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.

References

References
1.
Rothstein
,
J. P.
,
2010
, “
Slip on Superhydrophobic Surfaces
,”
Annu. Rev. Fluid Mech.
,
42
, pp.
89
109
.10.1146/annurev-fluid-121108-145558
2.
Vinogradova
,
O. I.
, and
Dubov
,
A. L.
,
2012
, “
Superhydrophobic Textures for Microfluidics
,”
Mendeleev Commun.
,
22
, pp.
229
236
.10.1016/j.mencom.2012.09.001
3.
Sahraoui
,
M.
, and
Kaviany
,
M.
,
1993
, “
Slip and No-Slip Temperature Boundary Conditions at Interface of Porous, Plain Media: Conduction
,”
Int. J. Heat Mass Transfer
,
36
, pp.
1019
1033
.10.1016/S0017-9310(05)80286-8
4.
Alazmi
,
B.
, and
Vafai
,
K.
,
2001
, “
Analysis of Fluid Flow and Heat Transfer Interfacial Conditions Between a Porous Medium and a Fluid Layer
,”
Int. J. Heat Mass Transfer
,
44
, pp.
1735
1749
.10.1016/S0017-9310(00)00217-9
5.
Enright
,
R.
,
Eason
,
C.
,
Dalton
,
T.
,
Hodes
,
M.
,
Salamon
,
T.
,
Kolodner
,
P.
, and
Krupenkin
,
T.
,
2006
, “
Friction Factors and Nusselt Numbers in Microchannels With Superhydrophobic Walls
,” ASME Paper No. ICNMM2006-96134.
6.
Maynes
,
D.
,
Webb
,
B. W.
, and
Davies
,
J.
,
2008
, “
Thermal Transport in a Microchannel Exhibiting Ultrahydrophobic Microribs Maintained at Constant Temperature
,”
ASME J. Heat Transfer
,
130
, p.
022402
.10.1115/1.2789715
7.
Maynes
,
D.
,
Webb
,
B. W.
,
Crockett
,
J.
, and
Soloviev
,
V.
,
2013
, “
Analysis of Laminar Slip-Flow Thermal Transport in Microchannels With Transverse Rib and Cavity Structured Superhydrophobic Walls at Constant Heat Flux
,”
ASME J. Heat Transfer
,
135
, p.
021701
.10.1115/1.4007429
8.
Rosengarten
,
G.
,
Stanley
,
C.
, and
Kwok
,
F.
,
2008
, “
Superinsulating Heat Transfer Surfaces for Microfluidic Channels
,”
Int. J. Transp. Phenom.
,
10
, pp.
293
306
.
9.
Kim
,
T. J.
,
Kanapuram
,
R.
,
Chhabra
,
A.
, and
Hidrovo
,
C.
,
2011
, “
Thermo-Wetting and Friction Reduction Characterization of Microtextured Superhydrophobic Surfaces
,”
ASME J. Fluids Eng.
,
134
, p.
114501
.10.1115/1.4007604
10.
Choi
,
C. H.
,
Ulmanella
,
U.
,
Kim
,
J.
,
Ho
,
C. M.
, and
Kim
,
C. J.
,
2006
, “
Effective Slip and Friction Reduction in Nanograted Superhydrophobic Microchannels
,”
Phys. Fluids
,
18
, p.
087105
.10.1063/1.2337669
11.
Maynes
,
D.
,
Jeffs
,
K.
,
Woolford
,
B.
, and
Webb
,
B. W.
,
2007
, “
Laminar Flow in a Microchannel With Hydrophobic Surface Patterned Microribs Oriented Parallel to the Flow Direction
,”
Phys. Fluids
,
19
, p.
093603
.10.1063/1.2772880
12.
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
, p.
123601
.10.1063/1.2815730
13.
Lee
,
C.
,
Choi
,
C. H.
, and
Kim
,
C. J.
,
2008
, “
Structured Surfaces for a Giant Liquid Slip
,”
Phys. Rev. Lett.
,
101
, p.
064501
.10.1103/PhysRevLett.101.064501
14.
Teo
,
C. J.
, and
Khoo
,
B. C.
,
2009
, “
Analysis of Stokes Flow in Microchannels With Superhydrophobic Surfaces Containing a Periodic Array of Micro-Grooves
,”
Microfluid. Nanofluid.
,
7
, pp.
353
382
.10.1007/s10404-008-0387-0
15.
Ng
,
C. O.
, and
Wang
,
C. Y.
,
2009
, “
Stokes Shear Flow Over a Grating: Implications for Superhydrophobic Slip
,”
Phys. Fluids
,
21
, p.
013602
.10.1063/1.3068384
16.
Ng
,
C. O.
, and
Wang
,
C. Y.
,
2010
, “
Apparent Slip Arising From Stokes Flow Over a Bidimensional Patterned Surface
,”
Microfluid. Nanofluid.
,
8
, pp.
361
371
.10.1007/s10404-009-0466-x
17.
Ng
,
C. O.
,
Chu
,
H. C. W.
, and
Wang
,
C. Y.
,
2010
, “
On the Effects of Liquid–Gas Interfacial Shear on Slip Flow Through a Parallel-Plate Channel With Superhydrophobic Grooved Walls
,”
Phys. Fluids
,
22
, p.
102002
.10.1063/1.3493641
18.
Lund
,
N. J.
,
Zhang
,
X. P.
,
Mahelona
,
K.
, and
Hendy
,
S. C.
,
2012
, “
Calculation of Effective Slip on Rough Chemically Heterogeneous Surfaces Using a Homogenization Approach
,”
Phys. Rev. E
,
86
, p.
046303
.10.1103/PhysRevE.86.046303
19.
Baier
,
T.
,
Steffes
,
C.
, and
Hardt
,
S.
,
2010
, “
Thermocapillary Flow on Superhydrophobic Surfaces
,”
Phys. Rev. E
,
82
, p.
037301
.10.1103/PhysRevE.82.037301
20.
Philip
,
J. R.
,
1972
, “
Flow Satisfying Mixed No-Slip and No-Shear Conditions
,”
ZAMP
,
23
, pp.
353
372
.10.1007/BF01595477
21.
Ng
,
C. O.
, and
Wang
,
C. Y.
,
2011
, “
Effective Slip for Stokes Flow Over a Surface Patterned With Two- or Three-Dimensional Protrusions
,”
Fluid Dyn. Res.
,
43
, p.
065504
.10.1088/0169-5983/43/6/065504
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