The Effects of Peristalsis on Dispersion of a Micropolar Fluid in the Presence of Magnetic Field
The paper presents an analytical solution for dispersion
of a solute in the peristaltic motion of a micropolar fluid in the
presence of magnetic field and both homogeneous and heterogeneous
chemical reactions. The average effective dispersion coefficient has
been found using Taylor-s limiting condition under long wavelength
approximation. The effects of various relevant parameters on the average
coefficient of dispersion have been studied. The average effective
dispersion coefficient increases with amplitude ratio, cross viscosity
coefficient and heterogeneous chemical reaction rate parameter. But it
decreases with magnetic field parameter and homogeneous chemical
reaction rate parameter. It can be noted that the presence of peristalsis
enhances dispersion of a solute.
[1] A. H. Shapiro, M. Y. Jaffrin and S. L. Weinberg, Peristaltic pumping with
with long wavelengths at low Reynold number, J. Fluid Mech., vol.37,
pp.799-825, 1969.
[2] Y. C. Fung, and C. S. Yih, Peristaltic transport, J. Appl. Mech. Trans.
ASME, vol.5, pp.669-675, 1968.
[3] J. C. Misra and S. K. Pandey, Peristaltic transport in a tapered tube, Mathl.
Comput. Modelling, vol.22, pp.137-151, 1995.
[4] J. C. Misra and S. K. Pandey, Peristaltic flow of a multilayered powerlaw
fluid through a cylindrical tube, International Journal of Engineering
Science, vol.39, pp.387-402, 2001.
[5] M. Mishra and A. R. Rao, Peristaltic transport of a power law fluid in a
porous tube, J. Non-Newtonian Fluid Mech., vol.121, pp.163-174, 2004,
.
[6] G. Radhakrishnamacharya, Long wavelength approximation to peristaltic
motion of a power law fluid, Rheologica Acta, vol.21, pp.30-35, 1982.
[7] D.Srinivasacharya, M. Mishra and A. R. Rao, Peristaltic pumping of a
micropolar fluid in a tube, Acta Mech., 161, 2003, 165-178.
[8] P. Muthu, B. V. Rathish Kumar and P. Chandra, On the influence of
wall properties in the Peristaltic Motion of Micropolar fluid, ANZIAM
J. vol.45, pp.245-260, 2003.
[9] G. C. Sankad, G. Radhakrishnamacharya and J. V. Ramanamurthy, Long
wavelength approximation to peristaltic motion of micropolar fluid with
wall effects, Adv. Appl. Math. Mech., vol.2, pp.222-237, 2010.
[10] Kh. S. Mekheimer, Peristaltic Flow of a Magneto-Micropolar Fluid:
Effect of Induced Magnetic Field, Journal of Applied Mathematics,
Article Id 570825, 23 pages, 2008.
[11] T. Hayat, Masood Khan, A. M. Siddiqui and S. Asghar, Non-linear
peristaltic flow of a non-Newtonian fluid under effect of a magnetic field
in a planar channel, Communications in Nonlinear Science and Numerical
Simulation, vol.12,pp.910-919, 2007.
[12] D. Srinivasacharya, and Mekonen Shiferaw, Magnetohydrodynamic flow
of a micropolar fluid in a circular pipe with hall effects, ANZIAM J.,
vol.51, pp.277-285, 2009.
[13] J. C. Misra, S. Maiti and G. C. Shit, Peristaltic Transport of a Physiological
Fluid in an Asymmetric Porous Channel in the Presence of an
External Magnetic Field, Journal of Mechanics in Medicine and Biology,
vol.8, pp.507-525, 2008.
[14] G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly
through a tube, Proc. Roy. Soc. Lond., vol.A 219, pp.186-203, 1953.
[15] G. I. Taylor, The dispersion of matter in turbulent flow through a pipe,
Proc. Roy. Soc. Lond., vol.A 223, pp.446-468, 1954a.
[16] G. I. Taylor, Conditions under which dispersion of a solute in a stream
of solvent can be used to measure molecular diffusion, Proc. Roy. Soc.
Lond., vol.A 225, pp. 473-477, 1954b.
[17] R. Aris, On the dispersion of a solute in a fluid flowing through a tube,
Proc. Roy. Soc. Lond., vol.A 235, pp.67-77, 1956.
[18] B. K. N. Dutta, N. C. Roy and A. S. Gupta, Dispersion of a solute in a
non-Newtonian fluid with simultaneous chemical reaction, Mathematica-
Mechanica fasc., vol.2, pp.78-82, 1974.
[19] J. B. Shukla, R. S. Parihar and B. R. P. Rao, Dispersion in non-
Newtonian fluids: Effects of chemical reaction, Rheologica Acta, vol.18,
pp.740-748, 1979.
[20] P. Chandra and R. P. Agarwal, Dispersion in simple microfluid flows,
International Journal of Engineering Science, vol.21, pp.431-442, 1983.
[21] Philip, D. and Chandra, P., Effects of heterogeneous and homogeneous
reactions on the dispersion of a solute in simple microfluid, Indian J. Pure
Appl. Math., vol.24, pp.551-561, 1993.
[22] P. S. Gupta and A. S. Gupta, Effect of homogeneous and heterogeneous
reactions on the dispersion of a solute in the laminar flow between two
plates, Proc. Roy. Soc. Lond., vol.A 330, pp.59-63, 1972.
[23] V. V. Ramana Rao and D. Padma, Homogeneous and heterogeneous
reaction on the dispersion of a solute in MHD Couette flow, Curr. Sci.,
vol.44, pp.803-804, 1975.
[24] V. V. Ramana Rao and D. Padma, Homogeneous and heterogeneous
reaction on the dispersion of a solute in MHD Couette flow II, Curr. Sci.,
vol.46, pp.42-43, 1977.
[25] D. Padma and V. V. Ramana Rao, Effect of Homogeneous and heterogeneous
reaction on the dispersion of a solute in laminar flow between two
parallel porous plates, Indian Journal of Technology, vol.14, pp.410-412,
1976.
[1] A. H. Shapiro, M. Y. Jaffrin and S. L. Weinberg, Peristaltic pumping with
with long wavelengths at low Reynold number, J. Fluid Mech., vol.37,
pp.799-825, 1969.
[2] Y. C. Fung, and C. S. Yih, Peristaltic transport, J. Appl. Mech. Trans.
ASME, vol.5, pp.669-675, 1968.
[3] J. C. Misra and S. K. Pandey, Peristaltic transport in a tapered tube, Mathl.
Comput. Modelling, vol.22, pp.137-151, 1995.
[4] J. C. Misra and S. K. Pandey, Peristaltic flow of a multilayered powerlaw
fluid through a cylindrical tube, International Journal of Engineering
Science, vol.39, pp.387-402, 2001.
[5] M. Mishra and A. R. Rao, Peristaltic transport of a power law fluid in a
porous tube, J. Non-Newtonian Fluid Mech., vol.121, pp.163-174, 2004,
.
[6] G. Radhakrishnamacharya, Long wavelength approximation to peristaltic
motion of a power law fluid, Rheologica Acta, vol.21, pp.30-35, 1982.
[7] D.Srinivasacharya, M. Mishra and A. R. Rao, Peristaltic pumping of a
micropolar fluid in a tube, Acta Mech., 161, 2003, 165-178.
[8] P. Muthu, B. V. Rathish Kumar and P. Chandra, On the influence of
wall properties in the Peristaltic Motion of Micropolar fluid, ANZIAM
J. vol.45, pp.245-260, 2003.
[9] G. C. Sankad, G. Radhakrishnamacharya and J. V. Ramanamurthy, Long
wavelength approximation to peristaltic motion of micropolar fluid with
wall effects, Adv. Appl. Math. Mech., vol.2, pp.222-237, 2010.
[10] Kh. S. Mekheimer, Peristaltic Flow of a Magneto-Micropolar Fluid:
Effect of Induced Magnetic Field, Journal of Applied Mathematics,
Article Id 570825, 23 pages, 2008.
[11] T. Hayat, Masood Khan, A. M. Siddiqui and S. Asghar, Non-linear
peristaltic flow of a non-Newtonian fluid under effect of a magnetic field
in a planar channel, Communications in Nonlinear Science and Numerical
Simulation, vol.12,pp.910-919, 2007.
[12] D. Srinivasacharya, and Mekonen Shiferaw, Magnetohydrodynamic flow
of a micropolar fluid in a circular pipe with hall effects, ANZIAM J.,
vol.51, pp.277-285, 2009.
[13] J. C. Misra, S. Maiti and G. C. Shit, Peristaltic Transport of a Physiological
Fluid in an Asymmetric Porous Channel in the Presence of an
External Magnetic Field, Journal of Mechanics in Medicine and Biology,
vol.8, pp.507-525, 2008.
[14] G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly
through a tube, Proc. Roy. Soc. Lond., vol.A 219, pp.186-203, 1953.
[15] G. I. Taylor, The dispersion of matter in turbulent flow through a pipe,
Proc. Roy. Soc. Lond., vol.A 223, pp.446-468, 1954a.
[16] G. I. Taylor, Conditions under which dispersion of a solute in a stream
of solvent can be used to measure molecular diffusion, Proc. Roy. Soc.
Lond., vol.A 225, pp. 473-477, 1954b.
[17] R. Aris, On the dispersion of a solute in a fluid flowing through a tube,
Proc. Roy. Soc. Lond., vol.A 235, pp.67-77, 1956.
[18] B. K. N. Dutta, N. C. Roy and A. S. Gupta, Dispersion of a solute in a
non-Newtonian fluid with simultaneous chemical reaction, Mathematica-
Mechanica fasc., vol.2, pp.78-82, 1974.
[19] J. B. Shukla, R. S. Parihar and B. R. P. Rao, Dispersion in non-
Newtonian fluids: Effects of chemical reaction, Rheologica Acta, vol.18,
pp.740-748, 1979.
[20] P. Chandra and R. P. Agarwal, Dispersion in simple microfluid flows,
International Journal of Engineering Science, vol.21, pp.431-442, 1983.
[21] Philip, D. and Chandra, P., Effects of heterogeneous and homogeneous
reactions on the dispersion of a solute in simple microfluid, Indian J. Pure
Appl. Math., vol.24, pp.551-561, 1993.
[22] P. S. Gupta and A. S. Gupta, Effect of homogeneous and heterogeneous
reactions on the dispersion of a solute in the laminar flow between two
plates, Proc. Roy. Soc. Lond., vol.A 330, pp.59-63, 1972.
[23] V. V. Ramana Rao and D. Padma, Homogeneous and heterogeneous
reaction on the dispersion of a solute in MHD Couette flow, Curr. Sci.,
vol.44, pp.803-804, 1975.
[24] V. V. Ramana Rao and D. Padma, Homogeneous and heterogeneous
reaction on the dispersion of a solute in MHD Couette flow II, Curr. Sci.,
vol.46, pp.42-43, 1977.
[25] D. Padma and V. V. Ramana Rao, Effect of Homogeneous and heterogeneous
reaction on the dispersion of a solute in laminar flow between two
parallel porous plates, Indian Journal of Technology, vol.14, pp.410-412,
1976.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:58939", author = "Habtu Alemayehu and G. Radhakrishnamacharya", title = "The Effects of Peristalsis on Dispersion of a Micropolar Fluid in the Presence of Magnetic Field", abstract = "The paper presents an analytical solution for dispersion
of a solute in the peristaltic motion of a micropolar fluid in the
presence of magnetic field and both homogeneous and heterogeneous
chemical reactions. The average effective dispersion coefficient has
been found using Taylor-s limiting condition under long wavelength
approximation. The effects of various relevant parameters on the average
coefficient of dispersion have been studied. The average effective
dispersion coefficient increases with amplitude ratio, cross viscosity
coefficient and heterogeneous chemical reaction rate parameter. But it
decreases with magnetic field parameter and homogeneous chemical
reaction rate parameter. It can be noted that the presence of peristalsis
enhances dispersion of a solute.", keywords = "Peristalsis, Dispersion, Chemical reaction, Magneticfield, Micropolar fluid", volume = "5", number = "3", pages = "420-7", }
