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Research Papers: Micro/Nanoscale Heat Transfer

# Variable Physical Properties in Natural Convective Gas Microflow

[+] Author and Article Information
Huei Chu Weng

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan, R.O.C

Cha’o-Kuang Chen1

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan, R.O.Cckchen@mail.ncku.edu.tw

1

Corresponding author.

J. Heat Transfer 130(8), 082401 (May 29, 2008) (8 pages) doi:10.1115/1.2927400 History: Received January 06, 2007; Revised March 11, 2008; Published May 29, 2008

## Abstract

Anisothermal flow prevails in a heated microchannel. It is desirable to understand the influence of temperature-dependent physical properties on the flow and heat transfer characteristics for natural convective gas microflow. In this study, formulas for the shear viscosity, thermal conductivity, constant-pressure specific heat, density, and molecular mean free path are proposed in power-law form and validated through experimental data. Natural convective gas flow with variable physical properties in a long open-ended vertical parallel-plate microchannel with asymmetric wall temperature distributions is further investigated. The full Navier–Stokes equations and energy equation combined with the first-order slip∕jump boundary conditions are employed. Analysis process shows that the compressibility and viscous dissipation terms in balance equations are negligible. Numerical solutions are presented for air at the standard reference state with complete accommodation. It is found that the effect of variable properties should be considered for hotter-wall temperatures greater than $306.88K$. The effect is to advance the velocity slip and temperature jump as well as the velocity symmetry and temperature nonlinearity. Moreover, it tends to reduce the mass flow rate and the local heat transfer rate excluding on the cooler-wall surface where the temperature-jump effect prevails over the temperature-nonlinearity effect. Increasing the cooler-wall temperature magnifies the effect on flow behavior but minifies that on thermal behavior.

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## Figures

Figure 1

Geometric sketch and parameters of natural convection in the microchannel

Figure 2

[(a)–(d)] Possible approximations of the experimental property data listed by Suryanarayana (11); T0=298.15K

Figure 3

Comparison of the results of the present study with those of available work: ξ=0.51: χ=0.1813, Kn0=1.38×10−5 (w=5.119mm, T0=312.57K); ξ=0.6: χ=0.0409, Kn0=1.48×10−5 (w=4.775mm, T0=312.57K)

Figure 4

Velocity and temperature distributions for different values of ξ with Kn0=0.03 and χ=1

Figure 5

Mass flow rate versus χ for different values of ξ with Kn0=0.03

Figure 6

Local heat transfer rate versus χ for different values of ξ with Kn0=0.03. The subscript 1 denotes the hotter-wall surface, and the subscript 2 denotes the cooler-wall surface.

Figure 7

Critical hotter-wall temperature parameter versus Kn0 for different values of ξ

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