ORIGINAL PAPER

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

1

Department of Mathematics, Gulbarga University, Gulbarga, Karnataka, India 585 106

2

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

Online publication date: 2016-09-10

Publication date: 2016-08-01

International Journal of Applied Mechanics and Engineering 2016;21(3):683-711

KEYWORDS

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.

REFERENCES (90)

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.

2.

3.

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

4.

5.

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.186-203.

6.

7.

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

8.

9.

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.

10.

11.

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

12.

13.

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.

14.

15.

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

16.

17.

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

18.

19.

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

20.

21.

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

22.

23.

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.

24.

25.

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.

26.

27.

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.

28.

29.

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.

30.

31.

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.

32.

33.

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.

34.

35.

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.

36.

37.

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

38.

39.

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

40.

41.

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

42.

43.

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

44.

45.

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

46.

47.

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

48.

49.

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

50.

51.

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

52.

53.

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

54.

55.

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

56.

57.

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.

58.

59.

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.

60.

61.

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

62.

63.

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

64.

65.

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.

66.

67.

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

68.

69.

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.

70.

71.

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.

72.

73.

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.

74.

75.

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.

76.

77.

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.

78.

79.

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.

80.

81.

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.

82.

83.

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.

84.

85.

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.

86.

87.

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.

88.

89.

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.

90.

Share

RELATED ARTICLE

You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.