Abstract

Microchannel heat sinks are potential devices that remove heat flux from high power density miniaturized electronic components. While the large surface-area-to-volume ratio and high heat transfer coefficient are the key features rendering benefits, the small flow rate and short channel lengths alongside high solid cross section to fluid free flow area make them susceptible to intense axial conduction loss. The conventional models for macrodevices based on the one-dimensional energy equation are often inappropriate in the microdomain. A novel multidimensional analytical model (capable of capturing axial heat transfer in microchannel heat sinks) has been used to study the thermal performance over a varied range of geometric and flow parameters. The effect of axial conduction has been seen in the solid–fluid temperature profiles, interfacial flux distribution and the average amount of heat transferred axially. The results indicate a skewed flux distribution at the fluid–solid interface leading to nonlinear temperature variation when axial conduction is dominant. Moreover, it has been shown that nonlinearity in the fluid temperature introduces significant errors in experimental data reduction, leading to apparently very low Nusselt number estimation. Moreover, this erroneous data interpretation is also linked to the prediction of a strong Reynolds number dependency of the average Nusselt number in the laminar flow regime.

References

1.
Garimella
,
S. V.
, and
Sobhan
,
C. B.
,
2003
, “
Transport in Microchannels–A Critical Review
,”
Annu. Rev. Heat Transfer
,
13
(
13
), pp.
1
50
.10.1615/AnnualRevHeatTransfer.v13.30
2.
Peiyi
,
W.
, and
Little
,
W. A.
,
1983
, “
Measurement of Friction Factors for the Flow of Gases in Very Fine Channels Used for Microminiature Joule-Thomson Refrigerators
,”
Cryogenics
,
23
(
5
), pp.
273
277
.10.1016/0011-2275(83)90150-9
3.
Dixit
,
T.
, and
Ghosh
,
I.
,
2013
, “
Low Reynolds Number Thermo-Hydraulic Characterization of Offset and Diamond Minichannel Metal Heat Sinks
,”
Exp. Therm. Fluid Sci.
, (
51
), pp.
227
238
.10.1016/j.expthermflusci.2013.08.002
4.
Wu
,
P.
, and
Little
,
W. A.
,
1984
, “
Measurement of the Heat Transfer Characteristics of Gas Flow in Fine Channel Heat Exchangers Used for Microminiature Refrigerators
,”
Cryogenics
,
24
(
8
), pp.
415
420
.10.1016/0011-2275(84)90015-8
5.
Peng
,
X. F.
,
Wang
,
B. X.
,
Peterson
,
G. P.
, and
Ma
,
H. B.
,
1995
, “
Experimental Investigation of Heat Transfer in Flat Plates With Rectangular Microchannels
,”
Int. J. Heat Mass Transfer
,
38
(
1
), pp.
127
137
.10.1016/0017-9310(94)00136-J
6.
Gad-el-Hak
,
M.
,
1999
, “
The Fluid Mechanics of Microdevices—The Freeman Scholar Lecture
,”
ASME J. Fluids Eng.
,
121
(
1
), pp.
5
33
.10.1115/1.2822013
7.
Agrawal
,
A.
,
2011
, “
A Comprehensive Review on Gas Flow in Microchannels
,”
Int. J. Micro-Nano Scale Transp.
, (
2
(
1
), pp.
1
40
.10.1260/1759-3093.2.1.1
8.
Peng
,
X. F.
, and
Peterson
,
G. P.
,
1995
, “
The Effect of Thermofluid and Geometrical Parameters on Convection of Liquids Through Rectangular Microchannels
,”
Int. J. Heat Mass Transfer
,
38
(
4
), pp.
755
758
.10.1016/0017-9310(95)93010-F
9.
Peng
,
X. F.
, and
Peterson
,
G. P.
,
1996
, “
Convective Heat Transfer and Flow Friction for Water Flow in Microchannel Structures
,”
Int. J. Heat Mass Transfer
,
39
(
12
), pp.
2599
2608
.10.1016/0017-9310(95)00327-4
10.
Herwig
,
H.
, and
Hausner
,
O.
,
2003
, “
Critical View on ‘New Results in Micro-Fluid Mechanics’: An Example
,”
Int. J. Heat Mass Transfer
,
46
(
5
), pp.
935
937
.10.1016/S0017-9310(02)00306-X
11.
Tso
,
C. P.
, and
Mahulikar
,
S. P.
,
2000
, “
Experimental Verification of the Role of Brinkman Number in Microchannels Using Local Parameters
,”
Int. J. Heat Mass Transfer
,
43
(
10
), pp.
1837
1849
.10.1016/S0017-9310(99)00241-0
12.
Rosa
,
P.
,
Karayiannis
,
T. G.
, and
Collins
,
M. W.
,
2009
, “
Single-Phase Heat Transfer in Microchannels: The Importance of Scaling Effects
,”
Appl. Therm. Eng.
,
29
(
17–18
), pp.
3447
3468
.10.1016/j.applthermaleng.2009.05.015
13.
Morini
,
G. L.
,
2004
, “
Single-Phase Convective Heat Transfer in Microchannels: A Review of Experimental Results
,”
Int. J. Therm. Sci.
,
43
(
7
), pp.
631
651
.10.1016/j.ijthermalsci.2004.01.003
14.
Caney
,
N.
,
Marty
,
P.
, and
Bigot
,
J.
,
2007
, “
Friction Losses and Heat Transfer of Single-Phase Flow in a Mini-Channel
,”
Appl. Therm. Eng.
,
27
(
10
), pp.
1715
1721
.10.1016/j.applthermaleng.2006.07.019
15.
Tiselj
,
I.
,
Hetsroni
,
G.
,
Mavko
,
B.
,
Mosyak
,
A.
,
Pogrebnyak
,
E.
, and
Segal
,
Z.
,
2004
, “
Effect of Axial Conduction on the Heat Transfer in Micro-Channels
,”
Int. J. Heat Mass Transfer
,
47
(
12–13
), pp.
2551
2565
.10.1016/j.ijheatmasstransfer.2004.01.008
16.
Moharana
,
M. K.
,
Singh
,
P. K.
, and
Khandekar
,
S.
,
2012
, “
Optimum Nusselt Number for Simultaneously Developing Internal Flow Under Conjugate Conditions in a Square Microchannel
,”
ASME J. Heat Transfer-Trans. ASME
,
134
(
7
), p.
071703
.10.1115/1.4006110
17.
Rao
,
M.
, and
Khandekar
,
S.
,
2009
, “
Simultaneously Developing Flows Under Conjugated Conditions in a Mini-Channel Array: Liquid Crystal Thermography and Computational Simulations
,”
Heat Transfer Eng.
,
30
(
9
), pp.
751
761
.10.1080/01457630802678573
18.
Baek
,
S.
,
Bradley
,
P. E.
, and
Radebaugh
,
R.
,
2018
, “
Heat Transfer Coefficient Measurement of LN2 and GN2 in a Microchannel at Low Reynolds Flow
,”
Int. J. Heat Mass Transfer
,
127
, pp.
222
233
.10.1016/j.ijheatmasstransfer.2018.07.145
19.
Chamarthy
,
P.
,
Wereley
,
S. T.
, and
Garimella
,
S. V.
,
2007
, “
Microscale Laser-Induced Fluorescence Method for Non-Intrusive Temperature Measurement
,”
ASME
Paper No. IMECE2007-41935.10.1115/IMECE2007-41935
20.
Huang
,
C. Y.
,
Wu
,
C. M.
,
Chen
,
Y. N.
, and
Liou
,
T. M.
,
2014
, “
The Experimental Investigation of Axial Heat Conduction Effect on the Heat Transfer Analysis in Microchannel Flow
,”
Int. J. Heat Mass Transfer
,
70
, pp.
169
173
.10.1016/j.ijheatmasstransfer.2013.10.059
21.
Lin
,
T.
, and
Kandlikar
,
S. G.
,
2012
, “
A Theoretical Model for Axial Heat Conduction Effects During Single-Phase Flow in Microchannels
,”
ASME J. Heat Transfer-Trans. ASME
,
134
(
2
), p. 0
20902
.10.1115/1.4004936
22.
Maranzana
,
G.
,
Perry
,
I.
, and
Maillet
,
D.
,
2004
, “
Mini- and Micro-Channels: Influence of Axial Conduction in the Walls
,”
Int. J. Heat Mass Transfer
,
47
(
17–18
), pp.
3993
4004
.10.1016/j.ijheatmasstransfer.2004.04.016
23.
Cole
,
K. D.
, and
Çetin
,
B.
,
2011
, “
The Effect of Axial Conduction on Heat Transfer in a Liquid Microchannel Flow
,”
Int. J. Heat Mass Transfer
, (
54
(
11–12
), pp.
2542
2549
.10.1016/j.ijheatmasstransfer.2011.02.007
24.
Lelea
,
D.
,
2009
, “
The Heat Transfer and Fluid Flow of a Partially Heated Microchannel Heat Sink
,”
Int. Commun. Heat Mass Transfer
,
36
(
8
), pp.
794
798
.10.1016/j.icheatmasstransfer.2009.05.003
25.
Koşar
,
A.
,
2010
, “
Effect of Substrate Thickness and Material on Heat Transfer in Microchannel Heat Sinks
,”
Int. J. Therm. Sci.
,
49
(
4
), pp.
635
642
.10.1016/j.ijthermalsci.2009.11.004
26.
Bergman, T. L., Lavine, A. S., Incropera
,
F. P.
, and
DeWitt
,
D. P.
,
2006
,
Fundamentals of Heat and Mass Transfer
(Chapter 8—Internal Flow),
Wiley Publication
, Hoboken,
NJ
, pp.
485
558
.
27.
Mitra
,
I.
, and
Ghosh
,
I.
,
2020
, “
Mini-Channel Heat Sink Parameter Sensitivity Based on Precise Heat Flux Re-Distribution
,”
Therm. Sci. Eng. Prog.
,
20
, p.
100717
.10.1016/j.tsep.2020.100717
28.
Mitra
,
I.
, and
Ghosh
,
I.
,
2021
, “
Analytical Closed-Form Solution for Fluid Flow Through Microchannel Heat Sinks Including Axial Conduction
,”
Int. Commun. Heat Mass Transfer
,
129
, p.
105732
.10.1016/j.icheatmasstransfer.2021.105732
29.
Spiga
,
M.
, and
Morini
,
G. L.
,
1996
, “
Nusselt Numbers in Laminar Flow for H2 Boundary Conditions
,”
Int. J. Heat Mass Transfer
,
39
(
6
), pp.
1165
1174
.10.1016/0017-9310(95)00205-7
30.
Rohatgi
,
A.
,
2021
, “WebPlotDigitizer,” WebPlotDigitizer, CA, accessed Apr. 12, https://automeris.io/
31.
Kandlikar
,
S. G.
,
Garimella
,
S.
,
Li
,
D.
,
Colin
,
S.
, and
King
,
M. R.
,
2014
,
Heat Transfer and Fluid Flow in Minichannels and Microchannels
(Chapter 3 – Single Phase Liquid Flow in Minichannels and Microchannels),
Elsevier Publication
,
Amsterdam, Netherlands
, pp.
103
174
.
32.
El-Genk
,
M. S.
, and
Pourghasemi
,
M.
,
2019
, “
Nusselt Number and Development Length Correlations for Laminar Flows of Water and Air in Microchannels
,”
Int. J. Heat Mass Transfer
,
133
, pp.
277
294
.10.1016/j.ijheatmasstransfer.2018.12.077
You do not currently have access to this content.