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Research Papers: Forced Convection

Asymmetrical Heating in Rarefied Flows Through Circular Microchannels

[+] Author and Article Information
Vocale Pamela

Department of Industrial Engineering,
University of Parma,
Parco Area delle Scienze n. 181/A,
Parma 43124, Italy
e-mail: pamela.vocale@unipr.it

Spiga Marco

Department of Industrial Engineering,
University of Parma,
Parco Area delle Scienze n. 181/A,
Parma 43124, Italy
e-mail: marco.spiga@unipr.it

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 10, 2013; final manuscript received May 28, 2014; published online June 24, 2014. Assoc. Editor: James A. Liburdy.

J. Heat Transfer 136(9), 091701 (Jun 24, 2014) (6 pages) Paper No: HT-13-1636; doi: 10.1115/1.4027786 History: Received December 10, 2013; Revised May 28, 2014

This work is aimed at contributing to the thermal analysis of slip flow through circular microducts, providing an analytical solution to the energy conservation equation for partially heated walls. A uniform wall heat flux (H2 boundary conditions) is considered on the heated perimeter of the cross section while the remaining arc length is assumed to be adiabatic. The gaseous flow is considered laminar, fully developed, in steady state condition, and forced convection. The temperature profile, wall temperature distribution, and Nusselt number are presented as functions of both the heated perimeter of the cross section and the Knudsen number, resorting to simple converging series of trigonometric functions. The proposed solution can be useful for the design of the microfluidic devices such as micro heat sinks and micro heat exchangers.

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Figures

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Fig. 1

Graphical representation of the considered cross section

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Fig. 2

Relative error in the Nusselt number as a function of the terms of the converging series (n) in Eq. (20): (a) α = π/4 and (b) α = π/2

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Fig. 3

Temperature profiles for different values of the azimuth angle α: (a) α = π/2 and (b) α = π

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Fig. 4

Wall temperature distributions for different values of the azimuth angle α: (a) α = π/2 and (b) α = π

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Fig. 5

Temperature profiles as a function of the azimuth angle α: (a) Kn = 0 and (b) Kn = 0.1

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