Research Papers: Forced Convection

Apparent Temperature Jump and Thermal Transport in Channels With Streamwise Rib and Cavity Featured Superhydrophobic Walls at Constant Heat Flux

[+] Author and Article Information
D. Maynes

e-mail: maynes@byu.edu

J. Crockett

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received November 29, 2012; final manuscript received July 10, 2013; published online October 25, 2013. Assoc. Editor: Wilson K. S. Chiu.

J. Heat Transfer 136(1), 011701 (Oct 25, 2013) (10 pages) Paper No: HT-12-1636; doi: 10.1115/1.4025045 History: Received November 29, 2012; Revised July 10, 2013

This paper presents an analytical investigation of constant property, steady, fully developed, laminar thermal transport in a parallel-plate channel comprised of metal superhydrophobic (SH) walls. The superhydrophobic walls considered here exhibit microribs and cavities aligned in the streamwise direction. The cavities are assumed to be nonwetting and contain air, such that the Cassie–Baxter state is the interfacial state considered. The scenario considered is that of constant heat flux through the rib surfaces with negligible thermal transport through the air cavity interface. Closed form solutions for the local Nusselt number and local wall temperature are presented and are in the form of infinite series expansions. The analysis show the relative size of the cavity regions compared to the total rib and cavity width (cavity fraction) exercises significant influence on the aggregate thermal transport behavior. Further, the relative size of the rib and cavity module width compared to the channel hydraulic diameter (relative module width) also influences the Nusselt number. The spatially varying Nusselt number and wall temperature are presented as a function of the cavity fraction and the relative module width over the ranges 0–0.99 and 0.01–1.0, respectively. From these results, the rib/cavity module averaged Nusselt number was determined as a function of the governing parameters. The results reveal that increases in either the cavity fraction or relative module width lead to decreases in the average Nusselt number and results are presented over a wide range of conditions from which the average Nusselt number can be determined for heat transfer analysis. Further, analogous to the hydrodynamic slip length, a temperature jump length describing the apparent temperature jump at the wall is determined in terms of the cavity fraction. Remarkably, it is nearly identical to the hydrodynamic slip length for the scenario considered here and allows straightforward determination of the average Nusselt number for any cavity fraction and relative rib/cavity module width.

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Grahic Jump Location
Fig. 1

Illustration of apparent slip and temperature jumps that exist at SH walls

Grahic Jump Location
Fig. 2

Schematic illustration of liquid channel flow over a heated SH surface with ribs aligned parallel (longitudinal) to the flow direction

Grahic Jump Location
Fig. 3

Schematic illustration of the surface characteristics and the control volume considered in analysis for the thermal transport analysis

Grahic Jump Location
Fig. 4

Velocity profiles in a SH channel with Fc = 0.98 and Wm = 0.02 (left) and Wm = 0.2 (right). Profiles are shown at the center of the rib (z/w = 0) and cavity (z/w = 0.5), in addition to the aggregate profile described by Eq. (3) and the classic no-slip profile

Grahic Jump Location
Fig. 5

θw as a function of z/w for Wm = 0.1 and at Fc = 0.3, 0.6, 0.9, and 0.96

Grahic Jump Location
Fig. 6

Nu as a function of z/w for Wm = 0.1 and at Fc = 0.3, 0.6, 0.9, and 0.96

Grahic Jump Location
Fig. 7

θw as a function of z/w for Fc = 0.9 and at Wm = 0.001, 0.01, 0.1, and 0.3

Grahic Jump Location
Fig. 8

Nu as a function of z/w for Fc = 0.9 and at Wm = 0.001, 0.01, 0.1, 0.3, and 1.0

Grahic Jump Location
Fig. 9

Rib-averaged value of the Nusselt number, Nur¯, as a function of the solid rib fraction, Fr, for Wm ranging from Wm = 0.001 to 1.0

Grahic Jump Location
Fig. 10

Rib and cavity module averaged value of the Nusselt number, Nu¯, as a function of the solid rib fraction, Fr, for Wm ranging from Wm = 0.001 to 1.0. Results are also shown from Ref. [30] for the transverse rib scenario where Pe = 100 and Wm = 0.1.

Grahic Jump Location
Fig. 11

Normalized temperature jump length, λT/w as a function of Fc for Wm ranging from 0.01 to 1.0. Also shown is the hydrodynamic slip length derived from Eq. (22) for this scenario. Results are also shown from Ref. [30] for the transverse rib scenario where Pe = 100 and Wm = 0.1.



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