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On dispersion of solute in steady flow through a channel with absorption boundary: an application to sewage dispersion

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Abstract

The paper describes the longitudinal dispersion of passive tracer materials released into an incompressible viscous fluid, flowing through a channel with walls having first-order reaction. Its model is based on a steady advection–diffusion equation with Dirichlet’s and mixed boundary conditions, and whose solution represents the concentration of the tracers in different downstream stations. For imposing the boundary conditions properly, artanh transformation is used to convert the infinite solution space to a finite one. A finite difference implicit scheme is used to solve the advection–diffusion equation in the computational region, and an inverse transformation is employed for the solution in the physical region. It is shown how the mixing of the tracer molecule influenced by the shear flow and due to the action of the absorption parameter at both the walls of the channel. For convection-dominated flow, uniform mesh is failed to capture the layer phenomena along the different downstream stations and a piecewise uniform mesh; namely, Shishkin mesh is used. The results are compared with existing experimental and numerical data available in the literature, and we have achieved an excellent agreement with them. The study plays a significant role to understand the basic mechanisms of sewage dispersion.

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Acknowledgements

One of us (Subham Dhar) is thankful to the CSIR, India, for financial support for pursuing this work (Grant No. 09/1219(0002)/2019-EMR-I). Dr. Kajal Kumar Mondal honestly acknoledges UGC, India, for partial financial support for pursuing this research work under project Grant No. F.PSW - 192/15-16 (ERO).

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Authors and Affiliations

  1. Department of Mathematics, Cooch Behar Panchanan Barma University, Cooch Behar, 736101, India

    Kajal Kumar Mondal & Subham Dhar

  2. Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India

    Bijoy Singha Mazumder

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  1. Kajal Kumar Mondal
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  2. Subham Dhar
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  3. Bijoy Singha Mazumder
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Correspondence to Subham Dhar.

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Communicated by Harindra Joseph Fernando.

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Mondal, K.K., Dhar, S. & Mazumder, B.S. On dispersion of solute in steady flow through a channel with absorption boundary: an application to sewage dispersion. Theor. Comput. Fluid Dyn. 34, 643–658 (2020). https://doi.org/10.1007/s00162-020-00539-7

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