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.

References

References
1.
Quéré
,
D.
,
2005
, “
Non-Sticking Drops
,”
Rep. Prog. Phys.
,
68
(
11
), pp.
2495
2532
.10.1088/0034-4885/68/11/R01
2.
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).
3.
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.
4.
Navier
,
C.
,
1823
, “
Mémoire Sur Les Lois du Mouvement Des Fluides
,”
Mémoires de l'Acad. R. Sci. Inst. Fr.
,
6
, pp.
389
440
.
5.
Lauga
,
E.
, and
Stone
,
H. A.
,
2003
, “
Effective Slip in Pressure-Driven Stokes Flow
,”
J. Fluid Mech.
,
489
, pp.
55
77
.10.1017/S0022112003004695
6.
Davis
,
A.
, and
Lauga
,
E.
,
2010
, “
Hydrodynamic Friction of Fakir-Like Superhydrophobic Surfaces
,”
J. Fluid Mech.
,
661
, pp.
402
411
.10.1017/S0022112010003460
7.
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
.10.1115/1.4024837
8.
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
.10.1063/1.2815730
9.
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.
10.
Ng
,
C.-O.
, and
Wang
,
C. Y.
,
2014
, “
Temperature Jump Coefficient for Superhydrophobic Surfaces
,”
ASME J. Heat Transfer
,
136
(
6
), p.
064501
.10.1115/1.4026499
11.
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
.10.1115/1.4025045
12.
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
.10.1016/j.ijheatmasstransfer.2014.08.033
13.
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
.10.1115/1.4026305
14.
Jiji
,
L.
,
2009
,
Heat Convection
,
Springer
, Berlin.10.1007/978-3-642-02971-4
15.
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
.10.1115/1.4000692
16.
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
.10.1115/1.4005063
17.
Rothstein
,
J. P.
,
2010
, “
Slip on Superhydrophobic Surfaces
,”
Annu. Rev. Fluid Mech.
,
42
(
1
), pp.
89
109
.10.1146/annurev-fluid-121108-145558
18.
Philip
,
J. R.
,
1972
, “
Flows Satisfying Mixed No-Slip and No-Shear Conditions
,”
J. Appl. Math. Phys. (ZAMP)
,
23
, pp.
353
372
.10.1007/BF01595477
19.
Carey
,
V. P.
,
1992
,
Liquid–Vapor Phase-Change Phenomena
,
Hemisphere
,
New York
.
20.
Schrage
,
R. W.
,
1953
,
A Theoretical Study of Interphase Mass Transfer
,
Columbia University Press
, New York.
21.
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
.
You do not currently have access to this content.