Contact Us

For Marketing, Sales and Subscriptions Inquiries
2637 E Atlantic Blvd #43110
Pompano Beach, FL 33062

Conference List

Journal of Atmosphere

June 2016, Volume 2, 1, pp 1-8

Theoretical Solution of the Diffusion Equation in Unstable Case

Khaled S.M. Essa


Aziz N. Mina


Hany S. Hamdy


Ayman A. khalifa

Khaled S.M. Essa 1

Aziz N. Mina 2 Hany S. Hamdy 2 Ayman A. khalifa 2 

  1. Department of Mathematics and theoretical physics, Nuclear Research Centre, Atomic energy Authority, Cairo, Egypt 1

  2. Faculty of science, Beni -Suef University 2

Pages: 1-8

DOI: 10.18488/journal.94/2016.2.1/

Share :


The diffusion equation is solved in two dimensions to obtain the concentration by using separation of variables under the variation of eddy diffusivity which depend on the vertical height in unstable case. Comparing between the predicted and the observed concentrations data of Sulfur hexafluoride (SF6) taken on the Copenhagen in Denmark is done. The statistical method is used to know the best model. One finds that there is agreement between the present, Laplace and separation predicted normalized crosswind integrated concentrations with the observed normalized crosswind integrated concentrations than the predicted Gaussian model.

Contribution/ Originality


Diffusion equation, Separation of variables, Laplace technique, Gaussian model, Eddy diffusivity.



  1. C. Demuth, "A contribution to the analytical steady solution of the diffusion equation," Atoms. Environ., vol. 12, pp. 1255-1258, 1978.
  2. S. M. E. Khaled, "Studying the effect of vertical eddy diffusivity on the solution of diffusion equation," Physical Science International Journal, vol. 4, pp. 355-365, 2014.
  3. G. I. Taylor, "Diffusion by continuous movements," Proc. London Math. Soc., vol. 20, pp. 196-211, 1921.
  4. M. S. John, "The mathematics of atmospheric dispersion modeling," Society for Industrial and Applied Mathematics, vol. 53, pp. 349-372, 2011.
  5. T. Tirabassi, M. M. Davidson, T. V. Marco, and P. D. C. Camila, "Comparison between non- Gaussian puff model and a model based on a time–dependent solution of advection equation," Journal of Environment, Protection, vol. 1, pp. 172-178, 2010.
  6. W. P. Elliot, "The vertical diffusion of gas from continuous source," Int. J. Air Water Pollut., vol. 4, pp. 33-46, 1961.
  7. R. C. Malhorta and J. E. Cermak, "Mass diffusion in neutral and unstably stratified boundary–layer flouss," J. Heat Mass Trans., vol. 7, pp. 169-186, 1964.
  8. A. A. Marrouf, S. M. Adel, I. Galal, and S. M. E. Khaled, "An analytical solution of two dimensional atmospheric diffusion equation in a finite boundary layer," International Journal of Advanced Research, vol. 1, pp. 356-365, 2013.
  9. S. P. Arya, "Modeling and parameterization of near –source diffusion in weak wind," J. Appl. Met., vol. 34, pp. 1112-1122, 1995.
  10. S. R. Hanna, "Confidence limit for air quality models as estimated by bootstrap and Jackknife resembling methods," Atom. Environ., vol. 23, pp. 1385-1395, 1989.


Google Scholor ideas Microsoft Academic Search bing Google Scholor


Competing Interests:


Related Article

( 1 ) Theoretical Solution of the Diffusion Equation in Unstable Case
( 2 ) Exsolution Lamellae in Orthopyroxene of Lherzolite from the Pauza Ultramafic Rocks, Ne Iraq: Evidence of Deep Mantle Signature in the Zagros Suture Zone
( 3 ) Thermodynamic Parameters for Solvation of Nano ZNO and Its Dopes In 50% DMSO - 50% DMF (V/V) Solutions at Different Temperatures
( 5 ) Biogas Technology in South Africa, Problems, Challenges and Solutions
( 6 ) Time Dependent Advection Diffusion Equation in Two Dimensions
( 8 ) Presentation of Empirical Equations for Estimating Internal Friction Angle of SP and SC Soils in Mashhad, Iran Using Standard Penetration and Direct Shear Tests and Comparison with Previous Equations
( 12 ) Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of Study: Charak Area, Iran)
( 13 ) Resolving Optimum Magnetic Signatures for Drill-Hole Targeting in Gold Exploration – A Case Study for Mbudzane in Gwanda, Zimbabwe
( 14 ) Development of Solar Energy in Sabah Malaysia: The Case of Trudgill’s Perception
( 15 ) Flood Hazard Assessment and Decisions Support Using Geographic Information System: A Case Study of Uyo Capital City, Akwa Ibom State, Nigeria
( 16 ) Inversion of Electrical Resistivity Data by VES Method for Water Exploring Case Study: South West of Iran
( 17 ) Problems of Mechanized Tunneling In Gassy Ground Conditions a Case Study: Nousoud Water Transmission Tunnel
( 18 ) Environmental and Health Impact of Solid Mineral Exploration and Exploitation in South-Northern Nigeria: A Case Study of Igarra in Edo State
( 19 ) Improved Analytical Approach of Vibration Behavior Destined To Ball Bearings in The Case of Angular Contact
( 20 ) Modeling and Optimization of Phenylacetyylcarbinol Synthesis via Benzaldehyde: A Case of Artificial Neural Network vs. Response Surface Methodology
( 21 ) Strategies for Tourism Development in National Parks with the Use of Swot Model (Case: Golestan National Park)
( 22 ) Investigating the Density Ratios of Geological Structure through Fractal Geometry Case Stady: (Dehno Region in Farss of Iran)
( 23 ) Comparative Assessment of Co2 Emission Factors Estimated Using Stack Flue Gas Measurement Data for Two Types of Brick Kiln: A Case Study in Phu Tho Province, Vietnam
( 24 ) Expanded of Informal Jobs in Iranian Border Cities, Case: Zabol-Iran
( 25 ) The Roles of Productive Safety Net Program (PSNP) On the Practices of Soil and Water Conservation in the Case of Sekela District, Amhara State, Ethiopia
( 26 ) Predicting Changes in the Land Use in Midsize Cities (Case Study: Urmia City of Iran in 2025)
( 27 ) The Effect of Ergonomics on Sustainable Urban Development: A Case Study
( 28 ) A Study on River Ecotourism Development: Case Study: Karaj River
( 30 ) Prioritization of Museums in Terms of Performance in Attracting Tourists (Case Study: Museum of North of Sistan and Baluchestan Province)
( 31 ) Residential Housing Quality Assessment Based on the Criteria of Sustainable Housing (Case Study: Residential Complex of 100 Units of Region 1 City of Zahedan)
( 32 ) Indicators of Sustainability in Vernacular Settlements Hot Dry Region of Iran, [Case Study: Kerman-Meymand]
( 33 ) Landfill Site Selection Using Simple Additive Weighting (SAW) Method and Artificial Neural Network Method; A Case Study from Lorestan Province, Iran
( 34 ) Net-Zero Energy Building – Case Study Al Khobar City, Saudi Arabia
( 35 ) The Role of Stratigraphy in Growth Strata Studies: A Case Study from the Middle-Late Cretaceous Deposits in Persian Gulf, SW Iran
( 36 ) Zoning of Natural and Man-Made Disasters for Relief and Rescue Centers Site Selection Using the Model Logic (Case Study: Guilan Rural Area)
( 37 ) 'Manifestations and Extent of Climate Change'. The Case of Merti District, Arsi Zone, Oromiya Region, Ethiopia
( 38 ) Determinants of Farmers’ Engagement in Off-Farm (Non-Farm Activities) as Copping Strategies to Climate Change: The Case of Merti, Arsi Zone, Oromiya Regional State, Ethiopia
( 39 ) The Relationship Between Low-Carbon Finance and Sustainable Development: A Case Study of Industrial Bank of China
( 40 ) Political Economy and Stakeholder Perspectives on Inclusive Low-Carbon Energy Transition: Case of Kenyan Rangelands