Abstract
This study focuses on the transient analysis of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar pipe flow of a Newtonian liquid under axi-symmetric conditions. The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation and the nonlinear governing equations of momentum, pollutant concentration are obtained together with and Oldroyd-B constitutive model for the polymer stress. The problem is solved numerically using a semi-implicit finite difference method. Solutions are presented in graphical form for various parameter values and given in terms of fluid velocity, pollutant concentration, polymer stress components, skin friction and wall mass transfer rate. The model can be a useful tool in understanding the dynamics of industrial pollution situations arising from improper discharge of hydrocarbon pollutants into, say, water bodies. The model can also be quite useful for available necessary early warning methods for detecting or predicting the scale of pollution and hence help mitigate related damage downstream by earlier instituting relevant decontamination measures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena, Wiley, New York (1960)
Taylor, G.I.: The dispersion of matter in turbulent flow through pipe. Proc. Roy. Soc. London 233, 446–448 (1954)
Shulka, P.: Analytical solutions for steady transport dispersion of non-conservative pollutant with time-dependent periodic waste discharge concentration, J. Hydraul. Eng. 129, 866–869 (2002)
Zheng, C., Bennett, G.D.: Applied Contaminant Transport Modelling: Theory and Practices. Van Nostrand Rienhold, New York (1995)
Dulal, P., Khan, S.: A time dependence mathematical model for dispersion of air pollutant from point sources. Int. J. Environ. Studies 35, 197–208 (1990)
Summerfield, M., Krebs, W.: Particle dispersion in a swirling confined jet flow source. Particle Characterization 7, 16–24 (1990)
Sini, J.F., Anquetin, S., Mestayer, P.G.: Pollutant dispersion and thermal effects in urban street canyon. Atmospheric Environment, Urban Atmospheric 30, 2659–2677 (1996)
Makinde, O.D., Moitsheki, R.J., Tau, B.A.: Similarity reductions of equations for river pollution. Appl. Math. Comput. 188, 1267–1273 (2007)
Moitsheki, R.J., Makinde, O.D.: Symmetry reductions and solutions for pollutant diffusion in a cylindrical system. Nonlinear Analysis: Real World Applications 10, 3420–3427 (2009)
Makinde, O.D., Chinyoka, T.: Transient analysis of pollutant dispersion in a cylindrical pipe with a nonlinear waste discharge concentration. Computers and Mathematics with Applications 60, 642–652 (2010)
Chinyoka, T., Renardy, Y.Y., Renardy, M., et al.: Twodimensional study of drop deformation under simple shear for Oldroyd-B liquids. Journal of Non-Newtonian Fluid Mechanics 31, 45–56 (2005)
Chinyoka, T.: Computational dynamics of a thermally decomposable viscoelastic lubricant under shear. Transactions of ASME, J. Fluids Engineering 130, 121201 (2008)
Chinyoka, T.: Suction-injection control of shear banding in non-isothermal and exothermic channel flow of Johnson-Segalman liquids. Transactions of ASME, J. Fluids Engineering 133, 071205 (2011)
Ireka, I.E., Chinyoka, T.: Non-isothermal flow of a Johnson-Segalman liquid in a lubricated pipe with wall slip. J. Non-Newtonian Fluid Mech. 192, 20–28 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chinyoka, T., Makinde, O.D. Viscoelastic modeling of the diffusion of polymeric pollutants injected into a pipe flow. Acta Mech Sin 29, 166–178 (2013). https://doi.org/10.1007/s10409-013-0016-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-013-0016-3