.jcebe.20190301.12

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@article{10.11648/j.jcebe.20190301.12,
  author = {Khaled Sadek Mohamed Essa and Sawsan Ibrahim Mohamed El Saied},
  title = {Mathematical Solution of Two Dimensional Advection-Diffusion Equations},
  journal = {Journal of Chemical, Environmental and Biological Engineering},
  volume = {3},
  number = {1},
  pages = {8-12},
  doi = {10.11648/j.jcebe.20190301.12},
  url = {https://doi.org/10.11648/j.jcebe.20190301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jcebe.20190301.12},
  abstract = {The Laplace conversion technique was applied to the Advection-Diffusion Equations (ADE) in two dimensions to obtain crosswind integrated normalized concentration, consider wind speed and the vertical eddy diffusivity 'Kz' are constant. Data set used from atmospheric diffusion experiments conducted in the northern part of Copenhagen, Denmark was observed for hexafluoride traceability (SF6). A comparison was made between current results, previous work results and data. One finds that the present and previous work crosswind integrated normalized concentration results are agreement well with observed data (one to one) and others lie inside the factor of two and four.},
 year = {2019}
}

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TY  - JOUR
T1  - Mathematical Solution of Two Dimensional Advection-Diffusion Equations
AU  - Khaled Sadek Mohamed Essa
AU  - Sawsan Ibrahim Mohamed El Saied
Y1  - 2019/06/12
PY  - 2019
N1  - https://doi.org/10.11648/j.jcebe.20190301.12
DO  - 10.11648/j.jcebe.20190301.12
T2  - Journal of Chemical, Environmental and Biological Engineering
JF  - Journal of Chemical, Environmental and Biological Engineering
JO  - Journal of Chemical, Environmental and Biological Engineering
SP  - 8
EP  - 12
PB  - Science Publishing Group
SN  - 2640-267X
UR  - https://doi.org/10.11648/j.jcebe.20190301.12
AB  - The Laplace conversion technique was applied to the Advection-Diffusion Equations (ADE) in two dimensions to obtain crosswind integrated normalized concentration, consider wind speed and the vertical eddy diffusivity 'Kz' are constant. Data set used from atmospheric diffusion experiments conducted in the northern part of Copenhagen, Denmark was observed for hexafluoride traceability (SF6). A comparison was made between current results, previous work results and data. One finds that the present and previous work crosswind integrated normalized concentration results are agreement well with observed data (one to one) and others lie inside the factor of two and four.
VL  - 3
IS  - 1
ER  -

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Author Information

Khaled Sadek Mohamed Essa

Department of Mathematics and Theoretical Physics, NRC, Atomic Energy Authority, Cairo, Egypt
Sawsan Ibrahim Mohamed El Saied

Department of Mathematics and Theoretical Physics, NRC, Atomic Energy Authority, Cairo, Egypt

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APA Style

Khaled Sadek Mohamed Essa, Sawsan Ibrahim Mohamed El Saied. (2019). Mathematical Solution of Two Dimensional Advection-Diffusion Equations. Journal of Chemical, Environmental and Biological Engineering, 3(1), 8-12. https://doi.org/10.11648/j.jcebe.20190301.12

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ACS Style

Khaled Sadek Mohamed Essa; Sawsan Ibrahim Mohamed El Saied. Mathematical Solution of Two Dimensional Advection-Diffusion Equations. J. Chem. Environ. Biol. Eng. 2019, 3(1), 8-12. doi: 10.11648/j.jcebe.20190301.12

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AMA Style

Khaled Sadek Mohamed Essa, Sawsan Ibrahim Mohamed El Saied. Mathematical Solution of Two Dimensional Advection-Diffusion Equations. J Chem Environ Biol Eng. 2019;3(1):8-12. doi: 10.11648/j.jcebe.20190301.12

Copy | Download

@article{10.11648/j.jcebe.20190301.12,
  author = {Khaled Sadek Mohamed Essa and Sawsan Ibrahim Mohamed El Saied},
  title = {Mathematical Solution of Two Dimensional Advection-Diffusion Equations},
  journal = {Journal of Chemical, Environmental and Biological Engineering},
  volume = {3},
  number = {1},
  pages = {8-12},
  doi = {10.11648/j.jcebe.20190301.12},
  url = {https://doi.org/10.11648/j.jcebe.20190301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jcebe.20190301.12},
  abstract = {The Laplace conversion technique was applied to the Advection-Diffusion Equations (ADE) in two dimensions to obtain crosswind integrated normalized concentration, consider wind speed and the vertical eddy diffusivity 'Kz' are constant. Data set used from atmospheric diffusion experiments conducted in the northern part of Copenhagen, Denmark was observed for hexafluoride traceability (SF6). A comparison was made between current results, previous work results and data. One finds that the present and previous work crosswind integrated normalized concentration results are agreement well with observed data (one to one) and others lie inside the factor of two and four.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Solution of Two Dimensional Advection-Diffusion Equations
AU  - Khaled Sadek Mohamed Essa
AU  - Sawsan Ibrahim Mohamed El Saied
Y1  - 2019/06/12
PY  - 2019
N1  - https://doi.org/10.11648/j.jcebe.20190301.12
DO  - 10.11648/j.jcebe.20190301.12
T2  - Journal of Chemical, Environmental and Biological Engineering
JF  - Journal of Chemical, Environmental and Biological Engineering
JO  - Journal of Chemical, Environmental and Biological Engineering
SP  - 8
EP  - 12
PB  - Science Publishing Group
SN  - 2640-267X
UR  - https://doi.org/10.11648/j.jcebe.20190301.12
AB  - The Laplace conversion technique was applied to the Advection-Diffusion Equations (ADE) in two dimensions to obtain crosswind integrated normalized concentration, consider wind speed and the vertical eddy diffusivity 'Kz' are constant. Data set used from atmospheric diffusion experiments conducted in the northern part of Copenhagen, Denmark was observed for hexafluoride traceability (SF6). A comparison was made between current results, previous work results and data. One finds that the present and previous work crosswind integrated normalized concentration results are agreement well with observed data (one to one) and others lie inside the factor of two and four.
VL  - 3
IS  - 1
ER  -

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