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Research Papers

Conjugate Thermal Transport in Gas Flow in Long Rectangular Microchannel

[+] Author and Article Information
Zhanyu Sun

Department of Mechanical and Aerospace Engineering,  Rutgers University, Piscataway, NJ 08854sunzhanyu@gmail.com

Yogesh Jaluria

Department of Mechanical and Aerospace Engineering,  Rutgers University, Piscataway, NJ 08854jaluria@jove.rutgers.edu

J. Electron. Packag 133(2), 021008 (Jun 23, 2011) (11 pages) doi:10.1115/1.4004218 History: Received May 04, 2010; Revised January 18, 2011; Published June 23, 2011; Online June 23, 2011

This paper is directed at the numerical simulation of pressure-driven nitrogen slip flow in long microchannels, focusing on conjugate heat transfer under uniform heat flux wall boundary condition. This problem has not been studied in detail despite its importance in many practical circumstances such as those related to the cooling of electronic devices and localized heat input in materials processing systems. For the gas phase, the two-dimensional momentum and energy equations are solved, considering variable properties, rarefaction, which involves velocity slip, thermal creep and temperature jump, compressibility, and viscous dissipation. For the solid, the energy equation is solved with variable properties. Four different substrate materials are studied, including commercial bronze, silicon nitride, pyroceram, and fused silica. The effects of substrate axial conduction, material thermal conductivity and substrate thickness are investigated in detail. It is found that substrate axial conduction leads to a flatter bulk temperature profile along the channel, lower maximum temperature, and lower Nusselt number. The effect of substrate thickness on the conjugate heat transfer is very similar to that of the substrate thermal conductivity. That is, in terms of axial thermal resistance, the increase in substrate thickness has the same impact as that caused by an increase in its thermal conductivity. By comparing the results from constant and variable property models, it is found that the effects of variation in substrate material properties are negligible.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

The schematic of the two-dimensional computational domain for the conjugate heat transfer problem, where the shaded areas represent the substrate and the blank area is the channel flow

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Figure 2

Calculated temperature profile at the channel cross-section x/H=250 for the case of fused silica as the substrate, with q−w=1×10-4, Hs/H=1.0, and PR=2.0

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Figure 3

Bulk temperature profiles for q−w=2×10-4, Hs/H=1.0, and PR=2.0. (a) Entire channel; (b) entrance region.

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Figure 4

The maximum temperatures for PR=2.0 and Hs/H=1.0, with q−w (qw,norm in the figure) ranging from 1×10-4 to 3×10-4

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Figure 5

The local Nusselt number for different substrate materials with q−w=2×10-4, Hs/H=1.0, and PR=2.0

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Figure 6

The local Nusselt number for PR=2.0, q−w (qw,norm in the figure) ranging from 1×10-4 to 3×10-4 and Hs/H=1.0. The substrate material is (a) fused silica; (b) pyroceram; (c) silicon nitride; (d) commercial bronze.

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Figure 7

Bulk temperature profiles along the microchannel for PR ranging from 1.5 to 2.5, q−w=2×10-4 and Hs/H=1.0. The substrate material is (a) fused silica; (b) pyroceram; (c) silicon nitride; (d) commercial bronze.

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Figure 8

The maximum temperatures for PR ranging from 1.5 to 2.5, q−w=2×10-4 and Hs/H=1.0

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Figure 9

The local Nusselt number along the microchannel for PR ranging from 1.5 to 2.5, q−w=2×10-4 and Hs/H=1.0. The substrate material is (a) fused silica; (b) pyroceram; (c) silicon nitride; (d) commercial bronze.

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Figure 10

Bulk temperature profiles along the microchannel for PR=2.0, q−w=2×10-4, and different Hs/H’s. The substrate material is (a) fused silica; (b) pyroceram; (c) silicon nitride; (d) commercial bronze.

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Figure 11

The maximum temperatures for PR=2.0, q−w=2×10-4 and different Hs/H’s

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Figure 12

The local Nusselt number along the microchannel for PR=2.0, q−w=2×10-4 and different values of Hs/H. The substrate material is (a) fused silica; (b) pyroceram; (c) silicon nitride; (d) commercial bronze.

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Figure 13

Comparison of the maximum temperatures between variable and constant property models for q−w (qw,norm in the figure) ranging from 1×10-4 to 3×10-4, Hs/H=1.0, and PR=2.0. Here, VP denotes the variable property model and CP denotes the constant property model: (a) Fused silica; (b) Pyroceram.

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