The analytical solution in the fully developed region of a slip flow in a circular microtube with constant wall temperature is obtained to verify the conventional temperature jump boundary condition when both viscous dissipation (VD) and substantial derivative of pressure (SDP) terms are included in the energy equation. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a microchannel with constant wall temperature when both viscous dissipation and substantial derivative of pressure terms are included in the energy equation. Numerical results are also obtained for a slip flow in a developing region of a circular tube. The results showed that the maximum heat transfer rate decreases with increasing Mach number.

References

References
1.
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
.
2.
Asako
,
Y.
,
2014
,
Notes on Energy Equation and 1st law of Thermodynamics
,
Kindle e-book
, ASIN: B00PGS516M.
3.
Maslen
,
H. S.
,
1958
, “
On Heat Transfer in Slip Flow
,”
J. Aeronaut. Sci.
,
25
(6), pp.
400
401
.
4.
Hadjiconstantinou
,
N. G.
,
2003
, “
The Effect of Viscous Heat Dissipation on Convective Heat Transfer Small-Scale Slipping Gaseous Flows
,”
First International Conference on Microchannels and Minichannels
(
ICMM
), Paper No. ICMM2003-1029.
5.
Shi
,
W.
,
Miyamoto
,
M.
,
Katoh
,
Y.
, and
Kurima
,
J.
,
2001
, “
Choked Flow of Low Density Gas in a Narrow Parallel-Plate Channel With Adiabatic Wall
,”
Int. J. Heat Mass Transfer
,
44
(
13
), pp.
2555
2565
.
6.
Miyamoto
,
M.
,
Shi
,
W.
,
Katoh
,
Y.
, and
Kodama
,
M.
,
2003
, “
Choked Flow and Heat Transfer of Rarefied Gas in a Narrow Parallel-Plate Channel With Uniformly Heating Walls
,”
Int. J. Heat Mass Transfer
,
46
(
14
), pp.
2685
2693
.
7.
Hong
,
C.
,
Asako
,
Y.
,
Turner
,
S. E.
, and
Faghri
,
M.
,
2007
, “
Friction Factor Correlations for Gas Flow in Slip Flow Regime
,”
ASME J. Fluids Eng.
,
129
(
10
), pp.
1268
1276
.
8.
Hong
,
C.
,
Asako
,
Y.
, and
Lee
,
J. H.
,
2007
, “
Heat Transfer Characteristics of Gaseous Flows in Micro-Channel With Constant Heat Flux
,”
Int. J. Therm. Sci.
,
46
(
11
), pp.
1153
1162
.
9.
Hong
,
C.
, and
Asako
,
Y.
,
2008
, “
Heat Transfer Characteristics of Gaseous Flows in Microtube With Constant Heat Flux
,”
Appl. Therm. Eng.
,
28
(11–12), pp.
1375
1385
.
10.
Hong
,
C.
, and
Asako
,
Y.
,
2008
, “
Heat Transfer Characteristics of Gaseous Flows in Micro-Channel With Negative Heat Flux
,”
Heat Transfer Eng.
,
29
(
9
), pp.
805
815
.
11.
Hong
,
C.
, and
Asako
,
Y.
,
2010
, “
Some Consideration on Thermal Boundary Condition of Slip Flow
,”
Int. J. Heat Mass Transfer
,
53
(
15–16
), pp.
3075
3079
.
12.
Deissler
,
R.
,
1964
, “
An Analysis of Second-Order Slip Flow and Temperature Jump Boundary Conditions for Rarefied Gases
,”
Int. J. Heat Mass Transfer
,
7
(
6
), pp.
681
694
.
13.
Xiao
,
N.
,
Elsnab
,
J.
, and
Amee
,
T.
,
2009
, “
Microtube Gas Flows With Second-Order Slip Flow and Temperature Jump Boundary Conditions
,”
Int. J. Therm. Sci.
,
48
(
2
), pp.
243
251
.
14.
Hong
,
C.
,
Asako
,
Y.
, and
Lee
,
J.-H.
,
2008
, “
Poiseuille Number Correlation for High Speed Micro-Flows
,”
J. Phys. D: Appl. Phys.
,
41
(
10
), p.
105111
.
15.
Hong
,
C.
,
Asako
,
Y.
,
Suzuki
,
K.
, and
Nahm
,
Y.
,
2010
, “
Heat Transfer Characteristics of Gaseous Slip Flow in a Micro-Channel
,”
J. Mech. Sci. Technol.
,
24
(
12
), pp.
2577
2585
.
16.
Asako
,
Y.
,
2016
, “
Energy Equation of Gas Flow With Low Velocity in a Micro-Channel
,”
ASME J. Heat Transfer
,
138
(
4
), p.
041702
.
17.
Kamidakis
,
G.
,
Beskok
,
A.
, and
Aluru
,
N.
,
2005
,
Microflows and Nanoflows: Fundamentals and Simulation
,
Springer
,
New York
, p.
16
.
18.
Patankar
,
S. V.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere
,
New York
, p.
90
.
19.
Burmeister
,
L. C.
,
1993
,
Convective Heat Transfer
,
2nd ed.
,
Wiley
,
New York
, p.
114
.
20.
Barron
,
R.
,
Wang
,
X.
,
Ameel
,
T. A.
, and
Warrington
,
R.
,
1997
, “
The Graetz Problem Extended to Slip-Flow
,”
Int. J. Heat Mass Transfer
,
40
(
8
), pp.
1817
1823
.
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