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Mathematical model on magneto-hydrodynamic dispersion in a porous medium under the influence of bulk chemical reaction

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Abstract

The mathematical model of hydrodynamic dispersion through a porous medium is developed in the presence of transversely applied magnetic fields and axial harmonic pressure gradient. The solute introduce into the flow is experienced a first-order chemical reaction with flowing liquid. The dispersion coefficient is numerically determined using Aris’s moment equation of solute concentration. The numerical technique employed here is a finite difference implicit scheme. Dispersion coefficient behavior with Darcy number, Hartmann number and bulk flow reaction parameter is investigated. This study highlighted that the dependency of Hartmann number and Darcy number on dispersion shows different natures in different ranges of these parameters.

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References

  • Ananthakrishnan, V., W.N. Gill, and A.J. Barduhn, 1965, Laminar dispersion in capillaries: Part I. mathematical analysis, AIChE J. 11, 1063–1072.

    CAS  Google Scholar 

  • Anastasiou, A.D., A.S. Spyrogianni, K.C. Koskinas, G.D. Giannoglou, and S.V. Paras, 2012, Experimental investigation of the flow of a blood analogue fluid in a replica of a bifurcated small artery, Med. Eng. Phys. 34, 211–218.

    CAS  Google Scholar 

  • Annapurna, N. and A. Gupta, 1979, Exact analysis of unsteady mhd convective diffusion, Proc. R. Soc. London, Ser. A 367, 281–289.

    Google Scholar 

  • Aris, R., 1956, On the dispersion of a solute in a fluid flowing through a tube, Proc. R. Soc. London, Ser. A 235, 67–77.

    Google Scholar 

  • Bailey, H.R. and W.B. Gogarty, 1962, Numerical and experimental results on the dispersion of a solute in a fluid in laminar flow through a tube, Proc. R. Soc. London, Ser. A. 269, 352–367.

    Google Scholar 

  • Balakotaiah, V., H.C. Chang, and F. Smith, 1995, Dispersion of chemical solutes in chromatographs and reactors, Philos. Trans. R. Soc. London, Ser. A 351, 39–75.

    CAS  Google Scholar 

  • Bandyopadhyay, S. and B.S. Mazumder, 1999, On contaminant dispersion in unsteady generalised couette flow, Int. J. Eng. Sci. 37, 1407–1423.

    Google Scholar 

  • Barton, N., 1983, On the method of moments for solute dispersion, J. Fluid Mech. 126, 205–218.

    Google Scholar 

  • Berger, S.A. and L.D. Jou, 2000, Flows in stenotic vessels, Annu. Rev. Fluid Mech. 32, 347–382.

    Google Scholar 

  • Bhargava, R., S. Rawat, H.S. Takhar, and O.A. Bég, 2007, Pulsatile magneto-biofluid flow and mass transfer in a non-darcian porous medium channel, Meccanica 42, 247–262.

    Google Scholar 

  • Chatwin, P. and C. Allen, 1985, Mathematical models of dispersion in rivers and estuaries, Annu. Rev. Fluid Mech. 17, 119–149.

    Google Scholar 

  • Das, K. and G.C. Saha, 2009, Arterial MHD pulsatile flow of blood under periodic body acceleration, Bulletin of Society of Mathematicians Banja Luka, 16, 21–42.

    Google Scholar 

  • Dash, R., K. Mehta, and G. Jayaraman, 1996, Casson fluid flow in a pipe filled with a homogeneous porous medium, Int. J. Eng. Sci. 34, 1145–1156.

    CAS  Google Scholar 

  • Debnath, S., S. Paul, and A.K. Roy, 2018, Transport of reactive species in oscillatory annular flow, J. Appl. Fluid Mech. 11, 405–417.

    Google Scholar 

  • Debnath, S., A.K. Saha, B. Mazumder, and A.K. Roy, 2017, Dispersion phenomena of reactive solute in a pulsatile flow of three-layer liquids, Phys. Fluids. 29, 097107.

    Google Scholar 

  • El-Shahed, M. 2003, Pulsatile flow of blood through a stenosed porous medium under periodic body acceleration, Appl. Math. Comput. 138, 479–488.

    Google Scholar 

  • Fallon, M.S., B.A. Howell, and A. Chauhan, 2009, Importance of taylor dispersion in pharmacokinetic and multiple indicator dilution modelling, Math. Med. Biol. 26, 263–296.

    Google Scholar 

  • Gill, W.N. and R. Sankarasubramanian, 1971, Dispersion of a non-uniform slug in time-dependent flow, Proc. R Soc. London, Ser. A. 322, 101–117.

    Google Scholar 

  • Grotberg, J., 1994, Pulmonary flow and transport phenomena, Annu. Rev. Fluid Mech. 26, 529–571.

    Google Scholar 

  • Gupta, A. and A. Chatterjee, 1968, Dispersion of soluble matter in the hydromagnetic laminar flow between two parallel plates, Math. Proc. Cambridge Philos. Soc. 64, 1209–1214.

    Google Scholar 

  • Gupta, P. and A. Gupta, 1972, Effect of homogeneous and heterogeneous reactions on the dispersion of a solute in the laminar flow between two plates, Proc. R. Soc. London, Ser. A. 330, 59–63.

    Google Scholar 

  • Haldar, K. and S. Ghosh, 1994, Effect of a magnetic field on blood flow through an indented tube in the presence of erythrocytes, Indian J. Pure Appl. Math. 25, 345–352.

    Google Scholar 

  • Jiang, W. and G. Chen, 2019, Solute transport in two-zone packed tube flow: Long-time asymptotic expansion, Phys. Fluids 31, 043303.

    Google Scholar 

  • Mazumder, B.S. and S. Paul, 2008, Dispersion in oscillatory couette flow with absorbing boundaries, Int. J. Fluid Mech. Res. 35, 475–492.

    CAS  Google Scholar 

  • Mazumder, B.S. and S.K. Das, 1992, Effect of boundary reaction on solute dispersion in pulsatile flow through a tube, J. Fluid Mech. 239, 523–549.

    CAS  Google Scholar 

  • Mehmood, O.U., N. Mustapha, and S. Shafie, 2012, Unsteady two-dimensional blood flow in porous artery with multi-irregular stenosis, Transport Porous Med. 92, 259–275.

    Google Scholar 

  • Mekheimer, K.S. and M. El Kot, 2007, The micropolar fluid model for blood flow through a stenotic artery, Indian J. Pure Appl. Math. 36, 393.

    Google Scholar 

  • Midya, C., G. Layek, A. Gupta, and T.R. Mahapatra, 2003, Magnetohydrodynamic viscous flow separation in a channel with constrictions, J. Fluids Eng. 125, 952–962.

    Google Scholar 

  • Mondal, K.K. and B.S. Mazumder, 2005, On the solute dispersion in a pipe of annular cross-section with absorption boundary, ZAMM — J. Appl. Math. Mech. 85, 422–430.

    Google Scholar 

  • Motta, M., Y. Haik, A. Gandhari, and C.-J Chen, 1998, High magnetic field effects on human deoxygenated hemoglobin light absorption, Bioelectrochem. Bioenerg. 47, 297–300.

    CAS  Google Scholar 

  • Ng, C.-O., 2004, A time-varying diffusivity model for shear dispersion in oscillatory channel flow, Fluid Dyn. Res. 34, 335–355.

    Google Scholar 

  • Ng, C.-O., 2006, Dispersion in steady and oscillatory flows through a tube with reversible and irreversible wall reactions, Proc. R. Soc. London, Ser. A. 462, 481–515.

    Google Scholar 

  • Pal, D., 1999, Effect of chemical reaction on the dispersion of a solute in a porous medium, Appl. Math. Modell. 23, 557–566.

    Google Scholar 

  • Paul, S., 2010, Effect of wall oscillation on dispersion in axisymmetric flows between two coaxial cylinders, ZAMM — J. Appl. Math. Mech. 91, 23–37.

    Google Scholar 

  • Paul, S. and B. Mazumder, 2009, Transport of reactive solutes in unsteady annular flow subject to wall reactions, Eur. J. Mech. B. Fluids 28, 411–419.

    Google Scholar 

  • Pedley, T.J., 1980, The fluid mechanics of large blood vessels, Cambridge University Press Cambridge.

    Google Scholar 

  • Ponalagusamy, R. and S. Priyadharshini, 2017, Couple stress fluid model for pulsatile flow of blood in a porous tapered arterial stenosis under magnetic field and periodic body acceleration, J. Mech. Med. Biol. 17, 1750109.

    Google Scholar 

  • Rao, A.R. and K. Deshikachar, 2013, Physiological-type flow in a circular pipe in the presence of a transverse magnetic field, J. Indian Inst. Sci. 68, 247.

    Google Scholar 

  • Roy, A.K., A.K. Saha, and S. Debnath, 2017, On dispersion in oscillatory annular flow driven jointly by pressure pulsation and wall oscillation, J. Appl. Fluid Mech. 10, 1487–1500.

    Google Scholar 

  • Roy, A.K., A.K. Saha, and S. Debnath, 2019, Hydrodynamic dispersion of solute under homogeneous and heterogeneous reactions, Int. J. Heat Technol. 37, 387–397.

    Google Scholar 

  • Roy, A.K., A.K. Saha, and S. Debnath, 2020, Effect of multiple reactions on the transport coefficients in pulsatile flow through an annulus, Int. Commun. Heat Mass Transfer 110, 104369.

    CAS  Google Scholar 

  • Sankarasubramanian, R. and W.N. Gill, 1972, Dispersion from a prescribed concentration distribution in time variable flow, Proc. R. Soc. London, Ser. A 329, 479–492.

    Google Scholar 

  • Sankarasubramanian and R.W.N. Gill, 1973, Unsteady convective diffusion with interphase mass transfer, Proc. R. Soc. London, Ser. A 333, 115–132.

    Google Scholar 

  • Taylor, G., 1953, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. R. Soc. London, Ser. A 219, 186–203.

    CAS  Google Scholar 

  • Tu, C. and M. Deville, 1996, Pulsatile flow of non-Newtonian fluids through arterial stenosis, J. Biomech. 29, 899–908.

    CAS  Google Scholar 

  • Voltairas, P., D. Fotiadis, and L. Michalis, 2002, Hydrodynamics of magnetic drug targeting, J. Biomech. 35, 813–821.

    CAS  Google Scholar 

  • Wang, P. and G. Chen, 2015, Environmental dispersion in a tidal wetland with sorption by vegetation, Commun. Nonlinear Sci. Numer. Simul. 22, 348–366.

    CAS  Google Scholar 

  • Wang, P., Z. Li, X. Wu, and Y. An, 2015, Taylor dispersion in a packed pipe with wall reaction: Based on the method of gill’s series solution, Int. J. Heat Mass Transfer 91, 89–97.

    CAS  Google Scholar 

  • Yadav, P., S. Jaiswal, and B. Sharma, 2018, Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel, Appl. Math. Mech. 39, 993–1006.

    Google Scholar 

  • Zeng, L. and G. Chen, 2011, Ecological degradation and hydraulic dispersion of contaminant in wetland, Ecol. Modell. 222, 293–300.

    CAS  Google Scholar 

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Acknowledgment

We thank the anonymous reviewers for their helpful suggestions.

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Authors and Affiliations

  1. Department of Science & Humanities, Tripura Institute of Technology, Agartala, Tripura, 799009, India

    Ashis Kumar Roy

  2. Department of Mathematics, National Institute of Technology, Agartala, Tripura, 799046, India

    Apu Kumar Saha

  3. Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamil Nadu, 620015, India

    R. Ponalagusamy

  4. Center for Theoretical Studies, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721302, India

    Sudip Debnath

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  1. Ashis Kumar Roy
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  2. Apu Kumar Saha
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  3. R. Ponalagusamy
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  4. Sudip Debnath
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Correspondence to Ashis Kumar Roy.

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Roy, A.K., Saha, A.K., Ponalagusamy, R. et al. Mathematical model on magneto-hydrodynamic dispersion in a porous medium under the influence of bulk chemical reaction. Korea-Aust. Rheol. J. 32, 287–299 (2020). https://doi.org/10.1007/s13367-020-0027-0

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