Peristaltic motion of Phan–Thien–Tanner fluid in the presence of slip condition

Springer Science and Business Media LLC - Tập 25 - Trang 8-17 - 2011
T. Hayat1,2, S. Noreen1, Awatif A. Hendi3
1Department of Mathematics Quaid-i-Azam University, Islamabad, Pakistan
2Department of Mathematics, College of Sciences, King Saud University, Riyadh , Saudi Arabia
3Department of Physics, Faculty of Science, King Saud University, Riyadh, Saudi Arabia

Tóm tắt

This investigation considers the peristaltic flow of a Phan–Thien–Tanner fluid in the presence of slip condition and induced magnetic field. By use of the long wavelength and low Reynolds number approximations, closed form series solutions for stream function, pressure gradient, magnetic force function, axial induced magnetic field, and current density were obtained. The pressure gradient and frictional forces per wavelength were computed by numerical integration. The velocity slip condition in terms of shear stress is taken into account. Graphical results show the comparison between no-slip and viscous fluid cases. Pumping and trapping phenomena are discussed.

Tài liệu tham khảo

Latham TW. Fluid motion in a peristaltic pump. Cambridge: MIT; 1966. Srinivas S, Pushparaj V. Non-linear peristaltic transport in an inclined asymmetric channel. Commun Nonlinear Sci Numer Simul. 2008;13:1782–95. Hayat T, Qureshi MU, Ali N The influence of slip on the peristaltic motion of a third order fluid in an asymmetric channel. Phys Lett A. 2008;372:2653–64. Elshehawey EF, Eldabe NT, Elghazy EM, Ebaid A. Peristaltic transport in an asymmetric channel through a porous medium. Appl Math Comput. 2006;182:140–50. Haroun MH. Non-linear peristaltic flow of a fourth grade fluid in an inclined asymmetric channel. Comput Mater Sci. 2007;39:333. Mekheimer KhS, Elmaboud YA. Peristaltic flow of a couple stress fluid in an annulus: application of an endoscope. Physica A. 2008;387:2403–15. Haroun MH. Effect of Deborah number and phase difference on peristaltic transport of a third grade fluid in an asymmetric channel. Commun Nonlinear Sci Numer Simul. 2007;12:1464–80. Srinivas S, Kothandapani M. Peristaltic transport in an asymmetric channel with heat transfer—a note. Int Commun Heat and Mass Transf. 2008;35:514–22. Hayat T, Alvi N, Ali N. Peristaltic mechanism of a Maxwell fluid in an asymmetric channel. Nonlinear Anal Real World Appl. 2008;9:1474–90. Kothandapani M, Srinivas S. Nonlinear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium. Phys Lett A. 2008;372:1265–76. Hariharan P, Seshadri V, Banerjee RK. Peristaltic transport of non-Newtonian fluid in a diverging tube with different wave forms. Math Comput Model. 2008;48:998–1017. Nadeem S, Akram S. Peristaltic flow of a Williamson fluid in an asymmetric channel. Commun Nonlinear Sci Numer Simul. 2010;15:1705–16. Hayat T, Ali N. Effects of an endoscope on the peristaltic flow of a micropolar fluid. Math Comput Model. 2008;48:721–33. Hayat T, Hussain Q, Ali N. Influence of partial slip on the peristaltic flow in a porous medium. Phys Lett A. 2008;387:3399–409. Vajravelu K, Sreenadh S, Babu VR Peristaltic pumping of a Herschel–Bulkley fluid in a channel. Appl Math Comput. 2005;169:726–35. Stud VK, Sephon GS, Mishra RK. Pumping action on blood flow by magnetic field. Bull Math Biol. 1977;39:385–90. Agrawal HL, Anwaruddin B. Peristaltic flow of a blood in a branch. Ranchi Univ Math J. 1984;15:111–21. Hayat T, Khan M, Siddiqui AM, Asghar S. Non-linear peristaltic flow of a non-Newtonian fluid under effect of a magnetic field in a planar channel. Commun Nonlinear Sci Numer Simul. 2007;12:910–9. Abd El Naby AEH, El Misiery AEM, El Shamy I. Hydromagnetic flow of generalized Newtonian fluid through a uniform tube with peristalsis. Appl Math Comput. 2006;173:856–71. Hayat T, Hussain Q, Ali N, Asghar S. Slip effects on the peristaltic transport of MHD fluid with variable viscosity. Phys Lett A. 2008;372:1477–89. Srinivas S, Gayathri R, Kothandapani M. The influence of slip conditions, wall properties and heat transfer on MHD peristaltic transport. Comput Phys Commun. 2009;180:2115–22. Hayat T, Ali N. Peristaltically induced motion of a MHD third grade fluid in a deformable tube. Physica A. 2006;370:225–39. Kothandapani M, Srinivas S. On the influence of wall properties in the MHD peristaltic transport with heat transfer and porous medium. Phys Lett A. 2008;372:4586–91. Mekheimer KhS, Elmaboud YA. The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus: application of an endoscope. Phys Lett A. 2008;372:1657–65. Ogulu A. Effect of heat generation on low Reynolds number fluid and mass transport in a single lymphatic blood vessel with uniform magnetic field. Int Commun Heat Mass Transf. 2006;33:790–9. Abd El Naby AEH, El Misery AEM, Abd El Kareem MF. Effects of magnetic field on trapping through peristaltic motion for generalized Newtonian fluid in channel. Physica A. 2006;367:79–92. Kothandapani M, Srinivas S. Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel. Int J Nonlinear Mech. 2008;43:915–24. Nadeem S, Akbar NS. Effects of heat transfer on the peristaltic transport of MHD Newtonian fluid with variable viscosity: application of Adomian decomposition method. Comm Nonlinear Sci Numer Simul. 2009;14:3844–55. Mekheimer KhS. Effect of induced magnetic field on peristaltic flow of a couple stress fluid. Phys Lett A. 2008;372:4271–8. Mekheimer KhS. Peristaltic flow of a magneto-micropolar fluid: effect of induced magnetic field. J Appl Math. 2008;2008:570825–48. Hayat T, Khan Y, Ali N, Mekheimer KhS. Effect of an induced magnetic field on the peristaltic flow of a third order fluid. Numer Methods Partial Differ Equ. 2010;26:345–60. Hayat T, Noreen S, Ali N. Effect of induced magnetic field on the peristaltic motion of Phan–Thien–Tanner fluid (PTT) fluid. ZNA. 2010;65a:665–76. Vinogradov GV, Ivanova LI. Wall slippage and elastic turbulence of polymers in the rubbery state. Rheol Acta. 1968;7:243–54. Luk S, Mutharasan R, Apelian D. Experimental observations of wall slip, tube and packed bed flow. Ind Eng Chem Res. 1987;26:1609–16. Piau JM, El Kissi N. Measurement and modelling of friction in polymer melts during macroscopic slip at the wall. J Non-Newtonian Fluid Mech. 1994;54:121–42. Kamerkar PA, Edwards BJ. An experimental study of slip flow in capillaries and semi hyperbolically converging dies. Polym Eng Sci. 2007;47:159–67. Cohen Y. Apparent slip flow of polymer solutions. J Rheol. 1985;29:67–102.