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

doi:10.1007/s10483-014-1823-6

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (6): 697-716.doi: https://doi.org/10.1007/s10483-014-1823-6

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

H. YASMIN¹, T. HAYAT^1,2, A. ALSAEDI², H. H. ALSULAMI²

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

收稿日期:2013-08-02 修回日期:2013-10-26 出版日期:2014-06-01 发布日期:2014-06-01
通讯作者: H. YASMIN, Ph.D., E-mail: qau2011@gmail.com E-mail:qau2011@gmail.com
基金资助:
We are grateful to the reviewers for their constructive suggestions.

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

H. YASMIN¹, T. HAYAT^1,2, A. ALSAEDI², H. H. ALSULAMI²

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:2013-08-02 Revised:2013-10-26 Online:2014-06-01 Published:2014-06-01
Supported by:
We are grateful to the reviewers for their constructive suggestions.

摘要/Abstract

摘要：

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.

关键词: asymmetric channel, solution space, Janet number, Nayler-Stokes equation, Johnson-Segalman fluid, convective condition, pumping and trapping

Abstract:

Key words: solution space, Janet number, Nayler-Stokes equation, convective condition, asymmetric channel, pumping and trapping, Johnson-Segalman fluid

中图分类号:

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 (English Edition), 2014, 35(6): 697-716.

参考文献

[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)

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

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

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 10

编辑推荐

Metrics

本文评价

[1]	A. AHMED, M. KHAN, J. AHMED. Thermal analysis in swirl motion of Maxwell nanofluid over a rotating circular cylinder[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(9): 1417-1430.
[2]	P. B. SAMPATH KUMAR, B. MAHANTHESH, B. J. GIREESHA, S. A. SHEHZAD. Quadratic convective flow of radiated nano-Jeffrey liquid subject to multiple convective conditions and Cattaneo-Christov double diffusion[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(9): 1311-1326.
[3]	T. HAYAT, S. NAZ, M. WAQAS, A. ALSAEDI. Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(10): 1373-1384.
[4]	T. HAYAT;T. HUSSAIN;S. A. SHEHZAD;A. ALSAEDI. Flow of Oldroyd-B fluid with nanoparticles and thermal radiation[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(1): 69-80.
[5]	T. HAYAT;S. NOREEN;A. ALSAEDI. Slip and induced magnetic field effects on peristaltic transport of Johnson-Segalman fluid[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(8): 1035-1048.
[6]	S.NADEEM N.S.AKBAR. Effects of induced magnetic field on peristaltic flow of Johnson-Segalman fluid in a vertical symmetric channel[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(8): 969-978.
[7]	施惟慧;沈春;王曰朋. Analytical solution of basic equations set of atmospheric motion[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(3): 385-385 .
[8]	施惟慧;陈达段;唐一鸣. ON THE EXACT SOLUTIQN TO CERTAIN NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(3): 259-265.
[9]	陈达段;刘晓明;施惟慧. ON THE STABILITY OF FORCED DISSIPATIVE NONLINEAR SYSTEM[J]. Applied Mathematics and Mechanics (English Edition), 1996, 17(6): 541-548.
[10]	施惟慧;方晓佐. STABILITY OF NAVIER-STOKES EQUATION(II)[J]. Applied Mathematics and Mechanics (English Edition), 1994, 15(10): 929-933.