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Research Papers: Forced Convection

# Heat Transfer Characteristics of Gaseous Slip Flow in Concentric Micro-Annular Tubes

[+] Author and Article Information
Chungpyo Hong1

Department of Mechanical Engineering, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japanhong@rs.noda.tus.ac.jp

Yutaka Asako

Department of Mechanical Engineering, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo 192-0397, Japan

Koichi Suzuki

Department of Mechanical Engineering, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

1

Corresponding author.

J. Heat Transfer 133(7), 071706 (Apr 04, 2011) (8 pages) doi:10.1115/1.4003605 History: Received August 19, 2010; Revised February 08, 2011; Published April 04, 2011; Online April 04, 2011

## Abstract

A concentric micro-annular passage is a basic and important microgeometry of microfluidic-systems from simple heat exchanger to the most complicated nuclear reactors. Therefore, heat transfer characteristics of gaseous flows in concentric micro-annular tubes with constant heat flux whose value was positive or negative were numerically investigated. The slip velocity, temperature jump, and shear stress work were considered on the slip boundary conditions. The numerical methodology was based on the arbitrary-Lagrangian–Eulerian method. The computations were performed for two thermal cases. That is, the heat flux that was constant at the inner wall and outer wall was adiabatic (case 1) and the heat flux that was constant at the outer wall and the inner wall was adiabatic (case 2). Each constant heat flux of $104 Wm−2$ for the positive value and $−104 Wm−2$ for the negative value was chosen. The outer tube radius ranged from $20 μm$ to $150 μm$ with the radius ratios of 0.02, 0.05, 0.1, 0.25, and 0.5 and the ratio of length to hydraulic diameter was 100. The stagnation pressure was chosen in such a way that the exit Mach number ranges from 0.1 to 0.8. The outlet pressure was fixed at the atmospheric pressure. The heat transfer characteristics in concentric micro-annular tubes were obtained. The wall and bulk temperatures with positive heat flux are compared with those of negative heat flux cases and also compared with those of the simultaneously developing incompressible flow. The results show that the Nusselt number of compressible slip flow is different from that of incompressible flow. However, the temperatures normalized by heat flux have different trends whether heat flux value is positive or negative. A correlation for the prediction of the heat transfer characteristics of gas slip flow in concentric micro annular tubes is proposed.

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## Figures

Figure 1

Schematic diagram and boundary conditions of the problem: (a) case 1 (q̇i=q̇w and q̇o=0) and (b) case 2 (q̇i=0 and q̇o=q̇w)

Figure 2

Contour plots of temperature (q̇w=104 Wm−2 and r∗=0.25): (a) ro=20 μm and ri=5 μm (Re=61 and Maout=0.096); (b) ro=20 μm and ri=5 μm (Re=500 and Maout=0.715); (c) ro=150 μm and ri=37.5 μm (Re=714 and Maout=0.148); and (d) ro=150 μm and ri=37.5 μm (Re=3764 and Maout=0.719)

Figure 3

Contour plots of temperature (q̇w=−104 Wm−2 and r∗=0.25): (a) ro=20 μm and ri=5 μm (Re=66 and Maout=0.097); (b) ro=20 μm and ri=5 μm (Re=505 and Maout=0.716); (c) ro=150 μm and ri=37.5 μm (Re=751 and Maout=0.149); and (d) ro=150 μm and ri=37.5 μm (Re=3801 and Maout=0.720)

Figure 4

Nu as a function of X∗ (q̇w=104 Wm−2 and r∗=0.25): (a) ro=20 μm, ri=5 μm and (b) ro=150 μm, ri=37.5 μm

Figure 5

Dimensionless inner wall temperature as a function of X∗ of q̇w=104 Wm−2: (a) ro=20 μm, ri=5 μm and (b) ro=150 μm, ri=37.5 μm

Figure 6

Dimensionless wall temperature as a function of X∗ of q̇w=−104 Wm−2: (a) ro=20 μm, ri=5 μm and (b) ro=150 μm, ri=37.5 μm

Figure 7

Dimensionless wall temperature differences as a function of X∗ of q̇w=104 Wm−2: (a) ro=20 μm, ri=5 μm and (b) ro=150 μm, ri=37.5 μm

Figure 8

Dimensionless wall temperature differences as a function of X∗ of q̇w=−104 Wm−2: (a) ro=20 μm, ri=5 μm and (b) ro=150 μm, ri=37.5 μm

Figure 9

Dimensionless bulk temperature differences as a function of X∗ of q̇w=104 Wm−2: (a) ro=20 μm, ri=5 μm and (b) ro=150 μm, ri=37.5 μm

Figure 10

Dimensionless bulk temperature differences as a function of X∗ of q̇w=−104 Wm−2: (a) ro=20 μm, ri=5 μm and (b) ro=150 μm, ri=37.5 μm

Figure 11

ζ as a function of Maout for case 1

Figure 12

ζ as a function of Maout for case 2

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