The transport of complex rheological fluids in physiological ducts is often facilitated by the dynamic phenomenon of peristalsis. Additionally, peristaltic transport assisted by cilia plays a significant role in various natural processes such as respiration, circulation, locomotion, and reproduction. This study focuses on magnetically induced flow bounded by non-uniform curved walls, motivated by the importance of peristalsis and micro-organism motility. To characterize the complex rheology of the fluid liner, a viscoelastic model described by the constitutive equation of Jeffrey's fluid is employed. The flow problem is mathematically formulated using curvilinear coordinates. Subsequently, linear transformations and scaling factors are applied to convert the equations into dimensionless form, while considering biotic restrictions such as creeping transport and long wavelength to reduce dependent variables. By utilizing the stream function and cross-differentiation, a fourth-order equation is obtained and numerically approximated using the shooting method. The effects of various parameters on the flow are illustrated through graphs, and a physical interpretation of the graphical results is provided. It is observed that ciliated walls of the channel enhance the velocity and pumping, while trapping phenomena are more pronounced in a non-uniform channel compared to a uniform channel.
REFERENCES
1.
T.
Omori
,
H.
Sugai
,
Y.
Imai
, and
T.
Ishikawa
, “
Nodal cilia-driven flow: Development of a computational model of the nodal cilia axoneme
,” J. Biomech.
61
, 242
–249
(2017
).2.
A.
Takamatsu
,
T.
Ishikawa
,
K.
Shinohara
, and
H.
Hamada
, “
Asymmetric rotational stroke in mouse node cilia during left-right determination
,” Phys. Rev. E
87
(5
), 050701
(2013
).3.
D.
Chen
,
D.
Norris
, and
Y.
Ventikos
, “
The active and passive ciliary motion in the embryo node: A computational fluid dynamics model
,” J. Biomech.
42
(3
), 210
–216
(2009
).4.
J.
Buceta
,
M.
Ibañes
,
D.
Rasskin-Gutman
,
Y.
Okada
,
N.
Hirokawa
, and
J. C.
Izpisúa-Belmonte
, “
Nodal cilia dynamics and the specification of the left/right axis in early vertebrate embryo development
,” Biophys. J.
89
(4
), 2199
–2209
(2005
).5.
D.
Chen
and
Y.
Zhong
, “
A computational model of dynein activation patterns that can explain nodal cilia rotation
,” Biophys. J.
109
(1
), 35
–48
(2015
).6.
K.
Javid
,
U. F.
Alqsair
,
M.
Hassan
,
M. M.
Bhatti
,
T.
Ahmad
, and
E.
Bobescu
, “
Cilia-assisted flow of viscoelastic fluid in a divergent channel under porosity effects
,” Biomech. Model. Mechanobiol.
20
, 1399
–1412
(2021
).7.
S.
Ijaz
,
M.
Abdullah
,
H.
Sadaf
, and
S.
Nadeem
, “
Generalized complex cilia tip modeled flow through an electroosmotic region
,” J. Cent. South Univ.
30
(4
), 1217
–1230
(2023
).8.
B.
Kada
,
A. A.
Pasha
,
Z.
Asghar
,
M. W. S.
Khan
,
I. B.
Aris
, and
M. S.
Shaikh
, “
Carreau–Yasuda fluid flow generated via metachronal waves of cilia in a micro-channel
,” Phys. Fluids
35
(1
), 013110
(2023
).9.
K.
Javid
,
M.
Ellahi
,
K.
Al-Khaled
,
M.
Raza
,
S. U.
Khan
,
M. I.
Khan
, and
M. I.
Khan
, “
EMHD creeping rheology of nanofluid through a micro-channel via ciliated propulsion under porosity and thermal effects
,” Case Stud. Therm. Eng.
30
, 101746
(2022
).10.
H.
Sadaf
,
Z.
Asghar
, and
N.
Iftikhar
, “
Metachronal wave impact in a channel flow in the presence of Prandtl fluid model,
” preprint, https://doi.org/10.21203/rs.3.rs-2878901/v1 (2023
).11.
K.
Maqbool
,
N.
Manzoor
,
S.
Poncet
, and
A. M.
Siddiqui
, “
Inertial flow of viscoelastic second-grade fluid in a ciliated channel under a magnetic field and Darcy's resistance
,” Appl. Sci.
11
(9
), 3819
(2021
).12.
K.
Ramesh
,
D.
Tripathi
, and
O. A.
Bég
, “
Cilia-assisted hydromagnetic pumping of bio-rheological couple stress fluids
,” Propul. Power Res.
8
(3
), 221
–233
(2019
).13.
H.
Sadaf
and
S.
Nadeem
, “
Fluid flow analysis of cilia beating in a curved channel in the presence of magnetic field and heat transfer
,” Can. J. Phys.
98
(2
), 191
–197
(2020
).14.
M. K.
Chaube
,
A.
Yadav
,
D.
Tripathi
, and
O. A.
Bég
, “
Electroosmotic flow of biorheological micropolar fluids through microfluidic channels
,” Korea-Australia Rheol. J.
30
, 89
–98
(2018
).15.
S.
Nadeem
,
A.
Munim
,
A.
Shaheen
, and
S.
Hussain
, “
Physiological flow of Carreau fluid due to ciliary motion
,” AIP Adv.
6
(3
), 035125
(2016
).16.
M. M.
Bhatti
,
A.
Zeeshan
, and
M. M.
Rashidi
, “
Influence of magnetohydrodynamics on metachronal wave of particle-fluid suspension due to cilia motion
,” Eng. Sci. Technol. Int. J.
20
(1
), 265
–271
(2017
).17.
Z.
Asghar
,
M. W. S.
Khan
,
M. A.
Gondal
, and
A.
Ghaffari
, “
Magneto-hydro-dynamic flow of Carreau Yasuda fluid inside a complex wavy passage formed by beating cilia: A finite-difference analysis
,” Proc. Inst. Mech. Eng., Part E
(published online 2023
).18.
S.
Munawar
, “
Significance of slippage and electric field in mucociliary transport of bio-magnetic fluid
,” Lubricants
9
(5
), 48
(2021
).19.
K.
Javid
,
M.
Riaz
,
Y. M.
Chu
,
M. I.
Khan
,
S. U.
Khan
, and
S.
Kadry
, “
Peristaltic activity for electro-kinetic complex driven cilia transportation through a non-uniform channel
,” Comput. Methods Programs Biomed.
200
, 105926
(2021
).20.
H.
Sadaf
,
Z.
Asghar
, and
N.
Iftikhar
, “
Cilia-driven flow analysis of cross fluid model in a horizontal channel
,” Comput. Part. Mech.
10
(4
), 943
–950
(2023
).21.
N. S.
Akbar
,
D.
Tripathi
,
Z. H.
Khan
, and
O. A.
Bég
, “
Mathematical modelling of pressure-driven micropolar biological flow due to metachronal wave propulsion of beating cilia
,” Math. Biosci.
301
, 121
–128
(2018
).22.
W. U.
Khan
,
A.
Imran
,
M. A. Z.
Raja
,
M.
Shoaib
,
S. E.
Awan
,
K.
Kausar
, and
Y.
He
, “
A novel mathematical modeling with solution for movement of fluid through ciliary caused metachronal waves in a channel
,” Sci. Rep.
11
(1
), 20601
(2021
).23.
R.
Ellahi
and
F.
Hussain
, “
Simultaneous effects of MHD and partial slip on peristaltic flow of Jeffrey's fluid in a rectangular duct
,” J. Magn. Magn. Mater.
393
, 284
–292
(2015
).24.
T.
Hayat
,
M.
Javed
, and
N.
Ali
, “
MHD peristaltic transport of a Jeffrey's fluid in a channel with compliant walls and porous space
,” Transp. Porous Media
74
, 259
–274
(2008
).25.
R.
Ellahi
,
M. M.
Bhatti
,
A.
Riaz
, and
M.
Sheikholeslami
, “
Effects of magnetohydrodynamics on peristaltic flow of Jeffrey's fluid in a rectangular duct through a porous medium
,” J. Porus Media
17
(2
), 143
–157
(2014
).26.
R.
Ellahi
,
M. M.
Bhatti
, and
I.
Pop
, “
Effects of hall and ion slip on MHD peristaltic flow of Jeffrey's fluid in a non-uniform rectangular duct
,” Int. J. Numer. Methods Heat Fluid Flow
26
(6
), 1802
–1820
(2016
).27.
Z.
Abbas
,
M. Y.
Rafiq
,
J.
Hasnain
, and
H.
Umer
, “
Impacts of Lorentz force and chemical reaction on peristaltic transport of Jeffrey's fluid in a penetrable channel with injection/suction at walls
,” Alexandria Eng. J.
60
(1
), 1113
–1122
(2021
).28.
X.
Li
,
A.
Abbasi
,
K.
Al-Khaled
,
H. F. M.
Ameen
,
S. U.
Khan
,
M. I.
Khan
, and
K.
Guedri
, “
Thermal performance of iron oxide and copper (Fe3O4, Cu) in hybrid nanofluid flow of Casson material with Hall current via complex wavy channel
,” Mater. Sci. Eng.: B
289
, 116250
(2023
).29.
A.
Abbasi
,
A.
Zaman
,
W.
Farooq
, and
M. F.
Nadeem
, “
Electro-osmosis modulated peristaltic flow of Oldroyd 4-constant fluid in a non-uniform channel
,” Indian J. Phys.
96
, 825
–837
(2022
).30.
T.
Hayat
,
H.
Zahir
,
A.
Alsaedi
, and
B.
Ahmad
, “
Peristaltic flow of rotating couple stress fluid in a non-uniform channel
,” Results Phys.
7
, 2865
–2873
(2017
).31.
K.
Javid
,
N.
Ali
, and
Z.
Asghar
, “
Numerical simulation of the peristaltic motion of a viscous fluid through a complex wavy non-uniform channel with magneto-hydro-dynamic effects
,” Phys. Scr.
94
(11
), 115226
(2019
).32.
J.-B.
Wu
and
L.
Li
, “
Pressure–flow rate relationship and its polynomial expansion for laminar flow in a circular pipe based on exponential viscosity-pressure characteristics: An extension of classical Poiseuille's law
,” Phys. Fluids
35
, 103613
(2023
).33.
L. R.
Mashiku
and
S.
Shaw
, “
Unsteady nano-magnetic drug dispersion for pulsatile Darcy flow through microvessel with drug elimination phenomena
,” Phys. Fluids
35
, 101909
(2023
).34.
D.
Zhang
,
C.
Duan
,
J.
Guan
,
S.
Chen
,
X.
Ha
,
T.
Liu
,
D.
Liu
, and
S.
Tang
, “
Molecular dynamics simulation of ultrasound cavitation occurring in copper–water nanofluid
,” Phys. Fluids
35
, 102021
(2023
).35.
M. I.
Khan
,
A.
Abbasi
,
S.
Danish
, and
W.
Farooq
, “
Computational analysis of cilia-mediated flow dynamics of Jeffrey's nanofluid in physiologically realistic geometries
,” Phys. Fluids
35
, 093107
(2023
).36.
N.
Ali
,
M.
Sajid
, and
T.
Hayat
, “
Long wavelength flow analysis in a curved channel
,” Z. Naturforsch. A
65
(3
), 191
–196
(2010
).37.
M.
Turkyilmazoglu
, “
Velocity slip and entropy generation phenomena in thermal transport through metallic porous channel
,” J. Non-Equilibrium Thermodyn.
45
(3
), 247
–256
(2020
).38.
Z.
Asghar
,
K.
Javid
,
M.
Waqas
,
A.
Ghaffari
, and
W. A.
Khan
, “
Cilia-driven fluid flow in a curved channel: Effects of complex wave and porous medium
,” Fluid Dyn. Res.
52
(1
), 015514
(2020
).39.
M.
Turkyilmazoglu
and
F. Z.
Duraihem
, “
Fully developed flow in a long triangular channel under an applied magnetic field
,” J. Magn. Magn. Mater.
578
, 170803
(2023
).40.
P. Y.
Xiong
,
K.
Javid
,
M.
Raza
,
S. U.
Khan
,
M. I.
Khan
, and
Y. M.
Chu
, “
MHD flow study of viscous fluid through a complex wavy curved surface due to bio-mimetic propulsion under porosity and second-order slip effects
,” Commun. Theor. Phys.
73
(8
), 085001
(2021
).41.
M.
Akermi
,
N.
Jaballah
,
I. M.
Alarifi
,
M.
Rahimi-Gorji
,
R. B.
Chaabane
,
H. B.
Hafedh Ben Ouada
, and
M.
Majdoub
, “
Synthesis and characterization of a novel hydride polymer P-DSBT/ZnO nano-composite for optoelectronic applications
,” J. Mol. Liq.
287
, 110963
(2019
).42.
M.
Turkyilmazoglu
, “
Eyring-Powell fluid flow through a circular pipe and heat transfer: Full solutions
,” Int. J. Numer. Methods Heat Fluid Flow
30
(11
), 4765
–4774
(2020
).43.
S. O.
Adesanya
,
A. S.
Onanaye
,
O. G.
Adeyemi
,
M.
Rahimi-Gorji
, and
I. M.
Alarifi
, “
Evaluation of heat irreversibility in couple stress falling liquid films along heated inclined substrate
,” J. Cleaner Prod.
239
, 117608
(2019
).44.
M.
Turkyilmazoglu
and
I.
Pop
, “
Induced flow and heat transfer due to inner stretching and outer stationary coaxial cylinders
,” Int. Commun. Heat Mass Transfer
146
, 106903
(2023
).45.
C.
Kumawat
,
B. K.
Sharma
,
Q. M.
Al-Mdallal
, and
M.
Rahimi-Gorji
, “
Entropy generation for MHD two phase blood flow through a curved permeable artery having variable viscosity with heat and mass transfer
,” Int. Commun. Heat Mass Transfer
133
, 105954
(2022
).46.
D.
Khan
,
G.
Ali
, and
H. A.
Ghazwani
, “
Enhancing heat transfer in MHD Falkner's-Skan flow with thermal radiation, free convection and dusty fluid between parallel plates
,” Heat Transfer
(published online 2024
).47.
S. C.
Saha
,
M. S.
Islam
,
M.
Rahimi-Gorji
, and
M. M.
Molla
, “
Aerosol particle transport and deposition in a CT-scan based mouth-throat model
,” AIP Conf. Proc.
2121
, 040011
(2019
).48.
M. A.
Aiyashi
,
S. M.
Abo-Dahab
, and
M. D.
Albalwi
, “
Effect of viscous dissipation and induced magnetic field on an unsteady mixed convective stagnation point flow of a non-homogenous nanofluid
,” Sci. Rep.
13
, 22529
(2023
).49.
S.
Akhtar
,
M. H.
Shahzad
,
S.
Nadeem
,
A. U.
Awan
,
S.
Almutairi
,
H. A.
Ghazwani
, and
M. M.
Sayed
, “
Analytical solutions of PDEs by unique polynomials for peristaltic flow of heated Rabinowitsch fluid through an elliptic duct
,” Sci. Rep.
12
, 12943
(2022
).50.
S.
Zhu
,
X.
Li
,
Y.
Bian
,
N.
Dai
,
J.
Yong
,
Y.
Hu
, and
J.
Chu
, “
Inclination-enabled generalized microfluid rectifiers via anisotropic slippery hollow tracks
,” Adv. Mater. Technol.
8
(16
), 2300267
(2023
).51.
Z.
Sheng
,
M.
Cheng
, and
J.
Wang
, “
Multi-wave effects on stability and performance in rotating detonation combustors
,” Phys. Fluids
35
(7
), 76119
(2023
).52.
Y.
Wang
,
M.
Lou
,
Y.
Wang
,
W.
Wu
, and
F.
Yang
, “
stochastic failure analysis of reinforced thermoplastic pipes under axial loading and internal pressure
,” China Ocean Eng.
36
(4
), 614
–628
(2022
).53.
L.
Sun
,
T.
Liang
,
C.
Zhang
, and
J.
Chen
, “
The rheological performance of shear-thickening fluids based on carbon fiber and silica nanocomposite
,” Phys. Fluids
35
(3
), 032002
(2023
).© 2024 Author(s). Published under an exclusive license by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.
