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Research Papers: Heat and Mass Transfer

Effect of Meniscus Curvature on Apparent Thermal Slip

[+] Author and Article Information
Lisa Steigerwalt Lam

Department of Mechanical Engineering,
Tufts University,
Medford, MA 02155
e-mail: lisa_lam@alum.mit.edu

Marc Hodes, Georgios Karamanis

Department of Mechanical Engineering,
Tufts University,
Medford, MA 02155

Toby Kirk

Department of Mathematics,
Imperial College,
London SW7 2AZ, UK

Scott MacLachlan

Department of Mathematics and Statistics,
Memorial University of Newfoundland,
St. John's, NL A1C 5S7, Canada

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 18, 2016; final manuscript received July 12, 2016; published online August 16, 2016. Assoc. Editor: Dr. Antonio Barletta.

J. Heat Transfer 138(12), 122004 (Aug 16, 2016) (9 pages) Paper No: HT-16-1019; doi: 10.1115/1.4034189 History: Received January 18, 2016; Revised July 12, 2016

We analytically consider the effect of meniscus curvature on heat transfer to laminar flow across structured surfaces. The surfaces considered are composed of ridges. Curvature of the menisci, which separates liquid in the Cassie state and gas trapped in cavities between the ridges, results from the pressure difference between the liquid and the gas. A boundary perturbation approach is used to develop expressions that account for the change in the temperature field in the limit of small curvature of a meniscus. The meniscus is considered adiabatic and a constant heat flux boundary condition is prescribed at the tips of the ridges in a semi-infinite and periodic domain. A solution for a constant temperature ridge is also presented using existing results from a mathematically equivalent hydrodynamic problem. We provide approximate expressions for the apparent thermal slip length as function of solid fraction over a range of small meniscus protrusion angles. Numerical results show good agreement with the perturbation results for protrusion angles up to ± 20 deg.

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Figures

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Fig. 1

Schematic of a curved meniscus between the ridges. The protrusion angle, α, is that between the line tangent to the meniscus at the triple contact line and the horizontal. The pitch of the structures is 2d. The width of the cavity is 2c.

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Fig. 2

Schematic of isoflux domain, a half-ridge and half-cavity of a parallel ridge structured surface with meniscus between the ridges. Dashed vertical lines indicate symmetry.

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Fig. 3

Dimensionless thermal slip length versus solid fraction, ϕ, for selected protrusion angles, α, for the case of an isoflux ridge

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Fig. 4

Dimensionless thermal slip length versus solid fraction, ϕ, for selected protrusion angles, α, for the case of an isothermal ridge

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Fig. 5

Dimensionless thermal slip length versus protrusion angle, α, for selected solid fractions, ϕ. Solid lines correspond to an isoflux ridge. Dashed lines correspond to an isothermal ridge.

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Fig. 6

Dimensionless slip length versus solid fraction for the case of an isoflux ridge. Solid lines are perturbation method results, and Δ's are values for β from the numerical results from matlab.

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Fig. 7

Dimensionless slip length versus solid fraction for the case of an isothermal ridge. Solid lines are perturbation method results from Ref. [18], and Δ's are values for β from the numerical results from matlab.

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