Peristaltic flow of a Casson fluid in an annulus

P. Nagarani; A. Lewis

Korea-Australia Rheology Journal, Vol.24, No.1, 1-9, March, 2012

DOI10.1007/s13367-012-0001-6 Export Citation

Peristaltic flow of a Casson fluid in an annulus

P. Nagarani^†, and A. Lewis

Department of Mathematics, The University of the West Indies, Mona Campus, Kingston 7, Jamaica, West Indies

E-mail:

Peristaltic transport of a non-Newtonian fluid through the annular gap between two coaxial tubes is studied. We assumed that the inner tube is rigid whereas the outer tube has sinusoidal wave travelling down its wall. We modelled the flowing fluid as a Casson fluid to study the combined effects of yield stress (plug width) and annular gap on peristaltic transport. The flow is investigated in a wave frame of reference moving with velocity of the wave under long wavelength and low Reynolds number assumption. The expressions for velocity, stream function, pressure rise, flow rate and frictional force on inner and outer wall are obtained. Results are shown graphically and discussed in the results and discussion section. It is observed that yield stress and annular gap both have significant impact on the pressure rise, frictional resistance on the walls and on the formation and variation of trapped bolus.

Keywords:peristaltic transport;non-Newtonian fluid;Casson fluid;trapping;frictional force

[References]

Hakeem AE, Naby AE, Misery AEME, Appl. Math. Comp., 128, 19 (2002)
Hakeem AE, Naby AE, Misery AEME, Shamy IIE, Appl. Math. Comp., 158, 497 (2004)
Aroesty J, Gross JF, Biorheology, 9, 33 (1972)
Aroesty J, Gross JF, Microvasc. Res., 4, 1 (1972)
Bird RB, Stewart WE, Lightfoot EN, 1960, Transport phenomena, New York, Wiley.
Dash RK, Jayaraman G, Mehta KN, J. Biomechanics, 29(7), 917 (1996)
Gopalan NP, Devanathan R, Indian J. Pure Appl. Math., 15(6), 657 (1984)
Kothandapani M, Srinivas S, Int. J. Non-Linear Mechanics, 43, 915 (2008)
Mekheimer, Kh. S, The Arabian Jour. For Sci. Eng., 30(1A), 69 (2005)
Mekheimer KS, elmaboud YA, Physica A, 387, 2403 (2008)
Mernone AV, Mazumdar JN, Australasian Phy. Eng. Sci. in Medicine, 23, 94 (2000)
Mernone AV, Mazumdar JN, Lucas SK, Mathematical Computer Modelling, 35, 894 (2002)
Nadeem S, Akbar NS, Commun Nonlinear Sci Numer Simulat, 14, 4100 (2009)
Nadeem S, Akbar NS, 2001, Exact and numerical simulation of peristaltic flow of a non-Newtonian fluid with inclined magnetic field in an endoscope, Int. Jour. for Numerical Methods in fluids, n/a.doi:10.1002/fld.2295.
Nagarani P, Sarojamma G, Australasian Phy. Eng. Sci. in Medicine, 27, 49 (2004)
Nagarani P, Korea-Aust. Rheol. J., 22(2), 105 (2010)
Shapiro AH, Jaffrin MY, Weinberg SL, J. Fluid Mech., 37, 799 (1969)
Srinivas S, Muthuraj R, Mathematical Computer Modelling, 54, 1213 (2011)
Srivastava LM, Srivastava VP, J. Biomechanics, 17, 821 (1984)

[Referenced By]

[1] Hakeem AE, Naby AE, Misery AEME, Appl. Math. Comp., 128, 19 (2002)

[2] Hakeem AE, Naby AE, Misery AEME, Shamy IIE, Appl. Math. Comp., 158, 497 (2004)

[3] Aroesty J, Gross JF, Biorheology, 9, 33 (1972)

[4] Aroesty J, Gross JF, Microvasc. Res., 4, 1 (1972)

[5] Bird RB, Stewart WE, Lightfoot EN, 1960, Transport phenomena, New York, Wiley.

[6] Dash RK, Jayaraman G, Mehta KN, J. Biomechanics, 29(7), 917 (1996)

[7] Gopalan NP, Devanathan R, Indian J. Pure Appl. Math., 15(6), 657 (1984)

[8] Kothandapani M, Srinivas S, Int. J. Non-Linear Mechanics, 43, 915 (2008)

[9] Mekheimer, Kh. S, The Arabian Jour. For Sci. Eng., 30(1A), 69 (2005)

[10] Mekheimer KS, elmaboud YA, Physica A, 387, 2403 (2008)

[11] Mernone AV, Mazumdar JN, Australasian Phy. Eng. Sci. in Medicine, 23, 94 (2000)

[12] Mernone AV, Mazumdar JN, Lucas SK, Mathematical Computer Modelling, 35, 894 (2002)

[13] Nadeem S, Akbar NS, Commun Nonlinear Sci Numer Simulat, 14, 4100 (2009)

[14] Nadeem S, Akbar NS, 2001, Exact and numerical simulation of peristaltic flow of a non-Newtonian fluid with inclined magnetic field in an endoscope, Int. Jour. for Numerical Methods in fluids, n/a.doi:10.1002/fld.2295.

[15] Nagarani P, Sarojamma G, Australasian Phy. Eng. Sci. in Medicine, 27, 49 (2004)

[16] Nagarani P, Korea-Aust. Rheol. J., 22(2), 105 (2010)

[17] Shapiro AH, Jaffrin MY, Weinberg SL, J. Fluid Mech., 37, 799 (1969)

[18] Srinivas S, Muthuraj R, Mathematical Computer Modelling, 54, 1213 (2011)

[19] Srivastava LM, Srivastava VP, J. Biomechanics, 17, 821 (1984)