Peristaltic Flow of Walter’s B Fluid in an Endoscope

S. Nadeem; Noreen Sher Akbar; T. Hayat; Awatif A. Hendi

doi:10.3879/j.issn.1000-0887.2011.06.002

Volume 32 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2011 > 32(6): 647-657

S. Nadeem, Noreen Sher Akbar, T. Hayat, Awatif A. Hendi. Peristaltic Flow of Walter’s B Fluid in an Endoscope[J]. Applied Mathematics and Mechanics, 2011, 32(6): 647-657. doi: 10.3879/j.issn.1000-0887.2011.06.002

Citation:

PDF( 895 KB)

Peristaltic Flow of Walter’s B Fluid in an Endoscope

doi: 10.3879/j.issn.1000-0887.2011.06.002

Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad 44000, Pakistan;

Received Date: 2010-09-17
Rev Recd Date: 2011-03-30
Publish Date: 2011-06-15

Abstract

Abstract

The peristaltic flow of a Walter's B fluid in an endoscope was studied.The problem was model in cylindrical coordinates system.The main theme of the present analysis was to study the endoscopic effects on the peristaltic flow of Walter's B fluid,because to the best of authors'knowledge no investigation had been made up to yet in peristaltic literature to study the Walter's B fluid in an endoscope.The analytical solutions were carried out using regular perturbation method by taking delta as erturbation parameter.The approximate analytical solutions for pressure rise and friction forces were evaluated using numerical integration.The effects of emerging parameters of Walter's B fluid were presented graphically.
- peristaltic flow,
- Walter’s B fluid,
- endoscope,
- perturbation solution

FullText(HTML)

References(23)

References

[1]	Nadeem S, Akbar N S. Influence of heat transfer on a peristaltic transport of Herschel Bulkley fluid in a non-uniform inclined tube[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(12): 4100-4113. doi: 10.1016/j.cnsns.2009.02.032
[2]	El Hakeem A, El Naby A, El Misery A E M, El Shamy I I. Separation in the flow through peristaltic motion of a Carreau fluid in uniform tube[J]. Physica A, 2004, 343: 1-14.
[3]	Ealshahed M, Haroun M H. Peristaltic transport of Johnson-Segalman fluid under effect of a magnetic field[J]. Mathematical Problems in Engineering, 2005, 6(2005):663-677.
[4]	Nadeem S, Akbar N S. Effects of heat transfer on the peristaltic transport of MHD Newtonian fluid with variable viscosity: application of Adomian decomposition method[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(11): 3844-3855. doi: 10.1016/j.cnsns.2008.09.010
[5]	Nadeem S, Akbar N S. Influence of heat transfer on a peristaltic transport of Herschel Bulkley fluid in a non-uniform inclined tube[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(12): 4100-4113. doi: 10.1016/j.cnsns.2009.02.032
[6]	El Hakeem A, El Naby A, El Misery A E M, El Shamy I I. Hydromagnetic flow of fluid with variable viscosity in a uniform tube with peristalsis[J]. J Phys A, 2003, 36(31): 8535-8547. doi: 10.1088/0305-4470/36/31/314
[7]	Haroun M H. Effect of Deborah number and phase difference on peristaltic transport of a third order fluid in an asymmetric channel[J]. Communications in Nonlinear Science and Numerical Simulation, 2007, 12(8): 1464-1480. doi: 10.1016/j.cnsns.2006.03.002
[8]	Mekheimer Kh S, Elmaboud Y Abd. Peristaltic flow of a couple stress fluid in an annulus: application of an endoscope[J]. Phy A, 2008, 387(11): 2403-2415. doi: 10.1016/j.physa.2007.12.017
[9]	El Hakeem A, El Naby A, El Misery A E M, El Shamy I I. Effects of an endoscope and generalized Newtonian fluid on peristaltic motion[J]. Appl Math Comput, 2002, 128(1): 19-35. doi: 10.1016/S0096-3003(01)00153-9
[10]	Mekheimer Kh S, Elmaboud Y Abd. The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus: an application of an endoscope[J]. Phys Lett A, 2008, 372(10):1657-1665. doi: 10.1016/j.physleta.2007.10.028
[11]	Hayat T, Momoniat E, Mahmood F M. Peristaltic MHD flow of a third grade fluid with an endoscope and variable viscosity[J]. J Nonlinear Math Phys,2008, 15(1): 91-104.
[12]	Hayat T, Ahmed N, Ali N. Effects of an endoscope and the magnetic field on the peristalsis involving Jeffrey fluid[J]. Communications in Nonlinear Science and Numerical Simulation, 2008, 13(8): 1581-1591. doi: 10.1016/j.cnsns.2007.02.008
[13]	Hakeem A M, El Naby A, El Misery A E M, El Shamy I I. Effects of an endoscope and fluid with variable viscosity on peristaltic motion[J]. Appl Math Comput, 2004, 158(2): 497-511. doi: 10.1016/j.amc.2003.09.008
[14]	El Misery A M, El Hakeem A, El Naby A, El Nagar A H. Effects of a fluid with variable viscosity and an endoscope on peristaltic motion[J]. J Phys Soc Jpn, 2001, 72: 89-93.
[15]	Hayat T, Ali N. Effects of an endoscope on peristaltic flow of a micropolar fluid[J]. Math Comput Model, 2008, 48(5/6): 721-733. doi: 10.1016/j.mcm.2007.11.004
[16]	Hayat T, Ali N, Asghar S, Siddiqui A M. Exact peristaltic flow in tubes with an endoscope[J]. Appl Math Comput, 2006, 182(1)：359-368. doi: 10.1016/j.amc.2006.02.052
[17]	Hayat T, Momoniat E, Mahomed F M. Endoscope effects on MHD peristaltic flow of a power-law fluid[J]. Mathematical Problems in Engineering, 2006, 2006(6): 1-19.
[18]	Baris S. Steady three-dimensional flow of a Walter’s B’ fluid in a vertical channel[J]. Turkish J Eng Env Sci, 2002, 26: 385-394.
[19]	Ariel P D. Flow of viscoelastic fluids through a porous channel—Ⅰ[J]. International Journal for Numerical Methods in Fluids, 1993, 17(7): 605-633. doi: 10.1002/fld.1650170705
[20]	Ariel P D. A new finite-difference algorithm for computing the boundary layer flow of viscoelastic fluids in hydromagnetics[J]. Comput Methods in Appl Mech Eng, 1995, 124(1/2): 1-13. doi: 10.1016/0045-7825(94)00729-7
[21]	Ariel P D. On extra boundary condition in the stagnation point flow of a second grade fluid[J]. Int J Eng Sci, 2002, 40(2): 145-162. doi: 10.1016/S0020-7225(01)00031-3
[22]	Sadeghy K, Sharifi M. Local similarity solution for the flow of a second grade viscoelastic fluid above a moving plate[J]. Int J Non-Linear Mech, 2004, 39(8):1265-1273. doi: 10.1016/j.ijnonlinmec.2003.08.005
[23]	Nadeem S, Akbar N S. Peristaltic flow of Walter’s B fluid in a uniform inclined tube[J]. Journal of Biorheology, 2010, 24(1): 22-28. doi: 10.1007/s12573-010-0018-8