Abstract
This article describes a new model for obtaining closed-form semi-analytical solutions of peristaltic flow induced by sinusoidal wave trains propagating with constant speed on the walls of a two-dimensional rotating infinite channel. The channel rotates with a constant angular speed about the z - axis and is filled with couple stress fluid. The governing equations of the channel deformation and the flow rate inside the channel are derived using the lubrication theory approach. The resulting equations are solved, using the homotopy perturbation method (HPM), for exact solutions to the longitudinal velocity distribution, pressure gradient, flow rate due to secondary velocity, and pressure rise per wavelength. The effect of various values of physical parameters, such as, Taylor’s number and couple stress parameter, together with some interesting features of peristaltic flow are discussed through graphs. The trapping phenomenon is investigated for different values of parameters under consideration. It is shown that Taylor’s number and the couple stress parameter have an increasing effect on the longitudinal velocity distribution till half of the channel, on the flow rate due to secondary velocity, and on the number of closed streamlines circulating the bolus.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Stokes V. K. Couple stress fluid [J]. Physics of Fluids, 1966, 9(9): 1709–1715.
Latham T. W. Fluid motion in a peristaltic pump [D]. Master Thesis, Massachusetts, USA: Massachusetts Institute of Technology, 1966.
Noreen S. A., Wahid B. A. Physiological transportation of casson fluid in a plumb duct [J]. Communications in Theoretical Physics, 2015, 63(3): 347–352.
Abd elmaboud Y. Thermomicropolar fluid flow in a porous channel with peristalsis [J]. Journal of Porous Media, 2011, 14(11): 1033–1045.
Abd elmaboud Y., Mekheimer Kh. S. Non-linear peristaltic transport of a second-order fluid through a porous medium [J]. Applied Mathematical Modelling, 2011, 35(6): 2695–2710.
Noreen S. A., Wahid B. A. Heat transfer analysis for the peristaltic flow of herschel-bulkley fluid in a nonuniform inclined channel [J]. Zeitschrift Für Naturforschung A, 2015, 70(1): 23–32.
Noreen S. A. Application of Eyring-Powell fluid model in peristalsis with nano particles [J]. Journal of Computational and Theoretical Nanosciences, 2015, 12(1): 94–100.
Ellahi R., Bhatti M. M., Riaz A. et al. The effects of magnetohydrodynamics on peristaltic flow of Jeffrey fluid in a rectangular duct through a porous medium [J]. Journal of Porous Media, 2014, 17(2): 143–157.
Hayat T., Asfar A., Khana M. et al. Peristaltic transport of a third order fluid under the effect of a magnetic field [J]. Computers and Mathematics with Applications, 2007, 53(7): 1074–1087.
Mekheimer Kh. S., Husseny S. Z. A., Abd elmaboud Y. Effects of heat transfer and space porosity on peristaltic flow in a vertical asymmetric channel [J]. Numerical Methods for Partial Differential Equations, 2010, 26(4): 747–770.
Ellahi R., Bhatti M. M., Vafai K. Effects of heat and mass transfer on peristaltic flow in a non-uniform rectan-gular duct [J]. International Journal of Heat and Mass Transfer, 2014, 71(4): 706–719.
Mekheimer Kh. S., Abd elmaboud Y. Peristaltic flow of a couple stress fluid in an annulus: Application of an endoscope [J]. Physica A, 2008, 387(11): 2403–2415.
Hayat T., Wang Y., Siddiqui A. M. et al. Peristaltic transport of a third order fluid in a circular cylindrical tube [J]. Mathematical Models and Methods in Applied Sciences, 2002, 12(12): 1691–1706.
Hayat T., Wang Y., Siddiqui A. M. et al. Peristaltic transport of an Oldroyd-B fluid in a planar channel [J]. Mathematical Problems in Engineering, 2004, 2004(4): 347–376.
Nadeem S., Riaz A., Ellahi R. et al. Heat and mass transfer analysis of peristaltic flow of nanofluid in a vertical rectangular duct by using the optimized series solution and genetic algorithm [J]. Computational and Theoretical Nanoscience, 2014, 11(4): 1133–1149.
Nadeem S., Riaz A., Ellahi R. Peristaltic flow of viscous fluid in a rectangular duct with compliant walls [J]. Computational Mathematics and Modeling, 2014, 25(3): 404–415.
Liao S. General boundary element method for non-linear heat transfer problems governed by hyperbolic heat conduction equation [J]. Computational Mechanics, 1997, 20(5): 397–406.
Liao S. Numerically solving nonlinear problems by the homotopy analysis method [J]. Computational Mechanics, 1997, 20(6): 530–540.
Ellahi R., Riaz A., Nadeem S. et al. Peristaltic flow of Carreau fluid in a rectangular duct through a porous medium [J]. Mathematical Problems in Engineering, 2012, Article ID 329639.
Abd Elmaboud Y., Mekheimer Kh. S., Mohamed M. S. Series solution of a natural convection flow for a Carreau fluid in a vertical channel with peristalsis [J]. Journal of Hydrodynamics, 2015, 27(6): 969–979.
Saadatmandi A., Dehghan M., Eftekhari A. Application of He’s homotopy perturbation method for non-linear system of second-order boundary value problems [J]. Nonlinear Analysis: Real World Applications, 2009, 10(3): 1912–1922.
Mekheimer Kh. S., Abdelmaboud Y., Abdellateef A. I. Particulate suspension flow induced by sinusoidal peristaltic waves through eccentric cylinders: Thread annular [J]. International Journal of Biomathematics, 2013, 6(4): 1350026.
Abd elmaboud Y., Mekheimer Kh. S., Abdellateef A. I. Thermal properties of couple-stress fluid flow in an asymmetric channel with peristalsis [J]. Journal of Heat Transfer, 2013, 135(4): 044502–1.
Ali N., Sajid M., Javed T. et al. Peristalsis in a rotating fluid [J]. Scientific Research and Essays, 2012, 7(32): 2891–2897.
Author information
Authors and Affiliations
Corresponding author
Additional information
Biography: Y. Abd elmaboud (1976-), Male, Ph. D., Associate Professor
Rights and permissions
About this article
Cite this article
Abd elmaboud, Y., Abdelsalam, S.I. & Mekheimer, K.S. Couple stress fluid flow in a rotating channel with peristalsis. J Hydrodyn 30, 307–316 (2018). https://doi.org/10.1007/s42241-018-0037-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42241-018-0037-2