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Technical Brief

Temperature Jump Coefficient for Superhydrophobic Surfaces

[+] Author and Article Information
Chiu-On Ng

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

C. Y. Wang

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

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 26, 2013; final manuscript received January 13, 2014; published online March 7, 2014. Assoc. Editor: Robert D. Tzou.

J. Heat Transfer 136(6), 064501 (Mar 07, 2014) (6 pages) Paper No: HT-13-1164; doi: 10.1115/1.4026499 History: Received March 26, 2013; Revised January 13, 2014

Mathematical models are developed for heat conduction in creeping flow of a liquid over a microstructured superhydrophobic surface, where because of hydrophobicity, a gas is trapped in the cavities of the microstructure. As gas is much lower in thermal conductivity than liquid, an interfacial temperature slip between the liquid and the surface will develop on the macroscale. In this note, the temperature jump coefficient is numerically determined for several types of superhydrophobic surfaces: a surface with parallel grooves, and surfaces with two-dimensionally distributed patches corresponding to the top of circular or square posts, and circular or square holes. These temperature jump coefficients are found to have a nearly constant ratio with the corresponding velocity slip lengths.

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Copyright © 2014 by ASME
Topics: Temperature
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Figures

Grahic Jump Location
Fig. 1

Cross section view of one periodic unit of a grooved surface, where the cavity (Region I) is filled with a gas, the solid rib (shaded area) has a constant temperature Ts, and the space above the surface (Region II) is occupied by a liquid with a constant far-field temperature gradient. The period length is 2L, and the cavity has the dimensions of b for depth and 2a for width.

Grahic Jump Location
Fig. 2

For the grooved surface, the temperature jump coefficient K∧ as a function of the groove depth b∧, the solid area fraction of the surface φs, and the ratio of thermal conductivities kr, where in (a) kr = 0.04, and in (b) b∧=4. The symbols in (b) are the hydrodynamic slip lengths given by the analytical formula of Eq. (16).

Grahic Jump Location
Fig. 3

(a) Four types of two-dimensional patterns on a square lattice: (i) circular and (ii) square patches of constant temperature on an otherwise nonconducting surface; (iii) circular and (iv) square nonconducting patches on an otherwise surface of constant temperature. (b) An isomeric view of the domain over one periodic unit of the patterned surface, where the period length is 2L in both x and y directions, and the temperature gradient is constant far above the surface.

Grahic Jump Location
Fig. 4

For the four types of two-dimensional patterned surfaces, the temperature jump coefficient K∧ as a function of the solid area fraction of the surface φs. In the insets, η=δ∧/K∧ is the ratio of the hydrodynamic slip length δ∧ to the temperature jump coefficient K∧, where the slip lengths were computed by Ng and Wang [16] for Stokes flow in the x direction over the patterned surfaces.

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