This article looks at the peristaltic flow of nanofluid in a channel with compliant walls. Brownian motion and thermophoresis effects are taken into consideration. Mathematical model is formulated by using long wavelength and low Reynolds number assumptions. The analytic expressions of temperature and nanoparticles concentration are developed by homotopy analysis method (HAM). The solutions are validated through the numerical solutions obtained by employing the built in routine for solving nonlinear boundary value problem via shooting method through software mathematica. Special emphasis is given to the role of key parameters including the Brownian motion parameter (Nb), thermophoresis parameter (Nt), Prandtl number (Pr), Eckert number (Ec) on temperature, and nanoparticles concentration. It is observed that both temperature and nanoparticles volume fraction increase when the Brownian motion and thermophoresis effects intensify. Moreover, the heat transfer coefficient is increasing function of Nb and Nt.
Issue Section:
Forced Convection
References
1.
Latham
, T. W.
, 1966
, “Fluid Motion in a Peristaltic Pump
,” M.S. thesis, MIT Cambridge, MA
.2.
Mekheimer
, K. S.
, 2003
, “Nonlinear Peristaltic Transport Through a Porous Medium in an Inclined Planar Channel
,” J. Porous Media
, 6
, pp. 78
–90
.10.1615/JPorMedia.v6.i3.403.
Reddy
, G. R.
, 2010
, “Peristaltic Transport of a Conducting Fluid in an Inclined Asymmetric Channel
,” Appl. Math. Sci.
, 4
, pp. 1729
–1741
.4.
Vasudev
, C.
, Rao
, U. R.
, Rao
, G. P.
, and Reddy
, M. V. S.
, 2011
, “Peristaltic Flow of a Newtonian Fluid Through a Porous Medium in a Vertical Tube Under the Effect of a Magnetic Field
,” Int. J. Curr. Sci. Res.
, 1
, pp. 105
–110
.5.
Mahmoud
, S. R.
, Afifi
, N. A. S.
, and Al-Isede
, H. M.
, 2011
, “Effect of Porous Medium and Magnetic Field on Peristaltic Transport of a Jeffrey Fluid
,” Int. J. Math. Anal.
, 5
, pp. 1025
–1034
.6.
Kavitha
, A.
, Reddy
, R. H.
, Sreenadh
, S.
, Saravana
, R.
, and Srinivas
, A. N. S.
, 2011
, “Peristaltic Flow of a Micropolar Fluid in a Vertical Channel With Longwave Length Approximation
,” Adv. Appl. Sci. Res.
, 2
, pp. 269
–279
.7.
Tripathi
, D.
, Pandey
, S. K.
, and Das
, S.
, 2000
, “Peristaltic Transport of a Generalized Burgers' Fluid: Application to the Movement of Chyme in Small Intestine
,” Acta Astronaut.
, 69
, pp. 30
–38
.10.1016/j.actaastro.2010.12.0108.
Nadeem
, S.
, and Akbar
, N. S.
, 2012
, “Effects of Heat and Mass Transfer on Peristaltic Flow of Williamson Fluid in a Vertical Annulus
,” Meccanica
, 47
, pp. 141
–151
.10.1007/s11012-010-9421-x9.
Akbar
, N. S.
, and Nadeem
, S.
, 2012
, “Characteristics of Heating Scheme and Mass Transfer on the Peristaltic Flow for an Eyring-Powell Fluid in an Endoscope
,” Int. J. Heat Mass Transfer
, 52
, pp. 375
–383
.10.1016/j.ijheatmasstransfer.2011.09.02910.
Akbar
, N. S.
, Hayat
, T.
, Nadeem
, S.
, and Obaidat
, S.
, 2012
, “Peristaltic Flow of a Williamson Fluid in an Inclined Asymmetric Channel With Partial Slip and Heat Transfer
,” Int. J. Heat Mass Transfer
, 55
, pp. 1855
–1862
.10.1016/j.ijheatmasstransfer.2011.11.03811.
Nadeem
, S.
, and Akbar
, N. S.
, 2012
, “Endoscopic and Heat Transfer Effects on the Peristaltic Flow of a Third Order Fluid With Chemical Reactions
,” Asia Pac. J. Chem. Eng.
, 7
, pp. 45
–54
.10.1002/apj.48912.
Nadeem
, S.
, Akbar
, N. S.
, and Ali
, M.
, 2012
, “Endoscopic Effects on the Peristaltic Flow of an Eyring Powell Fluid
,” Meccanica
, 47
, pp. 687
–697
.10.1007/s11012-011-9478-113.
Chu
, W. K. H.
, and Fang
, J.
, 2000
, “Peristaltic Transport in a Slip Flow
,” Eur. Phys. J. B
, 16
, pp. 543
–547
.10.1007/s10051007021514.
El Hakeem
, A.
, El Naby
, A.
, and El Shamy
, I. I. E.
, 2007
, “Slip Effects on Peristaltic Transport of Power-Law Fluid Through an Inclined Tube
,” Appl. Math. Sci.
, 1
, pp. 2967
–2980
.15.
Ali
, N.
, Hussain
, Q.
, Hayat
, T.
, and Asghar
, S.
, 2007
, “Slip Effects on the Peristaltic Transport of MHD Fluid With Variable Viscosity
,” Phys. Lett. A
, 372
, pp. 1477
–1489
.10.1016/j.physleta.2007.09.06116.
Sobh
, A. M.
, 2008
, “Interaction of Couple Stresses and Slip Flow on Peristaltic Transport in Uniform and Nonuniform Channels
,” Turk. J. Eng. Environ. Sci.
, 32
, pp. 117
–123
.17.
Ali
, N.
, Wang
, Y.
, Hayat
, T.
, and Oberlack
, M.
, 2009
, “Slip Effects on the Peristaltic Flow of a Third Grade Fluid in a Circular Cylindrical Tube
,” ASME J. Appl. Mech.
, 76
(1), p. 011006
.10.1115/1.299876118.
Chaube
, M. K.
, Pandey
, S. K.
, and Tripathi
, D.
, 2010
, “Slip Effect on Peristaltic Transport of Micropolar Fluid
,” Appl. Math. Sci.
, 4
, pp. 2105
–2117
.19.
Tripathi
, D.
, Gupta
, P. K.
, and Das
, S.
, 2011
, “Influence of Slip Condition on Peristaltic Transport of Viscoelastic Fluid With Fractional Burgers' Model
,” Therm. Sci.
, 15
, pp. 501
–515
.10.2298/TSCI100503061T20.
Hayat
, T.
, and Hina
, S.
, 2011
, “Effects of Heat and Mass Transfer on Peristaltic Flow of Williamson Fluid in a Non-Uniform Channel With Slip Conditions
,” Int. J. Num. Methods Fluids
, 67
, pp. 1590
–1604
.10.1002/fld.243321.
Hayat
, T.
, Javed
, M.
, and Asghar
, S.
, 2011
, “Slip Effects in Peristalsis
,” Numer. Methods Partial Differ. Equ.
, 27
, pp. 1003
–1015
.10.1002/num.2056422.
Hayat
, T.
, Hina
, S.
, and Hendi
, A. A.
, 2012
, “Slip Effects on Peristaltic Transport of a Maxwell Fluid With Heat and Mass Transfer
,” J. Mech. Med. Biol.
, 12
, p. 1250001
.10.1142/S021951941200437523.
Mitra
, T. K.
, and Prasad
, S. N.
, 1973
, “On the Influence of Wall Properties and Poiseuille Flow in Peristalsis
,” J. Biomech.
, 6
, pp. 681
–693
.10.1016/0021-9290(73)90024-924.
Radhakrishnamacharya
, G.
, and Srinivasulu
, C.
, 2007
, “Influence of Wall Properties on Peristaltic Transport With Heat Transfer
,” C. R. Mec.
, 335
, pp. 369
–373
.10.1016/j.crme.2007.05.00225.
Muthu
, P.
, Kumar
, B. V. R.
, and Chandra
, P.
, 2008
, “Peristaltic Motion of Micropolar Fluid in Circular Cylindrical Tubes: Effect of Wall Properties
,” Appl. Math. Model.
, 32
, pp. 2019
–2033
.10.1016/j.apm.2007.06.03426.
Srinivas
, S.
, Gayathri
, R.
, and Kothandapani
, M.
, 2009
, “The Influence of Slip Conditions, Wall Properties and Heat Transfer on MHD Peristaltic Transport
,” Comput. Phys. Commun.
, 180
, pp. 2115
–2122
.10.1016/j.cpc.2009.06.01527.
Srinivas
, S.
, and Kothandapani
, M.
, 2009
, “The Influence of Heat and Mass Transfer on MHD Peristaltic Flow Through a Porous Space With Compliant Walls
,” Appl. Math. Comput.
, 213
, pp. 197
–208
.10.1016/j.amc.2009.02.05428.
Hayat
, T.
, Javed
, M.
, and Hendi
, A. A.
, 2011
, “Peristaltic Transport of Viscous Fluid in a Curved Channel With Compliant Walls
,” Int. J. Heat Mass Transfer
, 54
, pp. 1615
–1621
.10.1016/j.ijheatmasstransfer.2010.11.02229.
Hayat
, T.
, Hina
, S.
, Hendi
, A. A.
, and Asghar
, S.
, 2011
, “Effect of Wall Properties on the Peristaltic Flow of a Third Grade Fluid in a Curved Channel With Heat and Mass Transfer
,” Int. J. Heat Mass Transfer
, 54
, pp. 5126
–5136
.10.1016/j.ijheatmasstransfer.2011.07.03630.
Choi
, S. U. S.
, 1995
, “Enhancing Thermal Conductivity of Fluids With Nanoparticle
,” Developments and Applications of Non-Newtonian Flows
, Vol. 231
, D. A.
Siginer
and H. P.
Wang
, eds., ASME FED
, pp. 99
–105
.31.
Buongiorno
, J.
, 2006
, “Convective Transport in Nanofluids
,” ASME J. Heat Transfer
, 128
(3), pp. 240
–250
.10.1115/1.215083432.
Kuznetsov
, A. V.
, and Nield
, D. A.
, 2010
, “Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate
,” Int. J. Therm. Sci.
, 49
, pp. 243
–247
.10.1016/j.ijthermalsci.2009.07.01533.
Nield
, D. A.
, and Kuznetsov
, A. V.
, 2009
, “The Cheng–Minkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid
,” Int. J. Heat Mass Transfer
, 52
, pp. 5792
–5795
.10.1016/j.ijheatmasstransfer.2009.07.02434.
Khan
, W. A.
, and Pop
, I.
, 2010
, “Boundary-Layer Flow of a Nanofluid Past a Stretching Sheet
,” Int. J. Heat Mass Transfer
, 53
, pp. 2477
–2483
.10.1016/j.ijheatmasstransfer.2010.01.03235.
Rana
, P.
, and Bhargava
, R.
, 2012
, “Flow and Heat Transfer of a Nanofluid Over a Nonlinearly Stretching Sheet: A Numerical Study
,” Commun. Nonlinear Sci. Numer. Simul.
, 17
, pp. 212
–226
.10.1016/j.cnsns.2011.05.00936.
Makinde
, O.
, and Aziz
, A.
, 2011
, “Boundary Layer Flow of a Nanofluid Past a Stretching Sheet With a Convective Boundary Condition
,” Int. J. Therm. Sci.
, 50
, pp. 1326
–1332
.10.1016/j.ijthermalsci.2011.02.01937.
Mustafa
, M.
, Hayat
, T.
, Pop
, I.
, Asghar
, S.
, and Obaidat
, S.
, 2011
, “Stagnation-Point Flow of a Nanofluid Towards a Stretching Sheet
,” Int. J. Heat Mass Transfer
, 54
, pp. 5588
–5594
.10.1016/j.ijheatmasstransfer.2011.07.02138.
Akbar
, N. S.
, and Nadeem
, S.
, 2011
, “Endoscopic Effects on Peristaltic Flow of a Nanofluid
,” Commun. Theor. Phys.
, 56
, pp. 761
–768
.10.1088/0253-6102/56/4/2839.
Akbar
, N. S.
, Nadeem
, S.
, Hayat
, T.
, and Hendi
, A. A.
, 2012
, “Peristaltic Flow of a Nanofluid With Slip Effects
,” Meccanica
, 47
, pp. 1283
–1294
.10.1007/s11012-011-9512-340.
Liao
, S. J.
, 2009
, “Notes on the Homotopy Analysis Method: Some Definitions and Theorems
,” Commun. Nonlinear Sci. Numer. Simul.
, 14
, pp. 983
–997
.10.1016/j.cnsns.2008.04.01341.
Liao
, S. J.
, 2010
, “On the Relationship Between the Homotopy Analysis Method and Euler Transform
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
, pp. 1421
–1431
.10.1016/j.cnsns.2009.06.00842.
Abbasbandy
, S.
, Shivanian
, E.
, and Vajravelu
, K.
, 2011
, “Mathematical Properties of -Curve in the Frame Work of the Homotopy Analysis Method
,” Commun. Nonlinear Sci. Numer. Simul.
, 16
, pp. 4268
–4275
.10.1016/j.cnsns.2011.03.03143.
Rashidi
, M. M.
, Pour
, S. A. M.
, and Abbasbandy
, S.
, 2011
, “Analytic Approximate Solutions for Heat Transfer of a Micropolar Fluid Through a Porous Medium With Radiation
,” Commun. Nonlinear Sci. Numer. Simul.
, 16
, pp. 1874
–1889
.10.1016/j.cnsns.2010.08.01644.
Hayat
, T.
, Mustafa
, M.
, and Asghar
, S.
, 2010
, “Unsteady Flow With Heat and Mass Transfer of a Third Grade Fluid Over a Stretching Surface in the Presence of Chemical Reaction
,” Nonlinear Anal.: Real World Appl.
, 11
, pp. 3186
–3197
.10.1016/j.nonrwa.2009.11.01245.
Hayat
, T.
, and Nawaz
, M.
, 2011
, “Unsteady Stagnation Point Flow of Viscous Fluid Caused by an Impulsively Rotating Disk
,” J. Taiwan Inst. Chem. Eng.
, 42
, pp. 41
–49
.10.1016/j.jtice.2010.04.006Copyright © 2013 by ASME
You do not currently have access to this content.
