In this paper, a lattice Boltzmann (LB) model is established to simulate the gaseous fluid flow and heat transfer in the slip regime under the curved boundary condition. A novel curved boundary treatment is proposed for the LB modeling, which is a combination of the nonequilibrium extrapolation scheme for the curved boundary and the counter-extrapolation method for the macroscopic variables on the curved gas–solid interface. The established numerical model can accurately predict the velocity slip and temperature jump of the microscale gas flow on the curved surface, which agrees well with the analytical solution for the microcylindrical Couette flow and heat transfer. Then, the slip flow and the heat transfer over the single microcylinder are numerically studied in this work. It shows that the velocity slip and the temperature jump are obviously influenced by the Knudsen number and the Reynolds number, and the local Nusselt number depends on which gas rarefaction effect (velocity slip or temperature jump) is dominant. An increase in the Prandtl number leads to a decrease in the temperature jump, which enhances the heat transfer on the microcylinder surface. The numerical simulation of the flow and heat transfer over two microcylinders in tandem configuration are carried out to investigate the wake interference effect. The results show that the slip flow and heat transfer characteristics of the downstream microcylinder are influenced by the wake region behind the upstream cylinder as the spacing is small.

References

References
1.
Rahim
,
K.
, and
Mian
,
A.
,
2017
, “
A Review on Laser Processing in Electronic and MEMS Packaging
,”
ASME J. Electron. Packag.
,
139
(
3
), p.
030801
.
2.
Qu
,
J.
,
Wu
,
H.
,
Cheng
,
P.
,
Wang
,
Q.
, and
Sun
,
Q.
,
2017
, “
Recent Advances in MEMS-Based Micro Heat Pipes
,”
Int. J. Heat Mass Transfer
,
110
, pp.
294
313
.
3.
Zhang
,
L.
,
Zhu
,
J.
,
Yan
,
Y.
,
Pan
,
W.
,
Yang
,
Z.
,
Chen
,
Y.
, and
Ji
,
X.
,
2014
, “
Numerical Investigation on the Transient Characteristics of Hydrogen Production From Catalytic Autothermal Reforming of Methane in a Micro Combustor With Multiple Cylinders
,”
J. Nat. Gas Sci. Eng.
,
19
, pp.
251
257
.
4.
Hong
,
C.
,
Asako
,
Y.
, and
Suzuki
,
K.
,
2011
, “
Heat Transfer Characteristics of Gaseous Slip Flow in Concentric Micro-Annular Tubes
,”
ASME J. Heat Transfer
,
133
(
7
), p.
071706
.
5.
Gerken
,
I.
,
Brandner
,
J. J.
, and
Dittmeyer
,
R.
,
2016
, “
Heat Transfer Enhancement With Gas-to-Gas Micro Heat Exchangers
,”
Appl. Therm. Eng.
,
93
, pp.
1410
1416
.
6.
Croce
,
G.
,
Rovenskaya
,
O.
, and
D'Agaro
,
P.
,
2015
, “
Computational Analysis of Conjugate Heat Transfer in Gaseous Microchannels
,”
ASME J. Heat Transfer
,
137
(
4
), p.
041701
.
7.
Vocale
,
P.
,
Morini
,
G. L.
, and
Spiga
,
M.
,
2016
, “
Convective Heat Transfer in Elliptical Microchannels Under Slip Flow Regime and h1 Boundary Conditions
,”
ASME J. Heat Transfer
,
138
(
4
), p.
044502
.
8.
Liu
,
Z.
,
Zhou
,
J.
, and
Wu
,
H.
,
2018
, “
Non-Isothermal Slip Flow Over Micro Spherical Particle at Low Reynolds Numbers
,”
Chem. Eng. Sci.
,
191
, pp.
19
30
.
9.
Liu
,
Z.
,
Zhou
,
J.
, and
Wu
,
H.
,
2018
, “
New Correlations for Slip Flow and Heat Transfer Over a Micro Spherical Particle in Gaseous Fluid
,”
Powder Technol.
,
338
, pp.
129
139
.
10.
Liu
,
Z.
,
Sunden
,
B.
, and
Wu
,
H.
,
2015
, “
Numerical Modeling of Multiple Bubbles Condensation in Subcooled Flow Boiling
,”
ASME J. Therm. Sci. Eng. Appl.
,
7
(
3
), p.
031003
.
11.
Luan
,
H. B.
,
Kuang
,
J. P.
,
Cao
,
Z.
,
Wu
,
Z.
,
Tao
,
W. Q.
, and
Sunden
,
B.
,
2017
, “
CFD Analysis of Two Types of Welded Plate Heat Exchangers
,”
Numer. Heat Transfer; Part A: Appl.
,
71
(
3
), pp.
250
269
.
12.
Liu
,
Z.
, and
Wu
,
H.
,
2016
, “
Numerical Modeling of Liquid–Gas Two-Phase Flow and Heat Transfer in Reconstructed Porous Media at Pore Scale
,”
Int. J. Hydrogen Energy
,
41
(
28
), pp.
12285
12292
.
13.
Cheng
,
P.
,
Zhang
,
C.
, and
Gong
,
S.
,
2017
, “
Lattice Boltzmann Simulations of Macro/Microscale Effects on Saturated Pool Boiling Curves for Heated Horizontal Surfaces
,”
ASME J. Heat Transfer
,
139
(
11
), p.
110801
.
14.
Paradis
,
H.
,
Andersson
,
M.
, and
Sunden
,
B.
,
2016
, “
Modeling of Mass and Charge Transport in a Solid Oxide Fuel Cell Anode Structure by a 3D Lattice Boltzmann Approach
,”
Heat Mass Transfer
,
52
(
8
), pp.
1529
1540
.
15.
Liu
,
Z.
, and
Wu
,
H.
,
2016
, “
Pore-Scale Study on Flow and Heat Transfer in 3D Reconstructed Porous Media Using Micro-Tomography Images
,”
Appl. Therm. Eng.
,
100
, pp.
602
610
.
16.
Liu
,
X.
, and
Guo
,
Z.
,
2013
, “
A Lattice Boltzmann Study of Gas Flows in a Long Micro-Channel
,”
Comput. Math. Appl.
,
65
(
2
), pp.
186
193
.
17.
Esfahani
,
J. A.
, and
Norouzi
,
A.
,
2014
, “
Two Relaxation Time Lattice Boltzmann Model for Rarefied Gas Flows
,”
Phys. A
,
393
, pp.
51
61
.
18.
Norouzi
,
A.
, and
Esfahani
,
J. A.
,
2016
, “
Capturing Non-Equilibrium Effects of Micro/Nano Scale Gaseous Flow Using a Novel Lattice Boltzmann Model
,”
J. Stat. Phys.
,
162
(
3
), pp.
712
726
.
19.
Yuan
,
Y.
, and
Rahman
,
S.
,
2016
, “
Extended Application of Lattice Boltzmann Method to Rarefied Gas Flow in Micro-Channels
,”
Phys. A
,
463
, pp.
25
36
.
20.
Tian
,
Z.-W.
,
Zou
,
C.
,
Liu
,
H.-J.
,
Guo
,
Z.-L.
,
Liu
,
Z.-H.
, and
Zheng
,
C.-G.
,
2007
, “
Lattice Boltzmann Scheme for Simulating Thermal Micro-Flow
,”
Phys. A
,
385
(
1
), pp.
59
68
.
21.
Guo
,
Z.-L.
,
Zheng
,
C.-G.
, and
Shi
,
B.-C.
,
2002
, “
Non-Equilibrium Extrapolation Method for Velocity and Pressure Boundary Conditions in the Lattice Boltzmann Method
,”
Chin. Phys.
,
11
(
4
), pp.
366
374
.
22.
Yin
,
X.
, and
Zhang
,
J.
,
2012
, “
An Improved Bounce-Back Scheme for Complex Boundary Conditions in Lattice Boltzmann Method
,”
J. Comput. Phys.
,
231
(
11
), pp.
4295
4303
.
23.
Szalmás
,
L.
,
2007
, “
Slip on Curved Boundaries in the Lattice Boltzmann Model
,”
Int. J. Mod. Phys. C
,
18
(
1
), pp.
15
24
.
24.
Guo
,
Z.
,
Shi
,
B.
, and
Zheng
,
C.
,
2011
, “
Velocity Inversion of Micro Cylindrical Couette Flow: A Lattice Boltzmann Study
,”
Comput. Math. Appl.
,
61
(
12
), pp.
3519
3527
.
25.
Suga
,
K.
,
2013
, “
Lattice Boltzmann Methods for Complex Micro-Flows: Applicability and Limitations for Practical Applications
,”
Fluid Dyn. Res.
,
45
(
3
), p.
034501
.
26.
Tao
,
S.
, and
Guo
,
Z.
,
2015
, “
Boundary Condition for Lattice Boltzmann Modeling of Microscale Gas Flows With Curved Walls in the Slip Regime
,”
Phys. Rev. E
,
91
(
4
), p.
043305
.
27.
Jahanshaloo
,
L.
,
Sidik
,
N. A. C.
,
Salimi
,
S.
, and
Safdari
,
A.
,
2014
, “
The Use of Thermal Lattice Boltzmann Numerical Scheme for Particle-Laden Channel Flow With a Cavity
,”
Numer. Heat Transfer; Part A: Appl.
,
66
(
4
), pp.
433
448
.
28.
Guo
,
Z.
,
Zheng
,
C.
, and
Shi
,
B.
,
2002
, “
Discrete Lattice Effects on the Forcing Term in the Lattice Boltzmann Method
,”
Phys. Rev. E
,
65
(
4
), p.
046308
.
29.
Guo
,
Z.
,
Shi
,
B.
, and
Zheng
,
C.
,
2002
, “
A Coupled Lattice BGK Model for the Boussinesq Equations
,”
Int. J. Numer. Methods Fluids
,
39
(
4
), pp.
325
342
.
30.
Lee
,
T.
, and
Lin
,
C.-L.
,
2005
, “
Rarefaction and Compressibility Effects of the Lattice-Boltzmann-Equation Method in a Gas Microchannel
,”
Phys. Rev. E
,
71
(
4
), p.
046706
.
31.
Gad-el-Hak
,
M.
,
1999
, “
Fluid Mechanics of Microdevices—The Freeman Scholar Lecture
,”
ASME J. Fluids Eng.
,
121
(
1
), pp.
5
33
.
32.
Le
,
G.
,
Oulaid
,
O.
, and
Zhang
,
J.
,
2015
, “
Counter-Extrapolation Method for Conjugate Interfaces in Computational Heat and Mass Transfer
,”
Phys. Rev. E
,
91
(
3
), p.
033306
.
You do not currently have access to this content.