0
Research Papers: Evaporation, Boiling, and Condensation

Effect of Evaporation and Condensation at Menisci on Apparent Thermal Slip

[+] Author and Article Information
Marc Hodes

Department of Mechanical Engineering,
Tufts University,
Medford, MA 02155
e-mail: marc.hodes@Tufts.edu

Lisa Steigerwalt Lam

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

Adam Cowley

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: adam.m.cowley@gmail.com

Ryan Enright

Thermal Management Research Group,
Efficient Energy Transfer (ηet) Department,
Bell Labs Ireland,
Alcatel-Lucent Ireland Ltd.,
Blanchardstown Business & Technology Park,
Dublin 15, Ireland
e-mail: ryan.enright@alcatel-lucent.com

Scott MacLachlan

Department of Mathematics and Statistics,
Memorial University of Newfoundland,
St Johns, NL A1C 5S7, Canada
e-mail: smaclachlan@mun.ca

The “vapor” phase normally has vapor and noncondensable gas components.

For pillar-geometry structures, the velocity and temperature fields in the inner problems are three-dimensional; therefore, velocities and temperatures are averaged over areas rather than line segments to compute slip lengths.

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 30, 2014; final manuscript received February 5, 2015; published online March 24, 2015. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 137(7), 071502 (Jul 01, 2015) (7 pages) Paper No: HT-14-1498; doi: 10.1115/1.4029818 History: Received July 30, 2014; Revised February 05, 2015; Online March 24, 2015

We semi-analytically capture the effects of evaporation and condensation at menisci on apparent thermal slip lengths for liquids suspended in the Cassie state on ridge-type structured surfaces using a conformal map and convolution. An isoflux boundary condition is prescribed at solid–liquid interfaces and a constant heat transfer coefficient or isothermal one at menisci. We assume that the gaps between ridges, where the vapor phase resides, are closed systems; therefore, the net rates of heat and mass transfer across menisci are zero. The reduction in apparent thermal slip length due to evaporation and condensation relative to the limiting case of an adiabatic meniscus as a function of solid fraction and interfacial heat transfer coefficient is quantified in a single plot. The semi-analytical solution method is verified by numerical simulation. Results suggest that interfacial evaporation and condensation need to be considered in the design of microchannels lined with structured surfaces for direct liquid cooling of electronics applications and a quantitative means to do so is elucidated. The result is a decrease in thermal resistance relative to the predictions of existing analyses which neglect them.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Quéré, D., 2005, “Non-Sticking Drops,” Rep. Prog. Phys., 68(11), pp. 2495–2532. [CrossRef]
Steigerwalt Lam, L., Hodes, M., and Enright, R., 2015, “Analysis of Galinstan Based Microgap Cooling Enhancement in the Presence of Apparent Slip,” ASME J. Heat Transfer (in press).
Hodes, M., Kolodner, P., Krupenkin, T., Lee, W., Lyons, A., Salamon, T., Taylor, J., and Weiss, D., 2007, “Techniques for Microchannel Cooling,” U.S. Patent No. 7,204,298.
Navier, C., 1823, “Mémoire Sur Les Lois du Mouvement Des Fluides,” Mémoires de l'Acad. R. Sci. Inst. Fr., 6, pp. 389–440.
Lauga, E., and Stone, H. A., 2003, “Effective Slip in Pressure-Driven Stokes Flow,” J. Fluid Mech., 489, pp. 55–77. [CrossRef]
Davis, A., and Lauga, E., 2010, “Hydrodynamic Friction of Fakir-Like Superhydrophobic Surfaces,” J. Fluid Mech., 661, pp. 402–411. [CrossRef]
Enright, R., Hodes, M., Salamon, T., and Muzychka, Y., 2013, “Isoflux Nusselt Number and Slip Length Formulae for Superhydrophobic Microchannels,” ASME J. Heat Transfer, 136(1), p. 012402. [CrossRef]
Ybert, C., Barentin, C., Cottin-Bizonne, C., Joseph, P., and Bocquet, L., 2007, “Achieving Large Slip With Superhydrophobic Surfaces: Scaling Laws for Generic Geometries,” Phys. Fluids, 19(12), p. 123601. [CrossRef]
Yovanovich, M., 1998, “Conduction and Thermal Contact Resistances (Conductances),” Handbook of Heat Transfer, 3rd ed., W.Rohsenow, and J. H. Y.Cho, eds., McGraw-Hill, New York.
Ng, C.-O., and Wang, C. Y., 2014, “Temperature Jump Coefficient for Superhydrophobic Surfaces,” ASME J. Heat Transfer, 136(6), p. 064501. [CrossRef]
Maynes, D., and Crockett, J., 2013, “Apparent Temperature Jump and Thermal Transport in Channels With Streamwise Rib and Cavity Featured Superhydrophobic Walls at Constant Heat Flux,” ASME J. Heat Transfer, 136(1), p. 011701. [CrossRef]
Cowley, A., Maynes, D., and Crockett, J., 2014, “Effective Temperature Jump Length and Influence of Axial Conduction for Thermal Transport in Superhydrophobic Channels,” Int. J. Heat Mass Transfer, 79, pp. 573–583. [CrossRef]
Steigerwalt Lam, L., Melnick, C., Hodes, M., Ziskind, G., and Enright, R., 2014, “Nusselt Numbers for Thermally Developing Couette Flow With Hydrodynamic and Thermal Slip,” ASME J. Heat Transfer, 136(5), p. 051703. [CrossRef]
Jiji, L., 2009, Heat Convection, Springer, Berlin. [CrossRef]
Duan, Z., and Muzychka, Y., 2010, “Slip Flow in the Hydrodynamic Entrance Region of Circular and Noncircular Microchannels,” ASME J. Fluids Eng., 132(1), p. 011201. [CrossRef]
Colin, S., 2012, “Gas Microflows in the Slip Flow Regime: A Critical Review on Convective Heat Transfer,” ASME J. Heat Transfer, 134(2), p. 020908. [CrossRef]
Rothstein, J. P., 2010, “Slip on Superhydrophobic Surfaces,” Annu. Rev. Fluid Mech., 42(1), pp. 89–109. [CrossRef]
Philip, J. R., 1972, “Flows Satisfying Mixed No-Slip and No-Shear Conditions,” J. Appl. Math. Phys. (ZAMP), 23, pp. 353–372. [CrossRef]
Carey, V. P., 1992, Liquid–Vapor Phase-Change Phenomena, Hemisphere, New York.
Schrage, R. W., 1953, A Theoretical Study of Interphase Mass Transfer, Columbia University Press, New York.
Lemmon, E., McLinden, M., and Friend, D., 2011, “Thermophysical Properties of Fluid Systems,” NIST Chemistry WebBook, NIST Standard Reference Database Number 69, P.Linstrom, and W.Mallard, eds., National Institute of Standards and Technology, Gaithersburg, MD.

Figures

Grahic Jump Location
Fig. 1

Liquid in Cassie state on ridge-type structures

Grahic Jump Location
Fig. 2

Liquid domain and ridge and vapor region beneath it

Grahic Jump Location
Fig. 3

Dimensionless thermal slip length versus solid fraction for adiabatic meniscus, finite dimensionless heat transfer coefficient at meniscus and isothermal meniscus when the boundary condition at the solid–liquid interface is constant heat flux. Triangles correspond to numerical verification of semi-analytical solution method.

Grahic Jump Location
Fig. 4

Interfacial heat transfer coefficient and maximum interfacial heat flux to which it applies as a function of temperature for water

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In