Impact of compliant walls on magnetohydrodynamics peristalsis of Jeffrey material in a curved configuration

Document Type : Article

Authors

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

2 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Abstract

Primary aim of current attempt is to analyze the peristaltic flow of non-Newtonian material in a curved channel subject to two salient features namely the Soret and Dufour and radial magnetic field. Channel walls are of compliant characteristics. Problem formulations for constitutive equations of Jeffrey fluid are made. Lubrication approach is implemented for the simplification of mathematical analysis. Dimensionless problems of stream function, temperature and concentration are computed numerically. Characteristics of distinct variables on the velocity, temperature, coefficient of heat transfer and concentration are examined. Besides this graphical results indicates that velocity profile enhances significantly for compliant wall parameters however due to the resistance characteristics of Lorentz force velocity profile decays. Furthermore it is noted that temperature profile enhances for larger Dufour number however reverse behavior is noticed in the concentration profile when Soret and Schmidt numbers are increased.

Keywords

Main Subjects


References
1. Latham, T.W. Fluid Motion in a Peristaltic Pump,
MIT, Cambridge MA (1966).
2. Shapiro, A.H., Ja rin, M.Y. and Weinberg, S.L. \Peristaltic
pumping with long wavelength at low Reynolds
number", J. Fluid Mech., 35, pp. 799-825 (1969).
3. Tripathi, D.A. \Mathematical model for swallowing of
food bolus through the esophagus under the in
uence
of heat transfer", Int. J. Therm. Sci., 51, pp. 91-101
(2012).
4. Mekheimer, Kh.S., Abd Elmaboud, Y. and Abdellateef,
A.I. \Particulate suspension
ow induced by sinusoidal
peristaltic waves through eccentric cylinders:
thread annular", Int. J. Biomath., 06, p. 1350026
(2013) .
5. Mustafa, M., Abbasbandy, S., Hina, S. and Hayat,
T. \Numerical investigation on mixed convective peristaltic

ow of fourth grade
uid with Dufour and Soret
e ects", J. Taiwan Inst. Chem. Eng., 45, pp. 308-316
(2014).
6. Mekheimer, Kh.S. and Abd elmaboud, Y. \Simultaneous
e ects of variable viscosity and thermal
conductivity on peristaltic
ow in a vertical asymmetric
channel", Can. J. Phys., 92, pp. 1541-1555 (2014).
7. Gad, N.S. \E ects of hall currents on peristaltic
transport with compliant walls", Appl. Math. Comput.,
235, pp. 546-554 (2014).
8. Sinha , A., Shit, G.C. and Ranjit, N.K. \Peristaltic
transport of MHD
ow and heat transfer in an asymmetric
channel: E ects of variable viscosity, velocityslip
and temperature jump, Alexandria", Eng. J., 54,
pp. 691-704 (2015).
9. Ellahi, R. Bhatti, M.M. Riaz, A. and Sheikoleslami, M.
\The e ect of magnetohydrodynamics on peristaltic

ow of Je rey
uid in a rectangular duct through a
porus medium", J. Porus Media., 17, pp. 1-20 (2014).
10. Awais, M., Farooq, S., Yasmin, H., Hayat, T. and
Alsaedi, A. \Convective heat transfer analysis for
MHD peristaltic
ow of Je rey
uid in an asymmetric
channel", Int. J. Biomath., 7, 1450023 (2014).
11. Kothandapani, M. and Srinivas, S. \Peristaltic transport
of Je rey
uid under the e ect of magnetic eld
in an asymmetric channel", Int. J. non-Linear Mech.,
43, pp. 915-924 (2012).
T. Hayat et al./Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 741{750 749
12. Hayat, T., Bibi, A., Yasmin, H. and Ahmad, B.
\Simultaneous e ects of Hall current and homogeneous/
heterogeneous reactions on peristalsis", J. Taiwan
Inst. Chem. Eng., 58, pp. 28-38 (2016).
13. Asghar, S., Minhas, T. and Ali, A. \Existence of a
Hartmann layer in the peristalsis of Sisko
uid", Chin.
Phys. B., 23, pp. 054702-054707 (2014).
14. Hina, S., Mustafa, M., Hayat , T. and Alotaibi,
N.D. \On peristaltic motion of pseudoplastic
uid
in a curved channel with heat/mass transfer an wall
properties", Appl. Math Comput., 263, pp. 378-391
(2015).
15. Hayat, T., Hina, S., Hendi, A.A. and Asghar, S.
\E ects of wall properties on the peristaltic
ow of
a third grade
uid in a curved channel with heat and
mass transfer", Int. J. Heat Mass Transfer., 54, pp.
5126-5136 (2012).
16. Ali, N., Sajid, M., Abbas, Z. and Javed, T. \Non-
Newtonian
uid
ow induced by peristaltic waves in
a curved channel", Eur. J. Mech. B/Fluids, 29, pp.
387-394 (2010).
17. Shehzad, S.A., Abbasi, F.M., Hayat, T., Alsaadi, F.
and Mousae, G. \Peristalsis in a curved channel with
slip condition and radial magnetic eld", Int. J. Heat
Mass Transfer., 91, pp. 562-569 (2015).
18. Vajravelua, K., Sreenadh, S. and Saravana, R. \Combined
in
uence of velocity slip, temperature and
concentration jump conditions on MHD peristaltic
transport of a Carreau
uid in a non-uniform channel",
Appl. Math. Comput., 225, pp. 656-676 (2013).
19. Hina, S., Mustafa, M. and Hayat, T. \On the exact
solution for peristaltic
ow of Couple-stress
uid with
wall properties, \Bulg. Chem. Commun"., 47, pp. 30-
37 (2015).
20. Abd-Alla, A.M. and Abo-Dahab, S.M. \Magnetic eld
and rotation e ects on peristaltic transport of a Je rey

uid in an asymmetric channel", J. Mag. Mag. Mater.,
374, pp. 680-689 (2015).
21. Hayat, T., Bibi, S., Alsaadi, F. and Ra q, M.,
\Peristaltic transport of Prandtl-Eyring liquid in a
convectively heated curved channel", PLoS One., 11,
e0156995 (2016).
22. Ellahi, R., Bhatti, M.M. and Pop, I. \E ects of hall
and ion slip on MHD peristaltic
ow of Je rey
uid
in a non-uniform rectangular duct", Int. J. Numer.
Methods Heat Fluid Flow., 26, pp. 1802-1820 (2016).
23. Hayat, T., Farooq, S., and Alsaedi, A. \MHD peristaltic

ow in a curved channel with convective condition",
J. Mech, 33, pp. 483-499 (2017).
24. Khan, A.A., Muhammad, S., Ellahi, R. and Zia,
Q.M. Z. \Bionic study of variable viscosity on MHD
peristaltic
ow of pseudoplastic
uid in an asymmetric
channel", J. Mag., 21, pp. 273-280 (2016).
25. Ellahi, R. and Hussain, F. \Simultaneous e ects of
MHD and partial slip on peristaltic
ow of Je ery
uid
in a rectangular duct", J. Mag. Mag. Mater., 393, pp.
284-292 (2015).
26. Bhatti, M.M., Zeeshan, A. and Ellahi, R. \Endoscope
analysis on peristaltic blood
ow of Sisko

uid with titanium magneto-nanoparticles", Computers
Bio. Med., 78, pp. 29-41 (2016).
27. Ellahi, R., Rahman, S.U., Nadeem, S. and Vafai, K.
\The blood
ow of Prandtl
uid through a tapered
stenosed arteries in permeable walls with magnetic
eld", Communi. Theor. Phy., 63, pp. 353-358 (2015).
28. Awais, M., Hayat, T., Nawaz, M. and Alsaedi, A.
\Newtonian heating, thermal-di usion and di usionthermo
e ects in an axisymmetric
ow of a Je ery
uid
over a stretching surface", Braz. J. Chem. Eng., 32,
pp. 555-561 (2015).
29. Hayat, T., Farooq, S., Ahmad, B. and Alsaedi, A.
\E ectiveness of entropy generation and energy transfer
on peristaltic
ow of Je rey material with Darcy
resistance", Int. J. Heat Mass Transfer., 106, pp. 244-
252 (2017).
30. Ali, N. Sajid, M. and Hayat, T. \Long wavelength

ow analysis in a curved channel", Zeitschrift fur
Naturforschung A. 65, pp. 191-196 (2010).
31. Srivastava, L.M. and Srivastava, V.P. \Peristaltic
transport of a power law
uid: Applications to the
ductus e erentes of the reproductive tract", Rheol.
Acta., 27, pp. 428-433 (1988).
32. Lew, S.H., Fung, Y.C. and Lowenstein, C.B. \Peristaltic
carrying and mixing of chyme", J. Biomech., 4,
pp. 297-315 (1971).

Volume 25, Issue 2
Transactions on Mechanical Engineering (B)
March and April 2018
Pages 741-750
  • Receive Date: 23 July 2016
  • Revise Date: 09 December 2016
  • Accept Date: 28 August 2017