A Solution to the Problem of Dispersion of Air Pollutants

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-1
Year of Publication : 2021
Authors : Prem Sagar Bhandari, Vijai Shanker Verma
  10.14445/22315373/IJMTT-V67I1P521

MLA

MLA Style: Prem Sagar Bhandari, Vijai Shanker Verma  "A Solution to the Problem of Dispersion of Air Pollutants" International Journal of Mathematics Trends and Technology 67.1 (2021):159-165. 

APA Style: Prem Sagar Bhandari, Vijai Shanker Verma(20A Solution to the Problem of Dispersion of Air Pollutants  International Journal of Mathematics Trends and Technology, 159-165.

Abstract
In this paper, an analytical solution to the problem of dispersion of air pollutants with constant removal rate and constant wind velocity emitted from a point source in unsteady state condition is studied where eddy diffusivity coefficients are also taken as constants. The methods of separation of variables and integral transform technique have been used for the solution of the problem. It is found that the value of concentration of pollutants first increases with some increasing value of vertical and downwind distance and becomes maximum at some height and then decreases and finally tends to zero.

Reference

[1] Kumar, A. and Goyal, A., Air quality prediction of PM10 through an analytical dispersion model for Delhi, Aerosol and Air quality Research, 14 (2014) 1487-1499.
[2] Costa, C.P., Vilhena, M.T., Moreina D.M. and Tirabassi, T., semi- analytical solution of the steady three- dimensional advection- diffusion equation in the planetary boundary layer, Atmospheric environment 40(2006) 5659-5669.
[3] Agarwal, M., Verma, V. S. and Srivastava, S., An analytical approach to the problem of dispersion of an air pollutant with variable wind velocity,J. Nat. Acad. Math., 22 (2008) 51-62.
[4] Sharan, M., Modani, M. and Yadav, A. K., Atmospheric dispersion: An overview of Mathematical Modeling ,Framework, Proc Indian Natn Sci Acad, 69, A, 6(2003) 725-744.
[5] Sharan, M., Singh, M.P. and Yadav, A. K. ,A mathematical model for the atmospheric dispersion in low winds with eddy diffusivities as linear function of downwind distance, Atmospheric Environment, 30(1996) 1137-1145.
[6] Macdonald, R. Theory and objectives of air dispersion modeling, Modeling Air Emissions for Compliance, Wind Engineering, MME 474A,(2003) 1-27.
[7] Essa Khaled, S.M.andFawzia, M., Using dispersion modeling for ground level Concentration, JKAU: Met. , Env. And Arid Land Agric.Sci., 22(1)(2011) 105-114.
[8] Essa Khaled, S.M., EtmanSoad, M.and El-Otaify,Maha, S.,Studying the effect of vertical variation of wind speed and eddy diffusivity on the advection-diffusion equation, Applied Science Reports 14(3)(2016) 250-257.
[9] Essa Khaled, S.M., Aziz S.Hamdy Hany, N.M. and Khalifa,Ayman, A., Theoretical solution of the diffusion equation in unstable case, Journal of Atmosphere,2(1)( 2016) 1-8.
[10] Essa Khaled, S.M., Studying the effect of the vertical eddy diffusivity on the solution of the diffusion equation, Journal of ecology of Health and Environment 3(2)(2015) 43-48.
[11] Srivastava, S., Agarwal, M., and Verma, V.S., A three-dimensional atmospheric diffusion model with variable removable rate and variable wind velocity, J.Nat.Acad.Math.Spl.,. (2009) 189-197.
[12] Verma, V.S. ,An analytical approach to the problem of Dispersion of an air pollutant with constant wind velocity and constant removal rate, Journal of international academy of physical sciences, 15(2011) 43-50.
[13] Verma ,V.S., Srivastava,S., and M. Agarwal, An analytical approach to the problem of dispersion of an air pollutant with variable and variable eddy diffusivity, South East Asian J.Math.And Math .Sc.9(2)(2011) 43-48.
[14] Verma, V.S. Srivastava, U. and Bhandari,P.S., A mathematical model on dispersion of air pollutants,Intenational Journal of Science and Research 4(2014) 1904-1907.
[15] Verma, V.S. Srivastava, U. and Bhandari,P.S., An analytical approach to a problem on dispersion of air pollutants , Intenational Journal of Recent Scientific Research, 7(10)(2016) 13850-13857.

Keywords : Dispersion of air pollutants, Point source, Constant wind velocity, Removal rate, Unsteady condition