This paper discusses the effects of magnetic field and heat and mass transfer on the peristaltic flow of an incompressible fluid in a channel with compliant walls. Mathematical formulation for the fourth grade fluid is presented. Relations of stream function, temperature, concentration field, and heat transfer coefficient are derived. The variations of the interesting parameters entering into the problem are carefully analyzed.
Issue Section:
Bio-Heat and Mass Transfer
References
1.
Latham
, T. W.
, 1966, “Fluid Motion in a Peristaltic Pump
,” M.S. thesis, MIT, Cambridge, MA.2.
Jaffrin
, M. Y.
, and Shapiro
, A. H.
, 1971, “Peristaltic Pumping
,” Annu. Rev. Fluid Mech.
, 3
, pp. 13
–16
.3.
Mekheimer
, K. S.
, 2008, “Effect of the Induced Magnetic Field on Peristaltic Flow of a Couple Stress Fluid
,” Phys. Lett. A
, 372
(23
), pp. 4271
–4278
.4.
Ebaid
, A.
, 2008, “Effects of Magnetic Field and Wall Slip Conditions on the Peristaltic Transport of a Newtonian Fluid in an Asymmetric Channel
,” Phys. Lett. A
, 372
(24
), pp. 4493
–4499
.5.
Haroun
, M. H.
, 2007, “Effect of Deborah Number and Phase Difference on Peristaltic Transport of a Third Order Fluid in an Asymmetric Channel
,” Commun. Nonlinear Sci. Numer. Simul.
, 12
(8
), pp. 1464
–1480
.6.
Haroun
, M. H.
, 2007, “Nonlinear Peristaltic Flow of a Fourth Grade Fluid in an Inclined Asymmetric Channel
,” Comput. Mater. Sci.
, 39
, pp. 324
–333
.7.
Rao
, A. R.
, and Mishra
, M.
, 2004, “Peristaltic Transport of a Power-Law Fluid in a Porous Tube
,” J. Non-Newtonian Fluid Mech.
, 121
(2–3
), pp. 163
–174
.8.
Kothandapani
, M.
, and Srinivas
, S.
, 2008, “Peristaltic Transport of a Jeffrey Fluid Under the Effect of Magnetic Field in an Asymmetric Channel
,” Int. J. Nonlinear Mech.
, 43
(9
), pp. 915
–924
.9.
Kothandapani
, M.
, and Srinivas
, S.
, 2008, “Nonlinear Peristaltic Transport of a Newtonian Fluid in an Inclined Asymmetric Channel Through a Porous Medium
,” Phys. Lett. A
, 372
(8
), pp. 1265
–1276
.10.
Hayat
, T.
, Hussain
, Q.
, Ali
, N.
, and Asghar
, S.
, 2008, “Slip Effects on the Peristaltic Transport of MHD Fluid With Variable Viscosity
,” Phys. Lett. A
, 372
(9
), pp. 1477
–1489
.11.
Hayat
, T.
, Ali
, N.
, and Asghar
, S.
, 2007, “Hall Effects on the Peristaltic Flow of Maxwell Fluid in a Porous Medium
,” Phys. Lett. A
, 363
(5–6
), pp. 397
–403
.12.
Hayat
, T.
, Hussain
, Q.
, and Ali
, N.
, 2008, “Influence of Partial Slip on the Peristaltic Flow in a Porous Medium
,” Phys. A
, 387
(14
), pp. 3399
–3409
.13.
Hayat
, T.
, Alvi
, N.
, and Ali
, N.
, 2008, “Peristaltic Mechanism of a Maxwell Fluid in an Asymmetric Channel
,” Nonlinear Anal.: Real World Appl.
, 9
(4
), pp. 1474
–1490
.14.
Hayat
, T.
, Qureshi
, M. U.
, and Ali
, N.
, 2008, “The Influence of Slip on the Peristaltic Motion of a Third Order Fluid in an Asymmetric Channel
,” Phys. Lett. A
, 372
(15
), pp. 2653
–2664
.15.
Wang
, Y.
, Ali
, N.
, Hayat
, T.
, and Oberlack
, M.
, 2009, “Slip Effects on the Peristaltic Flow of a Third Grade Fluid in Circular Cylinder
,” ASME J. Appl. Mech.
, 76
, p. 011006
.16.
Radhakrishnamacharya
, G.
, and Murty
, V. R.
, 1993, “Heat Transfer to Peristaltic Transport in a Non-Uniform Channel
,” Def. Sci. J.
, 43
(3
), pp. 275
–280
.17.
Srinivas
, S.
, and Kothandapani
, M.
, 2008, “Peristaltic Transport in an Asymmetric Channel With Heat Transfer—A Note
,” Int. Commun. Heat Mass Transfer
, 35
(4
), pp. 514
–522
.18.
Vajravelu
, K.
, Radhakrishnamacharya
, G.
, and Murty
, V. R.
, 2007, “Peristaltic Flow and Heat Transfer in a Vertical Annulus, With Long Wave Approximation
,” Int. J. Nonlinear Mech.
, 42
(5
), pp. 754
–759
.19.
Mekheimer
, K. S.
, and Abd elmaboud
, Y.
, 2008, “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
, 372
(10
), pp. 1657
–1665
.20.
Mekheimer
, K. S.
, Husseny
, S. Z. A.
, and Abd elmaboud
, Y.
, 2010, “Effects of Heat Transfer and Space Porosity on Peristaltic Flow in a Vertical Asymmetric Channel
,” Numer. Methods Partial Differ. Equ.
, 26
(4
), pp. 747
–770
.21.
Hayat
, T.
, Qureshi
, M. U.
, and Hussain
, Q.
, 2009, “Effect of Heat Transfer on the Peristaltic Flow of an Electrically Conducting Fluid in a Porous Space
,” Appl. Math. Model.
, 33
(4
), pp. 1862
–1873
.22.
Hayat
, T.
, Hina
, S.
, and Ali
, N.
, 2010, “Simultaneous Effects of Slip and Heat Transfer on the Peristaltic Flow
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
(6
), pp. 1526
–1537
.23.
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
(10
), pp. 2019
–2033
.24.
Abd Elnaby
, M. A.
, and Haroun
, M. H.
, 2008, “A New Model for Study the Effect of Wall Properties on Peristaltic Transport of a Viscous Fluid
,” Commun. Nonlinear Sci. Numer. Simul.
, 13
(4
), pp. 752
–762
.25.
Radhakrishnamacharya
, G.
, and Srinivasulu
, C.
, 2007, “Influence of Wall Properties on Peristaltic Transport With Heat Transfer
,” C. R. Mec.
, 335
(7
), pp. 369
–373
.26.
Hayat
, T.
, Javed
, M.
, and Ali
, N.
, 2008, “MHD Peristaltic Transport of Jeffery Fluid in a Channel With Compliant Walls and Porous Space
,” Transp. Porous Media
, 74
(3
), pp. 259
–274
.27.
Hayat
, T.
, Javed
, M.
, and Asghar
, S.
, 2008, “MHD Peristaltic Motion of Johnson-Segalman Fluid in a Channel With Compliant Walls
,” Phys. Lett. A
, 372
(30
), pp. 5026
–5036
.28.
Ali
, N.
, Hayat
, T.
, and Asghar
, S.
, 2009, “Peristaltic Flow of a Maxwell Fluid in a Channel With Compliant Walls
,” Chaos, Solitons Fractals
, 39
(1
), pp. 407
–416
.29.
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
(1
), pp. 197
–208
.30.
Eldabe
, N. T. M.
, El-Sayed
, M. F.
, Ghaly
, A. Y.
, and Sayed
, H. M.
, 2008, “Mixed Convection Heat and Mass Transfer in a Non-Newtonian Fluid at a Peristaltic Surface With Temperature-Dependent Viscosity
,” Arch. Appl. Mech.
, 78
(8
), pp. 599
–624
.31.
Hayat
, T.
, and Hina
, S.
, 2010, “The Influence of Wall Properties on the MHD Peristaltic Flow of a Maxwell Fluid With Heat and Mass Transfer
,” Nonlinear Anal.: Real World Appl.
, 11
(4
), pp. 3155
–3169
.32.
Nadeem
, S.
, Akbar
, N. S.
, Bibi
, N.
, and Ashiq
, S.
, 2010, “Influence of Heat and Mass Transfer on Peristaltic Flow of a Third Order Fluid in a Diverging Tube
,” Commun. Nonlinear Sci. Numer. Simul.
, 15
(10
), pp. 2916
–2931
.Copyright © 2012
by American Society of Mechanical Engineers
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