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Research Papers: Micro/Nanoscale Heat Transfer

Numerical Modeling of Slip Flow and Heat Transfer Over Microcylinders With Lattice Boltzmann Method

[+] Author and Article Information
Zhenyu Liu, Zhiyu Mu

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China

Huiying Wu

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: whysrj@sjtu.edu.cn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 12, 2017; final manuscript received January 23, 2019; published online February 27, 2019. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 141(4), 042401 (Feb 27, 2019) (13 pages) Paper No: HT-17-1537; doi: 10.1115/1.4042770 History: Received September 12, 2017; Revised January 23, 2019

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.

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Figures

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Fig. 2

Schematic of the microcylindrical Couette flow

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Fig. 3

The comparison between the numerical prediction and the analytical solution: (a) velocity and (b) temperature

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Fig. 1

Schematic illustration of the curved boundary

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Fig. 5

Streamline and velocity distribution around the microcylinder for different Kn numbers (Re=25): (a) Kn = 0.0025, (b) Kn = 0.005, and (c) Kn = 0.01

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Fig. 6

Temperature distribution around the micrcylinder for different Kn numbers (Re=25): (a) Kn = 0.0025, (b) Kn = 0.005, and(c) Kn = 0.01

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Fig. 7

Variable profiles on the microcylinder surface for different Kn numbers (Re=25): (a) velocity slip, (b) temperature jump, and (c) local Nusselt number

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Fig. 8

Streamline and velocity distribution around the microcylinder for different Re numbers: (a) Re = 5, (b) Re = 10, and (c) Re =20

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Fig. 9

Temperature distribution around the microcylinder for different Re numbers: (a) Re = 5, (b) Re =10, and (c) Re = 20

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Fig. 10

Variable profiles on the microcylinder surface for different Re numbers (Kn=0.01): (a) velocity slip, (b) temperature jump, and (c) local Nusselt number

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Fig. 4

Computational domain and boundary conditions: (a) a single microcylinder and (b) two microcylinders with tandem configuration

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Fig. 14

Velocity slip on the microcylinder surface for different spacings (Re=25 and Kn=0.01): (a) upstream cylinder and (b) downstream cylinder

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Fig. 15

Temperature distribution around the microcylinders for different spacings (Re=25): (a) S = 2D, (b) S = 3D, and (c) S = 4D

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Fig. 16

Temperature jump on the microcylinder surface for different spacings (Re=25 and Kn=0.01): (a) upstream cylinder and (b) downstream cylinder

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Fig. 11

Temperature distribution around the microcylinder for different Pr numbers (Re=25 and Kn=0.01): (a) Pr = 0.71, (b) Pr = 1.0, and (c) Pr = 1.5

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Fig. 12

Variable profiles on the microcylinder surface for different Pr numbers (Re=25 and Kn=0.01): (a) temperature jump and (b) local Nusselt number

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Fig. 13

Streamline and velocity distribution around the microcylinders for different spacings (Re=25): (a) S = 2D, (b) S = 3D, and (c) S = 4D

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Fig. 17

Local Nu number on the microcylinder surface for different spacings (Re=25): (a) upstream cylinder and (b) downstream cylinder

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