A mathematical model is presented to study the combined viscous electro-osmotic (EO) flow and heat transfer in a finite length microchannel with peristaltic wavy walls in the presence of Joule heating. The unsteady two-dimensional conservation equations for mass, momentum, and energy conservation with viscous dissipation, heat absorption, and electrokinetic body force, are formulated in a Cartesian co-ordinate system. Both single and train wave propagations are considered. The electrical field terms are rendered into electrical potential terms via the Poisson–Boltzmann equation, Debye length approximation, and ionic Nernst Planck equation. A parametric study is conducted to evaluate the impact of isothermal Joule heating and electro-osmotic velocity on axial velocity, temperature distribution, pressure difference, volumetric flow rate, skin friction, Nusselt number, and streamline distributions.

References

1.
Dasgupta
,
P. K.
, and
Liu
,
S.
,
1994
, “
Electroosmosis: A Reliable Fluid Propulsion System for Flow Injection Analysis
,”
Anal. Chem.
,
66
(
11
), pp.
1792
1798
.
2.
Buie
,
C.
,
Kim
,
D.
,
Litster
,
S.
, and
Santiago
,
J. G.
,
2006
, “
Free Convection Direct Methanol Fuel Cells Powered by Electroosmotic Pumps
,”
ECS Trans.
,
3
(
1
), pp.
1279
1287
.
3.
Jellinek
,
H.
, and
Masuda
,
H.
,
1981
, “
Osmo-Power. Theory and Performance of an Osmo-Power Pilot Plant
,”
Ocean Eng.
,
8
(
2
), pp.
103
128
.
4.
Lacey
,
R.
,
1980
, “
Energy by Reverse Electrodialysis
,”
Ocean Eng.
,
7
(
1
), pp.
1
47
.
5.
Eow
,
J. S.
,
Ghadiri
,
M.
, and
Sharif
,
A. O.
,
2007
, “
Electro-Hydrodynamic Separation of Aqueous Drops From Flowing Viscous Oil
,”
J. Pet. Sci. Eng.
,
55
(
1
), pp.
146
155
.
6.
Hunckler
,
M. D.
,
Tilley
,
J. M.
, and
Roeder
,
R. K.
,
2015
, “
Molecular Transport in Collagenous Tissues Measured by Gel Electrophoresis
,”
J. Biomech.
,
48
(
15
), pp.
4087
4092
.
7.
Li
,
G.
, and
Fu
,
B. M.
,
2011
, “
An Electrodiffusion Model for the Blood-Brain Barrier Permeability to Charged Molecules
,”
ASME J. Biomech. Eng.
,
133
(
2
), p.
021002
.
8.
Gu
,
W.
,
Lai
,
W.
, and
Mow
,
V.
,
1997
, “
A Triphasic Analysis of Negative Osmotic Flows Through Charged Hydrated Soft Tissues
,”
J. Biomech.
,
30
(
1
), pp.
71
78
.
9.
Lew
,
H.
,
Fung
,
Y.
, and
Lowenstein
,
C.
,
1971
, “
Peristaltic Carrying and Mixing of Chyme in the Small Intestine (An Analysis of a Mathematical Model of Peristalsis of the Small Intestine)
,”
J. Biomech.
,
4
(
4
), pp.
297
315
.
10.
Zheng
,
X.
,
Xue
,
Q.
,
Mittal
,
R.
, and
Beilamowicz
,
S.
,
2010
, “
A Coupled Sharp-Interface Immersed Boundary-Finite-Element Method for Flow-Structure Interaction With Application to Human Phonation
,”
ASME J. Biomech. Eng.
,
132
(
11
), p.
111003
.
11.
Aranda
,
V.
,
Cortez
,
R.
, and
Fauci
,
L.
,
2015
, “
A Model of Stokesian Peristalsis and Vesicle Transport in a Three-Dimensional Closed Cavity
,”
J. Biomech.
,
48
(
9
), pp.
1631
1638
.
12.
Taber
,
L. A.
,
Zhang
,
J.
, and
Perucchio
,
R.
,
2007
, “
Computational Model for the Transition From Peristaltic to Pulsatile Flow in the Embryonic Heart Tube
,”
ASME J. Biomech. Eng.
,
129
(
3
), pp.
441
449
.
13.
Bertuzzi
,
A.
,
Salinari
,
S.
,
Mancinelli
,
R.
, and
Pescatori
,
M.
,
1983
, “
Peristaltic Transport of a Solid Bolus
,”
J. Biomech.
,
16
(
7
), pp.
459
464
.
14.
Tripathi
,
D.
,
Akbar
,
N. S.
,
Khan
,
Z.
, and
Bég
,
O. A.
,
2016
, “
Peristaltic Transport of Bi-Viscosity Fluids Through a Curved Tube: A Mathematical Model for Intestinal Flow
,”
Proc. Inst. Mech. Eng. (H)
,
230
(
9
), pp.
817
828
.
15.
Tözeren
,
A.
,
Özkaya
,
N.
, and
Tözeren
,
H.
,
1982
, “
Flow of Particles Along a Deformable Tube
,”
J. Biomech.
,
15
(
7
), pp.
517
527
.
16.
Hayakawa
,
M.
,
Hosogi
,
Y.
,
Takiguchi
,
H.
,
Saito
,
S.
,
Shiroza
,
T.
,
Shibata
,
Y.
,
Hiratsuka
,
K.
,
Kiyama-Kishikawa
,
M.
, and
Abiko
,
Y.
,
2001
, “
Evaluation of the Electroosmotic Medium Pump System for Preparative Disk Gel Electrophoresis
,”
Anal. Biochem.
,
288
(
2
), pp.
168
175
.
17.
Zhu
,
Z.
,
Lu
,
J. J.
,
Almeida
,
M. I. G.
,
Pu
,
Q.
,
Kolev
,
S. D.
, and
Liu
,
S.
,
2015
, “
A Microfabricated Electroosmotic Pump Coupled to a Gas-Diffusion Microchip for Flow Injection Analysis of Ammonia
,”
Microchim. Acta
,
182
(
5–6
), pp.
1063
1070
.
18.
Yeh
,
H. C.
,
Yang
,
R.-J.
, and
Luo
,
W.-J.
,
2011
, “
Analysis of Traveling-Wave Electro-Osmotic Pumping With Double-Sided Electrode Arrays
,”
Phys. Rev. E
,
83
(
5
), p.
56326
.
19.
Chakraborty
,
S.
,
2006
, “
Augmentation of Peristaltic Microflows Through Electro-Osmotic Mechanisms
,”
J. Phys. Appl. Phys.
,
39
(
24
), p.
5356
.
20.
El-Dabe
,
N.
,
Moatimid
,
G.
,
Hassan
,
M.
, and
Mostapha
,
D.
,
2016
, “
Electrohydrodynamic Peristaltic Flow of a Viscoelastic Oldroyd Fluid With a Mild Stenosis: Application of an Endoscope
,”
J. Appl. Mech. Tech. Phys.
,
57
(
1
), pp.
38
54
.
21.
Roth
,
J. R.
,
2003
, “
Aerodynamic Flow Acceleration Using Paraelectric and Peristaltic Electrohydrodynamic Effects of a One Atmosphere Uniform Glow Discharge Plasma
,”
Phys. Plasmas
,
10
(
5
), pp.
2117
2126
.
22.
Tripathi
,
D.
,
Bhushan
,
S.
, and
Bég
,
O. A.
,
2016
, “
Transverse Magnetic Field Driven Modification in Unsteady Peristaltic Transport With Electrical Double Layer Effects
,”
Colloids Surf. Physicochem. Eng. Aspects
,
506
, pp.
32
39
.
23.
Si
,
D.
, and
Jian
,
Y.
,
2015
, “
Electromagnetohydrodynamic (EMHD) Micropump of Jeffrey Fluids Through Two Parallel Microchannels With Corrugated Walls
,”
J. Phys. Appl. Phys.
,
48
(
8
), p.
85501
.
24.
Tripathi
,
D.
,
Bushan
,
S.
, and
Beg
,
O.
,
2016
, “
Analytical Study of Electro-Osmosis Modulated Capillary Peristaltic Hemodynamics
,”
J. Mech. Med. Biol.
,
17
(
3
), p.
1750052
.
25.
Dukhin
,
S. S.
, and
Derjaguin
,
B. V.
,
1974
,
Electrokinetic Phenomena
,
Wiley
,
New York
.
26.
Gajda
,
I.
, Greenman, J., Melhuish, C., Santoro, C., Li, B., Cristiani, P., and Ieropoulos, I.,
2015
, “
Electro-Osmotic-Based Catholyte Production by Microbial Fuel Cells for Carbon Capture
,”
Water Res.
,
86
, pp.
108
115
.
27.
Gobie
,
W. A.
, and
Ivory
,
C. F.
,
1990
, “
Thermal Model of Capillary Electrophoresis and a Method for Counteracting Thermal Band Broadening
,”
J. Chromatogr. A
,
516
(
1
), pp.
191
210
.
28.
Zhou
,
Y.
,
Xie
,
Y.
,
Yang
,
C.
, and
Lam
,
Y. C.
,
2015
, “
Thermal Effect on Microchannel Electro-Osmotic Flow With Consideration of Thermodiffusion
,”
ASME J. Heat Transfer
,
137
(
9
), p.
91023
.
29.
Soong
,
C.
, and
Wang
,
S.
,
2003
, “
Theoretical Analysis of Electrokinetic Flow and Heat Transfer in a Microchannel Under Asymmetric Boundary Conditions
,”
J. Colloid Interface Sci.
,
265
(
1
), pp.
202
213
.
30.
Mukhopadhyay
,
A.
,
Banerjee
,
S.
, and
Gupta
,
C.
,
2009
, “
Fully Developed Hydrodynamic and Thermal Transport in Combined Pressure and Electrokinetically Driven Flow in a Microchannel With Asymmetric Boundary Conditions
,”
Int. J. Heat Mass Transfer
,
52
(
7
), pp.
2145
2154
.
31.
Chen
,
C.-H.
,
2016
, “
Heat Transfer Analysis of Mixed Electro-Osmosis Pressure-Driven Flow for Power-Law Fluids Through a Microtube
,”
ASME J. Heat Transfer
,
138
(
8
), p.
082001
.
32.
Cetin
,
B.
, and
Li
,
D.
,
2008
, “
Effect of Joule Heating on Electrokinetic Transport
,”
Electrophoresis
,
29
(
5
), pp.
994
1005
.
33.
Rathore
,
A. S.
,
2004
, “
Joule Heating and Determination of Temperature in Capillary Electrophoresis and Capillary Electrochromatography Columns
,”
J. Chromatogr. A
,
1037
(
1
), pp.
431
443
.
34.
Petersen
,
N. J.
,
Nikolajsen
,
R. P.
,
Mogensen
,
K. B.
, and
Kutter
,
J. P.
,
2004
, “
Effect of Joule Heating on Efficiency and Performance for Microchip-Based and Capillary-Based Electrophoretic Separation Systems: A Closer Look
,”
Electrophoresis
,
25
(
2
), pp.
253
269
.
35.
Vocale
,
P.
,
Geri
,
M.
,
Cattani
,
L.
,
Morini
,
G.
, and
Spiga
,
M.
,
2013
, “
Electro-Osmotic Heat Transfer in Elliptical Microchannels Under H1 Boundary Condition
,”
Int. J. Therm. Sci.
,
72
, pp.
92
101
.
36.
Escandón
,
J.
,
Bautista
,
O.
,
Méndez
,
F.
, and
Bautista
,
E.
,
2011
, “
Theoretical Conjugate Heat Transfer Analysis in a Parallel Flat Plate Microchannel Under Electro-Osmotic and Pressure Forces With a Phan-Thien-Tanner Fluid
,”
Int. J. Therm. Sci.
,
50
(
6
), pp.
1022
1030
.
37.
Geri
,
M.
,
Lorenzini
,
M.
, and
Morini
,
G.
,
2012
, “
Effects of the Channel Geometry and of the Fluid Composition on the Performances of DC Electro-Osmotic Pumps
,”
Int. J. Therm. Sci.
,
55
, pp.
114
121
.
38.
Tripathi
,
D.
,
2012
, “
A Mathematical Model for Swallowing of Food Bolus Through the Oesophagus Under the Influence of Heat Transfer
,”
Int. J. Therm. Sci.
,
51
, pp.
91
101
.
39.
Li
,
M.
, and
Brasseur
,
J. G.
,
1993
, “
Non-Steady Peristaltic Transport in Finite-Length Tubes
,”
J. Fluid Mech.
,
248
, pp.
129
151
.
40.
Sadeghi
,
A.
,
Fattahi
,
M.
, and
Saidi
,
M. H.
,
2011
, “
An Approximate Analytical Solution for Electro-Osmotic Flow of Power-Law Fluids in a Planar Microchannel
,”
ASME J. Heat Transfer
,
133
(
9
), p.
091701
.
You do not currently have access to this content.