This paper investigates the electro-thermo-convection of power-law non-Newtonian fluids between a square enclosure and inner cylinder subjected to the simultaneous actions of external thermal and electric fields via lattice Boltzmann method. We concentrate on the flow structure transition, heat transfer efficiency as well as the bifurcation criteria concerning the electric Rayleigh number T for various power index 0.6n1.4. In addition, in order to comprehensively examine the impacts of buoyancy, two different Rayleigh numbers (Ra=103,105) are considered, corresponding to the weak and strong buoyancy. The cases for Newtonian fluids are used as the basic result to compare with the non-Newtonian cases. Based on the simulations, it is found that the flow motion and bifurcation criteria depend strongly on the power-law index. Specifically, the shear-shinning characteristic decreases the bifurcation threshold and exhibits a smaller hysteresis loop compared with Newtonian fluid, and the opposite effect and more evolution details about the transformation of charge void region with different shapes can be captured for shear-thickening characteristic. Additionally, the flow motions with stronger thermal convection illustrate more complex bifurcation diagrams and hysteresis loops due to the cooperation and competition between the buoyant and Coulomb forces, while it is not obvious for shear-thickening fluids.

1.
Electrohydrodynamics
, edited by
A.
Castellanos
(
Springer Science and Business Media
,
1998
).
2.
P.
Atten
,
F. M. J.
Mccluskey
, and
A. T.
Pérez
, “
Electroconvection and its effect on heat transfer
,”
IEEE Trans. Electr. Insul.
23
,
659
(
1988
).
3.
Y.
Feng
and
J.
Seyed-Yagoobi
, “
Understanding of electrohydrodynamic conduction pumping phenomenon
,”
Phys. Fluids
16
,
2432
(
2004
).
4.
S.
Laohalertdecha
,
P.
Naphon
, and
S.
Wongwises
, “
A review of electrohydrodynamic enhancement of heat transfer
,”
Renewable Sustainable Energy Rev.
11
,
858
(
2007
).
5.
A.
Jaworek
,
A.
Marchewicz
,
A. T.
Sobczyk
,
A.
Krupa
, and
T.
Czech
, “
Two-stage electrostatic precipitators for the reduction of PM2.5 particle emission
,”
Prog. Energy Combust.
67
,
206
(
2018
).
6.
P. A.
Vázquez
,
M.
Talmor
,
J.
Seyed-Yagoobi
,
P.
Traoré
, and
M.
Yazdani
, “
Indepth description of electrohydrodynamic conduction pumping of dielectric liquids: Physical model and regime analysis
,”
Phys. Fluids
31
,
113601
(
2019
).
7.
F. M. J.
Mc Cluskey
,
P.
Atten
, and
A. T.
Perez
, “
Heat transfer enhancement by electro-convection resulting from an injected space charge between parallel plates
,”
Int. J. Heat Mass Transfer
34
,
2237
(
1991
).
8.
P.
Traoré
,
A. T.
Pérez
,
D.
Koulova
, and
H.
Romat
, “
Numerical modelling of finite amplitude electro-thermo-convection in a dielectric liquid layer subjected to both unipolar injection and temperature gradient
,”
J. Fluid Mech.
658
,
279
(
2010
).
9.
W.
Hassen
,
L.
Kolsi
,
H. F.
Oztop
,
A. A. A.
Al-Rashed
,
M. N.
Borjini
, and
K.
Al-Salem
, “
Electro-thermo-capillary-convection in a square layer of dielectric liquid subjected to a strong unipolar injection
,”
Appl. Math. Modell.
63
,
349
(
2018
).
10.
W.
Hassen
,
L.
Kolsi
,
H. A.
Mohammed
,
K.
Ghachem
,
M.
Sheikholeslami
, and
M. A.
Almeshaal
, “
Transient electrohydrodynamic convective flow and heat transfer of MWCNT—Dielectric nanofluid in a heated enclosure
,”
Phys. Lett. A
384
,
126736
(
2020
).
11.
K.
Luo
,
J.
Wu
,
H.-L.
Yi
, and
H.-P.
Tan
, “
Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids
,”
Phys. Rev. E
93
,
023309
(
2016
).
12.
K.
Luo
,
J.
Wu
,
H. L.
Yi
, and
H. P.
Tan
, “
Lattice Boltzmann modelling of electro-thermo-convection in a planar layer of dielectric liquid subjected to unipolar injection and thermal gradient
,”
Int. J. Heat Mass Transfer
103
,
832
(
2016
).
13.
F.
Pontiga
and
A.
Castellanos
, “
Physical mechanisms of instability in a liquid layer subjected to an electric field and a thermal gradient
,”
Phys. Fluids
6
,
1684
(
1994
).
14.
J.
Lacroix
,
P.
Atten
, and
E.
Hopfinger
, “
Electro-convection in a dielectric liquid layer subjected to unipolar injection
,”
J. Fluid Mech.
69
,
539
(
1975
).
15.
A. T.
Pérez
,
P. A.
Vázquez
,
J.
Wu
, and
P.
Traoré
, “
Electrohydrodynamic linear stability analysis of dielectric liquids subjected to unipolar injection in a rectangular enclosure with rigid sidewalls
,”
J. Fluid Mech.
758
,
586
(
2014
).
16.
J.
Wu
,
P.
Traoré
,
A. T.
Pérez
, and
M.
Zhang
, “
Numerical analysis of the subcritical feature of electro-thermo-convection in a plane layer of dielectric liquid
,”
Physica D
311-312
,
45
(
2015
).
17.
Z. M.
Lu
,
G. Q.
Liu
, and
B. F.
Wang
, “
Flow structure and heat transfer of electro-thermo-convection in a dielectric liquid layer
,”
Phys. Fluids
31
,
064103
(
2019
).
18.
Y.
Hu
,
D.
Li
,
X.
Niu
, and
S.
Shu
, “
An immersed boundary-lattice Boltzmann method for electro-thermo-convection in complex geometries
,”
Int. J. Therm. Sci.
140
,
280
(
2019
).
19.
M.
Shojaeian
and
A.
Kosar
, “
Convective heat transfer and entropy generation analysis on Newtonian and non-Newtonian fluid flows between parallel-plates under slip boundary conditions
,”
Int. J. Heat Mass Transfer
70
,
664
(
2014
).
20.
L.
Khezzar
,
D.
Siginer
, and
I.
Vinogradov
, “
Natural convection of power law fluids in inclined cavities
,”
Int. J. Therm. Sci.
53
,
8
(
2012
).
21.
C. L.
Zhao
and
C.
Yang
, “
A review on electrokinetic phenomena in non-Newtonian fluids
,”
Adv. Colloid Interface Sci.
201–202
,
94
(
2013
).
22.
A.
Sadeghi
,
M. H.
Saidi
,
H.
Veisi
, and
M.
Fattahi
, “
Thermally developing electroosmotic flow of power-law fluids in a parallel plate microchannel
,”
Int. J. Therm. Sci.
61
,
106
(
2012
).
23.
M.
Patel
,
S. S.
Harish Kruthiventi
, and
P.
Kaushik
, “
Rotating electroosmotic flow of power-law fluid through polyelectrolyte grafted microchannel
,”
Colloids Surf., B
193
,
111058
(
2020
).
24.
O.
Turan
,
A.
Sachdeva
,
N.
Chakraborty
, and
R. J.
Poole
, “
Laminar natural convection of power-law fluids in a square enclosure with differently heated side walls subjected to constant temperature
,”
J. Non-Newtonian Fluid Mech.
166
,
1049
(
2011
).
25.
L.
Alves
and
A.
Barletta
, “
Convective instability of the Darcy-Bénard problem with through flow in a porous layer saturated by a power-law fluid
,”
Int. J. Heat Mass Transfer
62
,
495
(
2013
).
26.
G. H. R.
Kefayati
, “
Simulation of magnetic field effect on natural convection of non-Newtonian power-law fluids in a sinusoidal heated cavity using FDLBM
,”
Int. Commun. Heat Mass Tranfer.
53
,
139
(
2014
).
27.
G. H. R.
Kefayati
and
H.
Tang
, “
MHD thermosolutal natural convection and entropy generation of Carreau fluid in a heated enclosure with two inner circular cold cylinders, using LBM
,”
Int. J. Heat Mass Transfer
126
,
508
(
2018
).
28.
F.
Li
,
S. Y.
Ke
,
X. Y.
Yin
, and
X. Z.
Yin
, “
Effect of finite conductivity on the nonlinear behaviour of an electrically charged viscoelastic liquid jet
,”
J. Fluid Mech.
874
,
5
(
2019
).
29.
Z. G.
Su
,
Y. M.
Zhang
,
K.
Luo
, and
H. L.
Yi
, “
Instability of electroconvection in viscoelastic fluids subjected to unipolar injection
,”
Phys. Fluids
32
,
104102
(
2020
).
30.
Z. G.
Su
,
T. F.
Li
,
K.
Luo
,
J.
Wu
, and
H. L.
Yi
, “
Electro-thermo-convection in non-Newtonian power-law fluids within rectangular enclosures
,”
J. Non-Newtonian Fluid Mech.
288
,
104470
(
2021
).
31.
B.
Ma
,
L.
Wang
,
K.
He
,
D. G.
Li
, and
X. D.
Liang
, “
A lattice Boltzmann analysis of the electro-thermo convection and heat transfer enhancement in a cold square enclosure with two heated cylindrical electrodes
,”
Int. J. Therm. Sci.
164
,
106885
(
2021
).
32.
M.
Corcione
, “
Interactive free convection from a pair of vertical tube-arrays at moderate Rayleigh numbers
,”
Int. J. Heat Mass Transfer
50
,
1061
1074
(
2007
).
33.
M.
Sairamu
,
N.
Nirmalkar
, and
R. P.
Chhabra
, “
Natural convection from a circular cylinder in confined Bingham plastic fluids
,”
Int. J. Heat Mass Transfer
60
,
567
(
2013
).
34.
K.
Luo
,
J.
Wu
,
H. L.
Yi
, and
H. P.
Tan
, “
Numerical investigation of heat transfer enhancement in electro-thermo-convection in a square enclosure with an inner circular cylinder
,”
Int. J. Heat Mass Transfer
113
,
1070
(
2017
).
35.
P.
Atten
and
J.
Lacroix
, “
Non-linear hydrodynamic stability of liquids subjected to unipolar injection
,”
J. Mec.
18
,
469
(
1979
).
36.
S.
Chen
and
G. D.
Doolen
, “
Lattice Boltzmann method for fluid flows
,”
Annu. Rev. Fluid Mech.
30
,
329
(
1998
).
37.
L.
Wang
,
Z. C.
Wei
,
T. F.
Li
,
Z. H.
Chai
, and
B. C.
Shi
, “
A lattice Boltzmann modelling of electrohydrodynamic conduction phenomenon in dielectric liquids
,”
Appl. Math. Model.
95
,
361
(
2021
).
38.
L.
Wang
,
Z. H.
Chai
, and
B. C.
Shi
, “
Regularized lattice Boltzmann simulation of double-diffusive convection of power-law nanofluids in rectangular enclosures
,”
Int. J. Heat Mass Transfer
102
,
381
(
2016
).
39.
Z. H.
Chai
,
B. C.
Shi
,
Z. L.
Guo
 et al, “
Multiple-relaxation-time lattice Boltzmann model for generalized Newtonian fluid flows
,”
J. Non-Newtonian Fluid Mech.
166
,
332
(
2011
).
40.
G.
Bin Kim
,
J.
Min Hyun
, and
H. S.
Kwak
, “
Transient buoyant convection of a power-law non-Newtonian fluid in an enclosure
,”
Int. J. Heat Mass Transfer
46
,
3605
(
2003
).
41.
H.
Huang
,
T. S.
Lee
, and
C.
Shu
, “
Thermal curved boundary treatment for the thermal lattice Boltzmann equation
,”
Int. J. Mod. Phys. C
17
,
631
(
2006
).
42.
Z. L.
Guo
,
C. G.
Zheng
, and
B. C.
Shi
, “
An extrapolation method for boundary conditions in lattice Boltzmann method
,”
Phys. Fluids
14
,
2007
(
2002
).
43.
Z.
Chai
and
B.
Shi
, “
A novel lattice Boltzmann model for the Poisson equation
,”
Appl. Math. Modell.
32
,
2050
(
2008
).
44.
A. T.
Pérez
and
A.
Castellanos
, “
Role of charge diffusion in finite-amplitude electroconvection
,”
Phys. Rev. A
40
(
10
),
5844
(
1989
).
You do not currently have access to this content.