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Technical Brief

Convective Heat Transfer in Elliptical Microchannels Under Slip Flow Regime and H1 Boundary Conditions

[+] Author and Article Information
Pamela Vocale

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

Gian Luca Morini

DIN,
Alma Mater Studiorum—University of Bologna,
Viale Risorgimento n. 2,
Bologna 40136, Italy
e-mail: gianluca.morini3@unibo.it

Marco Spiga

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 March 25, 2015; final manuscript received October 9, 2015; published online December 29, 2015. Assoc. Editor: Wilson K. S. Chiu.

J. Heat Transfer 138(4), 044502 (Dec 29, 2015) (7 pages) Paper No: HT-15-1227; doi: 10.1115/1.4032173 History: Received March 25, 2015; Revised October 09, 2015

In this work, hydrodynamically and thermally fully developed gas flow through elliptical microchannels is numerically investigated. The Navier–Stokes and energy equations are solved by considering the first-order slip flow boundary conditions and by assuming that the wall heat flux is uniform in the axial direction, and the wall temperature is uniform in the peripheral direction (i.e., H1 boundary conditions). To take into account the microfabrication of the elliptical microchannels, different heated perimeter lengths are analyzed along the microchannel wetted perimeter. The influence of the cross section geometry on the convective heat transfer coefficient is also investigated by considering the most common values of the elliptic aspect ratio, from a practical point of view. The numerical results put in evidence that the Nusselt number is a decreasing function of the Knudsen number for all the considered configurations. On the contrary, the role of the cross section geometry in the convective heat transfer depends on the thermal boundary condition and on the rarefaction degree. With the aim to provide a useful tool for the designer, a correlation that allows evaluating the Nusselt number for any value of aspect ratio and for different working gases is proposed.

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Figures

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Fig. 1

(a) Semi-elliptical grooves micromachined in a copper foil and (b) elliptical microchannel obtained by coupling two copper foils (courtesy of J. J. Brandner, IMVT, KIT)

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Fig. 3

Nusselt number as a function of the grid elements number (N) for γ = 0.125: (a) Kn = 0 and (b) Kn = 0.1

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Fig. 4

Temperature distribution for air through an elliptical microchannel with γ = 0.333 heated along the whole wetted perimeter (configuration 4) with Kn = 0 (a) and Kn = 0.1 (b)

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Fig. 5

Temperature distribution for air through an elliptical microchannel with γ = 0.333 with half-perimeter heated (configuration 2S) with Kn = 0 (a) and Kn = 0.1 (b)

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Fig. 6

Temperature distribution for air through an elliptical microchannel with γ = 0.333 with half-perimeter heated (configuration 2L) with Kn = 0 (a) and Kn = 0.1 (b)

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Fig. 7

Peripheral trend of the local heat flux (∂θ/∂n)|w as a function of a curvilinear coordinate s for γ = 0.333 and for Kn = 0, Kn = 0.01, and Kn = 0.1: (a) configuration 4 and (b) configuration 2S

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Fig. 8

Nusselt number as a function of Kn and γ: (a) configuration 2L, (b) configuration 2S, and (c) configuration 4

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