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Research Papers: Forced Convection

# Energy Equation of Gas Flow With Low Velocity in a Microchannel

[+] Author and Article Information
Yutaka Asako

Fellow ASME
Malaysia-Japan International
Institute of Technology,
University Technology Malaysia,
Jalan Semarak, 54100 Kuala Lumpur, Malaysia
e-mail: y.asako@utm.my

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 25, 2014; final manuscript received November 26, 2015; published online January 20, 2016. Assoc. Editor: Ali Khounsary.

J. Heat Transfer 138(4), 041702 (Jan 20, 2016) (5 pages) Paper No: HT-14-1769; doi: 10.1115/1.4032330 History: Received November 25, 2014; Revised November 26, 2015

## Abstract

The energy equation for constant density fluid flow with the viscous dissipation term is often used for the governing equations of gas flow with low velocity in microchannels. If the gas is an ideal gas with low velocity, the average temperatures at the inlet and the outlet of an adiabatic channel are the same based on the first law of the thermodynamics. If the gas is a real gas with low velocity, the average temperature at the outlet is higher or lower than the average temperature at the inlet. However, the outlet temperature which is obtained by solving the energy equation for constant density fluid flow with the viscous dissipation term is higher than the inlet gas temperature, since the viscous dissipation term is always positive. This inconsistency arose from choice of the relationship between the enthalpy and temperature that resulted in neglecting the substantial derivative of pressure term in the energy equation. In this paper, the energy equation which includes the substantial derivative of pressure term is proposed to be used for the governing equation of gas flow with low velocity in microchannels. The proposed energy equation is verified by solving it numerically for flow in a circular microtube. Some physically consistent results are demonstrated.

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## References

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## Figures

Fig. 4

Contour of average dimensionless temperature at outlet obtained by solving Eq. (16)

Fig. 1

Schematic diagram of a problem

Fig. 2

Contour of dimensionless temperature obtained by solving Eq. (16) (Re = 20 and Ma = 0.1)

Fig. 3

Contour of dimensionless temperature obtained by solving Eq. (12) (Re = 20 and Ma = 0.1)

Fig. 5

Contour of average dimensionless temperature at outlet obtained by solving Eq. (12)

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