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International Journal of Applied Mechanics and Engineering

The Journal of University of Zielona Góra

Editor-in-Chief: Walicki, Edward

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CiteScore 2016: 0.12

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2353-9003
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Effect of Electric Field on Dispersion of a Solute in an MHD Flow through a Vertical Channel With and Without Chemical Reaction

J.C. Umavathi / J.P. Kumar / R.S.R. Gorla
  • Corresponding author
  • Department of Mechanical Engineering, Cleveland State University, Cleveland-44115, OHIO, USA; Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta-577 451, Shimoga, Karnataka, India
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/ B.J. Gireesha
  • Department of Mechanical Engineering, Cleveland State University, Cleveland-44115, OHIO, USA; Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta-577 451, Shimoga, Karnataka, India
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Published Online: 2016-09-10 | DOI: https://doi.org/10.1515/ijame-2016-0041

Abstract

The longitudinal dispersion of a solute between two parallel plates filled with two immiscible electrically conducting fluids is analyzed using Taylor’s model. The fluids in both the regions are incompressible and the transport properties are assumed to be constant. The channel walls are assumed to be electrically insulating. Separate solutions are matched at the interface using suitable matching conditions. The flow is accompanied by an irreversible first-order chemical reaction. The effects of the viscosity ratio, pressure gradient and Hartman number on the effective Taylor dispersion coefficient and volumetric flow rate for an open and short circuit are drawn in the absence and in the presence of chemical reactions. As the Hartman number increases the effective Taylor diffusion coefficient decreases for both open and short circuits. When the magnetic field remains constant, the numerical results show that for homogeneous and heterogeneous reactions, the effective Taylor diffusion coefficient decreases with an increase in the reaction rate constant for both open and short circuits.

Keywords: Taylor dispersion; immiscible fluids; conducting fluid; MHD; chemical reaction

References

  • [1]

    Levenspiel O. and Smith W.K. (1957): Notes on the diffusion-type model for the longitudinal mixing of fluids in flow. – Chem. Engng. Sci., vol.6, pp.27–233.Google Scholar

  • [2]

    Danckwerts P.V. (1953): The effect of incomplete mixing on homogeneous reactions. – Chem. Engng. Sci., vol.8, No.1-2, pp.93-102.Google Scholar

  • [3]

    Taylor G.I. (1953): Dispersion of soluble matter in solvent flowing slowly through a tube. – Proceedings of the Royal Society of London A, vol.219, pp.186-203Google Scholar

  • [4]

    Taylor G.I. (1954): The dispersion of matter in turbulent flow through a pipe. – Proceedings of the Royal Society of London A, 223, pp.446-468Google Scholar

  • [5]

    Taylor G.I. (1954): Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion. – Proceedings of the Royal Society of London A, 225, pp.473-477.Google Scholar

  • [6]

    Batchelor G.K. (1981): Preoccupations of a journal editor. – J. Fluid Mech., vol.106, pp.1-25.Google Scholar

  • [7]

    Aris R. (1956): On the dispersion of a solute in a fluid flowing through a tube. – Proceedings of Royal Society London A 235, pp.67–77.Google Scholar

  • [8]

    Horn F.J.M. and Kipp JR R.L. (1971): Induced transport in pulsating flow. – AIChE Journal, vol.17, pp.621–626.Google Scholar

  • [9]

    Brenner H. (1980): A general theory of Taylor dispersion phenomena. – Physicochem. Hydrodyn., vol.1, pp.91–123.Google Scholar

  • [10]

    Brenner H. and Edwards D.A. (1982): Macrotransport Process. – Butterworth-Heinemann, Boston, 714.Google Scholar

  • [11]

    Philip J.R. (1963): The theory of dispersal during laminar flow in tubes. – I. Australian J. Physics, vol.16, pp.287–299.Google Scholar

  • [12]

    Gill W.N. and Sankarasubramanian R. (1970): A note on the solution of transient dispersion problems. – Proceedings of the Royal Society A, vol.316, pp.341–350.Google Scholar

  • [13]

    Gill W.N. and Sankarasubramanian R. (1972): Dispersion of non-uniformly distributed time-variable continuous sources in time-dependent flow. – Proceedings of Royal Society London A, vol.327, pp.191-208.Google Scholar

  • [14]

    DeGance A.E. and Johns L.E. (1978a): The theory of dispersion of chemically active solutes in a rectilinear flow field. – Appl. Sci. Res., vol.34, pp.189-225.Google Scholar

  • [15]

    DeGance A.E. and Johns L.E. (1980): On the construction of dispersion approximations to the solution of the convective diffusion equation. – AIChE Journal, vol.26, pp.411–419.Google Scholar

  • [16]

    Hatton T.A. and Lightfoot E.N. (1982): On the significance of the dispersion coefficient in two-phase flow. – Chem. Engng. Sci., vol.37, pp.1289-1307.Google Scholar

  • [17]

    Hatton T.A. and Lightfoot E.N. (1984a): Dispersion, mass transfer and chemical reaction in multiphase contactors: part I: theoretical developments. – AIChE journal 30, pp.235-243.Google Scholar

  • [18]

    Hatton T.A. and Lightfoot E.N. (1984b): Dispersion, mass transfer and chemical reaction in multiphase contactors: Part II: Numerical examples. – AIChE Journal, vol.30, pp.243-249.Google Scholar

  • [19]

    Yamanaka T. (1983): Projection operator theoretical approach to unsteady convective diffusion phenomena. – J. Chem. Engng. Japan, vol.16, pp.29-35.Google Scholar

  • [20]

    Yamanaka T. (1983b): Generalization of Taylor’s approximate solution for dispersion phenomena. – J. Chem. Engng. Japan, vol.16, pp.511-512.Google Scholar

  • [21]

    Yamanaka T. and Inui S. (1994): Taylor dispersion models involving nonlinear irreversible reactions. – J. Chem. Engng. Japan, vol.27, pp.434–435.Google Scholar

  • [22]

    Smith R. (1981): A delay-diffusion description for contaminant dispersion. – J. Fluid Mech., vol.105, pp.469-486.Google Scholar

  • [23]

    Smith R. (1987): Diffusion in shear flows made easy: the Taylor limit. – J. Fluid Mech., vol.175, pp.201-214.Google Scholar

  • [24]

    Cleland F.A. and Wilhelm R.H. (1956): Diffusion and reaction in viscous-flow tubular reactor. – AIChE Journal, vol.2, pp.489-497.Google Scholar

  • [25]

    Katz S. (1959): Chemical reactions catalysed on a tube wall. – Chem. Engng. Sci., vol.10, pp.202-211.Google Scholar

  • [26]

    Walker R. (1961): Chemical reaction and diffusion in a catalytic tubular reactor. – Physics of Fluids, vol.4, pp.1211-1216.Google Scholar

  • [27]

    Solomon R.L. and Hudson J.L. (1967): Heterogeneous and homogeneous reactions in a tubular reactor. – AIChE. J., vol.13, pp.545-550.Google Scholar

  • [28]

    Packham B.A. and Shail R. (1971): Stratified laminar flow of two immiscible fluids. – Mathematical Proceedings Cambridge Philosophical Society, vol.69, pp.443-448.Google Scholar

  • [29]

    Alireza S. and Sahai V. (1990): Heat transfer in developing magnetohydrodynamic Poiseuille flow and variable transport properties. – Int. J. Heat and Mass Transfer, vol.33, pp.1711–1720.Google Scholar

  • [30]

    Malashetty M.S. and Leela V. (1991): Magnetohydrodynamic heat transfer in two fluid flow. – Proc. of National Heat Transfer Conferences sponsored by AIChE and ASME–HTD, Phase Change Heat Transfer, vol.159, pp.171-175.Google Scholar

  • [31]

    Malashetty M.S. and Leela V. (1992): Magnetohydrodynamic heat transfer in two-phase flow. – Int. J. Engng. Sci., vol.30, pp.371-377.Google Scholar

  • [32]

    Lohrasbi J. and Sahai V. (1988): Magnetohydrodynamic heat transfer in two-phase flow between parallel plates. – Appl. Sci. Res., vol.45, pp.53-66.Google Scholar

  • [33]

    Malashetty M.S. and Umavathi J.C. (1997): Magnetohydrodynamic two phase flow in an inclined channel. – Int. J. Multiphase Flow, vol.23, pp.545-560.Google Scholar

  • [34]

    Chamkha A.J. (1999): Flow of two-immiscible fluids in porous and nonporous channels. – ASME. J. Fluids Eng., vol.122, pp.117-124.Google Scholar

  • [35]

    Malashetty M.S. Umavathi J.C. and Kumar J.P. (2001): Two fluid magneto convection flow in an inclined channel. – Int. J. Transport Phenomena, vol.3, pp.73-84.Google Scholar

  • [36]

    Malashetty M.S. Umavathi J.C. and Kumar J.P. (2001): Convective magneto hydrodynamic two fluid flow and heat transfer in an inclined channel. – Heat and Mass Transfer J., vol.37, pp.259-264.Google Scholar

  • [37]

    Malashetty M.S. Umavathi J.C. and Kumar J.P. (2001): Convective flow and heat transfer in an inclined composite porous medium. – J. Porous Media, vol.4, pp.15-22.Google Scholar

  • [38]

    Umavathi J.C., Liu I.C. and Kumar J.P. (2010): Magnetohydrodynamic Poseuille-Coutte flow and heat transfer in an inclined channel. – J. Mech., vol.26, pp.525-532.Google Scholar

  • [39]

    Umavathi J.C. and Shekar M. (2011): Mixed convective flow of two immiscible viscous fluids in a vertical wavy channel with traveling thermal waves. – Heat Transfer-Asian Res., vol.40, pp.721-743.Google Scholar

  • [40]

    Kumar J.P., Umavathi J.C. and Shivakumar M. (2011): Effect of first order chemical reaction on magneto convection of immiscible fluids in a vertical channel. – Heat Transfer Asian Res., vol.40, pp.608-640.Google Scholar

  • [41]

    Kumar J.P., Umavathi J.C., Chamkha A.J and Ashok Basawaraj (2012): Solute dispersion between two parallel plates containing porous and fluid layers. – J. Porous Media, vol.15, pp.1031-1047.Google Scholar

  • [42]

    Gupta A.S. and Chatterjee A.S. (1968): Dispersion of soluble matter in the hydromagnetic laminar flow between two parallel plates. – Mathematical Proceedings of the Cambridge Philosophical Society, vol.64, pp.1209-1214.Google Scholar

  • [43]

    Wooding R.A. (1960): Instability of a viscous liquid of variable density in a vertical Hele-Shaw cell. – J. Fluid Mech., vol.7, pp.501–515.Google Scholar

  • [44]

    Sudhanshu, Ghoshal K., Subhash Sikdar Ch. and Ajit K. (1976): Dispersion of solutes in laminar hydromagnetic flows with homogeneous and heterogeneous chemical reactions. – Proceedings of the Indian National Science Academy. Part A, Physical Sci., vol.43, pp.370-379.Google Scholar

  • [45]

    Gupta A.S. and Chatterjee A.S. (1968): Dispersion of soluble matter in the hydromagnetic laminar flow between two parallel plates. – In Mathematical Proceedings of the Cambridge Philosophical Society, vol.64, pp.1209-1214.Google Scholar

About the article

Received: 2015-10-16

Revised: 2016-06-05

Published Online: 2016-09-10

Published in Print: 2016-08-01


Citation Information: International Journal of Applied Mechanics and Engineering, ISSN (Online) 2353-9003, ISSN (Print) 1734-4492, DOI: https://doi.org/10.1515/ijame-2016-0041.

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© 2016 J.C. Umavathi et al., published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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