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Technical Brief

Natural Convection in a Vertical Slit Microchannel With Superhydrophobic Slip and Temperature Jump

[+] Author and Article Information
C. Y. Wang

Department of Mathematics,
Michigan State University,
East Lansing, MI 48824

Chiu-On Ng

Department of Mechanical Engineering,
The University of Hong Kong,
Pokfulam Road,
Hong Kong, China
e-mail: cong@hku.hk

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 16, 2013; final manuscript received October 20, 2013; published online December 19, 2013. Assoc. Editor: Oronzio Manca.

J. Heat Transfer 136(3), 034502 (Dec 19, 2013) (6 pages) Paper No: HT-13-1243; doi: 10.1115/1.4025822 History: Received May 16, 2013; Revised October 20, 2013

Recent developments in microscale heat exchangers have heightened the need for the understanding of fluid flow and heat transfer in a microchannel. In this study, we look into fully-developed buoyancy-driven flow in a vertical parallel-plate microchannel, which has one wall exhibiting superhydrophobic slip and temperature jump, and another wall being a normal no-slip surface. Analytical solutions are derived for free convection in the channel, where the heating is applied to either one of the two walls, and by either constant wall temperature or constant heat flux. We examine how the superhydrophobic slip and temperature jump may affect the volume flow rate and the Nusselt number under various heating conditions. There exists a critical value of the temperature jump coefficient, above which the flow rate will be larger by heating the no-slip surface than by heating the superhydrophobic surface, whether by constant wall temperature or by constant heat flux. The opposite is true when the temperature jump coefficient is below the critical value. Also, the temperature jump can have a negative effect on the flow rate when the heating is by constant temperature on the superhydrophobic side of the channel, but will have a positive effect when the heating is on the no-slip side of the channel.

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Figures

Grahic Jump Location
Fig. 1

Definition sketch of the present problem: fully-developed free convection in an open-ended vertical parallel-plate microchannel, with one wall heated by constant wall temperature or constant heat flux, and the other wall maintained at ambient temperature. The left wall is a superhydrophobic surface with hydrodynamic slip length λ and temperature jump coefficient γ, and the right wall is a normal no-slip surface.

Grahic Jump Location
Fig. 2

For case I (heating due to constant wall temperature), the flow rates QIA (dashed lines; superhydrophobic surface heated) and QIB (solid lines; no-slip surface heated) as functions of normalized slip length λ∧ and normalized temperature jump coefficient γ∧. The dotted line is Eq. (40), for which QIA = QIB. Above the dotted line: QIB > QIA; below the dotted line: QIA > QIB.

Grahic Jump Location
Fig. 3

For case II (heating due to constant heat flux), the flow rates QIIA (dashed lines; superhydrophobic surface heated) and QIIB (solid lines; no-slip surface heated) as functions of normalized slip length λ∧ and normalized temperature jump coefficient γ∧. The dotted line is Eq. (40), for which QIIA=QIIB. Above the dotted line: QIIB > QIIA; below the dotted line: QIIA > QIIB.

Grahic Jump Location
Fig. 4

Velocity profiles for the four cases: (a) w∧IA(y∧), (b) w∧IB(y∧), (c) w∧IIA(y∧), (d) w∧IIB(y∧), for several values of the normalized slip length λ∧ and normalized temperature jump coefficient γ∧, where the subscripts “I” and “II” stand for heating by constant wall temperature and by constant heat flux, respectively, and the superscripts “A” and “B” stand for heating applied to the superhydrophobic surface and to the no-slip surface, respectively.

Grahic Jump Location
Fig. 5

The Nusselt numbers NuA (dashed line; superhydrophobic surface heated) and NuB (solid lines; no-slip surface heated) as functions of λ∧ and γ∧, where NuA is independent of γ∧.

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