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Peristaltic flow of Johnson-Segalman fluid in asymmetric channel with convective boundary condition

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  • 1. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan;
    2. Nonlinear Analysis and Applied Mathematics NAAM Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received date: 2013-08-02

  Revised date: 2013-10-26

  Online published: 2014-06-01

Supported by

We are grateful to the reviewers for their constructive suggestions.

Abstract

This work is concerned with the peristaltic transport of the Johnson-Segalman fluid in an asymmetric channel with convective boundary conditions. The mathematical modeling is based upon the conservation laws of mass, linear momentum, and energy. The resulting equations are solved after long wavelength and low Reynolds number are used. The results for the axial pressure gradient, velocity, and temperature profiles are obtained for small Weissenberg number. The expressions of the pressure gra-dient, velocity, and temperature are analyzed for various embedded parameters. Pumping and trapping phenomena are also explored.

Cite this article

H. YASMIN;T. HAYAT;A. ALSAEDI;H. H. ALSULAMI . Peristaltic flow of Johnson-Segalman fluid in asymmetric channel with convective boundary condition[J]. Applied Mathematics and Mechanics, 2014 , 35(6) : 697 -716 . DOI: 10.1007/s10483-014-1823-6

References

[1] Truesdell, C. and Noll, W. The non-linear field theories of mechanics. Encyclopedia of Physics, Springer, Berlin, 1-591 (1965)
[2] Rajagopal, K. R. On boundary conditions for fluids of the differential type. Navier-Stokes Equations and Related Non-Linear Problems, Plenum Press, New York, 273-278 (1995)
[3] Rajagopal, K. R. and Kaloni, P. N. Some remarks on boundary conditions for fluids of the differ-ential type. Continuum Mechanics and Its Applications, Hemisphere, New York, 935-942 (1989)
[4] Rajagopal, K. R. and Gupta, A. S. An exact solution for the flow of a non-Newtonian fluid past an infinite plate. Mechanica, 19, 158-160 (1984)
[5] Hayat, T., Masood, K., Siddiqui, A. M., and Asghar, S. Transient flows of a second grade fluid. International Journal of Non-Linear Mechanics, 39, 1621-1633 (2004)
[6] Fetecau, C., Fetecau, C., Jamil, M., and Mahmood, A. Flow of fractional Maxwell fluid between coaxial cylinders. Archive of Applied Mechanics, 81, 1153-1163 (2011)
[7] Fetecau, C., Mahmood, A., and Jamil, M. Exact solutions for the flow of a viscoelastic fluid induced by a circular cylinder subject to a time dependent shear stress. Communications in Nonlinear Science and Numerical Simulation, 15, 3931-3938 (2010)
[8] Tan, W. C. and Masuoka, T. Stokes' first problem for second grade fluid in a porous half space. International Journal of Non-Linear Mechanics, 40, 515-522 (2005)
[9] Rashidi, M. M., Mohimanian-Pour, S. A., and Laraqi, N. A semi-analytical solution of micropolar flow in a porous channel with mass injection by using differential transform method. Nonlinear Analysis: Modelling and Control, 15, 341-350 (2010)
[10] Ellahi, R., Riaz, A., Nadeem, S., and Ali, M. Peristaltic flow of Carreau fluid in a rectangular duct through a porous medium. Mathematical Problems in Engineering, 2012, 329639 (2012)
[11] Aksoy, Y. and Pakdemirli, M. Approximate analytical solutions for flow of a third-grade fluid through a parallel-plate channel filled with a porous medium. Transport in Porous Media, 83, 375-395 (2010)
[12] Noreen, S., Hayat, T., and Alsaedi, A. Study of slip and induced magnetic field on the peristaltic flow of pseudoplastic fluid. International Journal of Physical Sciences, 6, 8018-8026 (2011)
[13] Hina, S., Hayat, T., Asghar, S., and Hendi, A. A. Influence of compliant walls on peristaltic motion with heat/mass transfer and chemical reaction. International Journal of Heat and Mass Transfer, 55, 3386-3394 (2012)
[14] Hina, S., Hayat, T., Asghar, S., Alhothuali, M. S., and Alhomaidan, A. MHD nonlinear peristaltic flow in a compliant wall channel with heat and mass transfer. Journal of Heat Transfer, 14, 071101 (2012)
[15] Hayat, T., Hina, S., and Ali, N. Simultaneous effects of slip and heat transfer on the peristaltic flow. Communications in Nonlinear Science and Numerical Simulation, 15, 1526-1537 (2010)
[16] Latham, T. W. Fluid Motion in a Peristaltic Pump, M. Sc. dissertation, Massachusetts Institute of Technology, Massachusetts (1966)
[17] Shapiro, A. H., Jaffrin, M. Y., and Weinberg, S. L. Peristaltic pumping with long wavelengths at low Reynolds number. Journal of Fluid Mechanics, 37, 799-825 (1969)
[18] Eytan, O. and Elad, D. Analysis of intreuterine fluid motion induced by uterine contraction. Bulletin of Mathematical Biology, 61, 221-238 (1999)
[19] Sobh, A. M., Al-Azab, S. S., and Madi, H. H. Heat transfer in peristaltic flow of viscoelastic fluid in an asymmetric channel. Applied Mathematical Sciences, 4, 1583-1606 (2010)
[20] Mekheimer, K. S., Husseny, S. Z. A., and Abd-Elmaboud, Y. Effects of heat transfer and space porosity on peristaltic flow in a vertical asymmetric channel. Numerical Methods for Partial Differential Equations, 26, 747-770 (2010)
[21] Srinivas, S. and Kothandapani, M. Peristaltic transport in an asymmetric channel with heat transfer—a note. International Communications in Heat and Mass Transfer, 35, 514-522 (2008)
[22] Tripathi, D., Pandey, S. K., and Das, S. Peristaltic transport of a generalized Burgers' fluid: application to the movement of chyme in small intestine. Acta Astronautica, 69, 30-38 (2011)
[23] Mehmood, O. U., Shafie, S., and Mustapha, N. Peristaltic transport of Walter's B fluid in an asymmetric channel. International Journal of Applied Mathematics and Mechanics, 7, 1-19 (2011)
[24] Ravi-Kumar, Y. V. K., Krishna-Kumari, P. S. V. H. N., Ramana-Murthy, M. V., and Sreenadh, S. Peristaltic transport of a power-law fluid in an asymmetric channel bounded by permeable walls. Advances in Applied Science Research, 2, 396-406 (2011)
[25] Nadeem, S. and Akbar, N. S. Influence of heat and chemical reactions on the peristaltic flow of a Johnson-Segalman fluid in a vertical asymmetric channel with induced MHD. Journal of the Taiwan Institute of Chemical Engineers, 42, 58-66 (2011)
[26] Nadeem, S. and Akbar, N. S. Influence of heat transfer on peristaltic transport of a Johnson-Segalman fluid in an inclined asymmetric channel. Communications in Nonlinear Science and Numerical Simulation, 15, 2860-2877 (2010)
[27] Hayat, T., Saleem, N., and Ali, N. Effect of induced magnetic field on peristaltic transport of a Carreau fluid. Communications in Nonlinear Science and Numerical Simulation, 15, 2407-2423 (2010)
[28] Hayat, T., Noreen, S., and Alsaedi, A. The slip and induced magnetic field effects on the peristaltic transport with heat transfer. Journal of Mechanics in Medicine and Biology, 12, 1250068 (2012)
[29] Hayat, T., Hina, S., and Hendi, A. A. Slip effects on peristaltic transport of a Maxwell fluid with heat and mass transfer. Journal of Mechanics in Medicine and Biology, 12, 1250001 (2012)
[30] Nadeem, S., Akbar, N. S., Hayat, T., and Hendi, A. A. Peristaltic flow of Walter's B fluid in endoscope. Applied Mathematics and Mechanics (English Edition), 32(6), 689-700 (2012) DOI 10.1007/s10483-011-1449-7
[31] Johnson, M. W., Jr. and Segalman, D. A model for viscoelastic fluid behavior which allows non-affine deformation. Journal of Non-Newtonian Fluid Mechanics, 2, 255-270 (1977)

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