The Time Evolution of a Constant Mass of Air Pollutant Emitted by a Point Source

M.H.A. Hassan, I.A. Eltayeb

Abstract


The transient behaviour of a constant mass (i.e. a blob) of pollutant released from a point source at a height, , above ground level at time  is studied. The time dependent atmospheric diffusion equation in the presence of diffusion in both horizontal and vertical directions is used to model the problem. The model is found to be governed by an initial-boundary-value problem for the concentration of the pollutant. The solution is obtained in closed form using integral transform methods. The solution is illustrated graphically using appropriate numerical integrations. As time passes, the pollutant blob moves with a central point of accumulation of pollutant while the blob increases in volume to spread the pollutant around it. The motion of the accumulation point in space and time is strongly influenced by wind and gravity while the spread of the pollutant is governed by diffusion. The time taken by the blob to diffuse into space is estimated as a function of the parameters governing wind, gravity and diffusion.

 

 


Keywords


Initial-boundary value problem, pollutant, diffusion equation, analytic solution, time-dependence, point source.

Full Text:

PDF

References


BEIRUTI, A.A.R. and ALOMSHY, H.K. 1985. Traffic atmospheric diffusion-model. Atmospheric environ. 19: 1519-1524.

BRIAN,, P.L.T. and LEE, G.K. 1998. Use of point source models for the dispersion of releases of finite size. J. Hazardous Materials 59: 235-250.

CHATWIN, P.C., LEWIS, D.M. and MOLE, N. 1996. Atmospheric diffusion: some new mathematical models. Adv. Comp. Math. 6: 227-242.

DUFFY, D.G. 1994. Transform methods for solving partial differential equations. CRC Press, Inc.

DUMBAULD, R.K. and BOWERS, J.F. 1976. Point-source atmospheric diffusion-model. Atmospheric environ. 10: 418-418.

EL-BAZ, F., ELTAYEB, I.A. and HASSAN, M.H.A. 1990. Sand Transport and Desertification in Arid and Semi-Arid Lands, World Scientific Publishing Co., Singapore.

ELTAYEB, I.A. and HASSAN, M.H.A. 2000. Diffusion of dust particles from a point-source. Geophys. J. International 142: 26-438.

KELLER, J. and Lambrecht, R. 1995. Road dust as an indicator for air-pollution transport and deposition – an application of spot imagery. Remote Sensing of Environ. 54: 1-12.

LIN, J.-S. and HILDEMANN, L.M. 1996. Analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities. Atmos. Environ. 30: 239-254.

LIN, J.S. and HILDEMANN, L.M. 1997 ‘ A generalized mathematical scheme to analytically solve the atmospheric diffusion equation with dry deposition. Atmospheric Environment. 31: 59-71.

NAGAI, K. 2005. Wind tunnel modeling of hourly observed atmospheric diffusion by oscillating blade cascade. J. Wind Eng. Indusr. Aerodyn. 93: 99-113.

NGUYENVANCHI, G. and SAAB, A. 1976. 3-Dimensional numerical-model of atmospheric diffusion - analytical and experimental validation. Bull. Amer. Metrol. Soc. 57: 838-639.

PASQUILL, F. and SMITH, F.B. 1984. Atmospheric diffusion, 3rd edition. John Wiley, New York.

PIESSENS, R., DE DONCKER-KAPENGA, E., UBERHUBER, C., and KAHANER, D. 1983. QUADPACK, a subroutine package for automatic integration. Springer Verlag.

RAGLAND, K.W. and DENNIS, R.L. 1975. Point source atmospheric diffusion-model with variable wind and diffusivity profiles. Atmospheric Environ. 9: 175-189.

SEINFELD, J.W. 1986 Atmospheric Chemistry and physics of air pollution. John Wiley &Sons, New York.

SEMETOV, B.L., ARUTYUNYAN, R.V., GORSHKOV, V.E., TARASIV, V.I and TKALYA, E.V. 1996. A confidence region of source term parameters from statistical analysis of environmental measurements following an accidental release to the atmosphere. Radiation protection Dosimetry 67: 85-94.

SHARAN, M., YADAV, A.K., SINGH, M.P, AGRAWAL, P and NIGAM, S. 1996. A mathematical model for the dispersion of air pollutants in low wind conditions. Atmos. Environ. 30: 1209-1220.

SPANOMITSIOS, G.K. 2001. Determining the maximum air pollutant concentration for plume trapping conditions. Fresenius Environ. Bulletin 10: 684-687.

THOMPSON, N. 1976. Point source atmospheric diffusion-model with variable wind and diffusivity profiles. Atmospheric Environ. 10: 493-493.

VAN ULDEN, A.P and HOLTSLAG, A.A.M. 1985 Estimation of atmospheric boundary layer parameters for diffusion applications. I. Climate & appl. Meorol. 24: 1196-1207.

VANDERHOVEN, I. 1976. Survey of wind-measurements of atmospheric diffusion under low wind-speed inversion conditions. Nuclear safety 17: 223-230.

VOGT, S. 1977. Forecast of atmospheric diffusion coefficients after hypothetical accidents at nuclear-plants. Atomkernenergie 29: 282-286.

YOSHIKAWA, Y., KUNIMI, H and ISHIZAWA, S. 1996. Estimation of air quality by three-dimensional air simulation model – (effect of low-emission vehicles on air quality improvement in the Greater Los Angeles area). JSME International J: B-fluids and thermal Eng. 39: 647-652.




DOI: http://dx.doi.org/10.24200/squjs.vol11iss0pp79-93

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 M.H.A. Hassan, I.A. Eltayeb

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

SQUJS 2017-CC BY-ND

This journal and its content is licensed under a Attribution-NoDerivatives 4.0 International.

Flag Counter