Journal of Chemical, Environmental and Biological Engineering

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Mathematical Solution of Two Dimensional Advection-Diffusion Equations

Received: 08 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 '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.

DOI 10.11648/j.jcebe.20190301.12
Published in Journal of Chemical, Environmental and Biological Engineering (Volume 3, Issue 1, June 2019)
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), 2024. Published by Science Publishing Group

Keywords

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

References
[1] John M. (2011) The mathematical of atmospheric dispersion modeling. Society for Industrial Applied Mathematics. 53. 349-372.
[2] Demuth, C. (1978) A contribution to the analytical steady solution of the diffusion equation". Atom. Environ. 12, 1255.
[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.
[9] Murray R. Spiegel (1992) Advanced mathematics for engineers and scientists. McGrhill Publishing House.
[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.
[11] Gryning, S. E. Holtslag, A. A. M. Irwin, J. S. Sivertsen, B. (1987) Applied dispersion modeling based on meteorological scaling parameters. Atmos. Environ. 21 (1), 79-89.
[12] Hanna, S. R. (1989). Confidence limit for air quality models as estimated by bootstrap and Jackknife resem¬bling methods. Atom. Environ. 23, 1385-1395.
[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.
Author Information
  • Department of Mathematics and Theoretical Physics, NRC, Atomic Energy Authority, Cairo, Egypt

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

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    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://download.sciencepg.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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    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.
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