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Research Papers: Micro/Nanoscale Heat Transfer

On Temperature Jump Condition for Slip Flow in a Microchannel With Constant Wall Temperature

[+] Author and Article Information
Yutaka Asako

Fellow ASME
Department of Mechanical Precision
Engineering,
Malaysia-Japan International Institute
of Technology,
University Technology Malaysia,
Jalan Sultan Yahya Petra,
Kuala Lumpur 54100, Malaysia
e-mail: y.asako@utm.my

Chungpyo Hong

Department of Mechanical Engineering,
Kagoshima University,
1-21-40 Korimoto,
Kagoshima 890-0065, Japan
e-mail: hong@mech.kagoshima-u.ac.jp

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 5, 2016; final manuscript received January 30, 2017; published online April 4, 2017. Assoc. Editor: Laura Schaefer.

J. Heat Transfer 139(7), 072402 (Apr 04, 2017) (7 pages) Paper No: HT-16-1004; doi: 10.1115/1.4036076 History: Received January 05, 2016; Revised January 30, 2017

The analytical solution in the fully developed region of a slip flow in a circular microtube with constant wall temperature is obtained to verify the conventional temperature jump boundary condition when both viscous dissipation (VD) and substantial derivative of pressure (SDP) terms are included in the energy equation. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a microchannel with constant wall temperature when both viscous dissipation and substantial derivative of pressure terms are included in the energy equation. Numerical results are also obtained for a slip flow in a developing region of a circular tube. The results showed that the maximum heat transfer rate decreases with increasing Mach number.

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References

Figures

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Fig. 1

Schematic diagram of the problem

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Fig. 2

Temperature variation, θ−θw, in the cross section of thermally fully developed region

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Fig. 3

Total and static temperature variations, θ−θw, in the cross section of thermally fully developed region (Kn = 0.1 and Ma = 0.8)

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Fig. 4

Contour of θ (Kn = 0.01): (a) Ma = 0.2, (b) Ma = 0.5, (c) Ma = 0.8, and (d) Ma = 1

Grahic Jump Location
Fig. 5

Contour of θ (Kn = 0.1): (a) Ma = 0.2, (b) Ma = 0.5, (c) Ma = 0.8, and (d) Ma = 1

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Fig. 6

Averaged temperatures in the cross section of thermally fully developed region: (a) static temperature in fully developed region, θfd−θw, (b) total temperature in fully developed region, θT,fd−θw, (c) total temperature at inlet, θT,in, and (d) total temperature decrease, θT,fd−θw−θT,in

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Fig. 7

(( TT(X*)−TT,in)/(TT,fd−TT,in)) as a function of X* (Kn = 0.01)

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Fig. 8

( (TT(X*)−TT,in)/(TT,fd−TT,in)) as a function of X* (Kn = 0.05)

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Fig. 9

(( TT(X*)−TT,in)/(TT,fd−TT,in)) as a function of X* (Kn = 0.1)

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Fig. 10

(( TT,fd−TT,in)/(Tw−Tin)) as a function of Ma

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