Proceedings of the Fifth International Conference on Nanochannels, Microchannels and Minichannels
ICNMM2007
Proceedings of ASME ICNMM2007
th
5 International Conference on Nanochannels, Microchannels
and Minichannels
June 18-20, 2007,
Puebla, Mexico
June 18-20, 2007, Puebla, Mexico
ICNMM2007-30186
ICNMM2007-30186
Effect Of Non Uniform Flow Distribution On Single Phase Heat Transfer In Parallel
Microchannels
Akhilesh V. Bapat
1
2
Satish G. Kandlikar
Department of Mechanical Engineering
Rochester Institute of Technology, NY, USA
1
[email protected]
2
[email protected]
ABSTRACT
OBJECTIVE
The continuum assumption has been widely accepted for
single phase liquid flows in microchannels. There are however
a number of publications which indicate considerable deviation
in thermal and hydrodynamic performance during laminar flow
in microchannels. In the present work, experiments have been
performed on six parallel microchannels with varying crosssectional dimensions. A careful assessment of friction factor
and heat transfer in is carried out by properly accounting for
flow area variations and the accompanying non-uniform flow
distribution in individual channels. These factors seem to be
responsible for the discrepancy in predicting friction factor and
heat transfer using conventional theory.
INTRODUCTION
Ever since the introduction of microchannels for cooling of
VLSI chips in the 1980’s by Tuckerman and Pease [1], many
investigations have been carried out on single-phase flow in
both laminar and turbulent ranges. Because of their inherent
characteristics of high surface area to volume ratio, and also
due to the area enhancement, microchannels provide a better
thermal performance over large diameter channels. Very high
heat transfer coefficients are observed as a result. Although the
accompanying pressure gradients are also high, suitable header
arrangements can be employed to address this problem
Kandlikar et al. [2]. Many studies have been carried out to find
the validity of classical theory on microchannel flows, and a
clear affirmation of the applicability of the heat transfer models
in the laminar fully developed and entry regions is still lacking.
An experimental investigation is carried out to study the
pressure drop and heat transfer characteristics of a set of six
parallel microchannels in the laminar and transition regimes.
Water is used as the working fluid. The objectives of this paper
are: i) to study the effect of non-uniform flow distribution on
pressure drop and heat transfer predictions, and (ii) to examine
the validity of the conventional heat transfer and pressure drop
models based on continuum assumptions during single-phase
liquid flow in microchannels.
PREVIOUS STUDIES
A brief summary of previous investigations on singlephase flow in microchannels and their performance prediction
using macroscale correlations are described in this section.
Table 1 presents a summary of some of the important
investigations in this area [3-12]. Many investigations have
reported aberrant behavior of flow and heat transfer in
microchannels.
Peng et al. [12] experimentally investigated heat transfer in
rectangular microchannels with hydraulic diameters of 133367µm. Their experiments indicated early transition to
turbulent regime and fully developed flow was observed for Re
400-1500. Nusselt number in the laminar regime was found to
be dependent on Re0.62. Fluid properties were calculated at the
fluid inlet temperature. The relationship between friction factor
and Nusselt number was observed to be significantly different
for the laminar flow. Authors stated that for microchannels the
1
Copyright © 2007 by ASME
Table 1. Summary of selected investigations on single-phase liquid flow in microchannels
Classical
Theory
Predictions in
Laminar
Regime
Agreement for
friction factor,
no heat transfer
study
Agreement
with theory for
fRe, no heat
transfer study
Experimental
Uncertainties
Rotameter
Agreement for
fRe and Nu
6.5% in f, 3.3%
in heat flux
estimation
Rotameter
fRe
underpredicted,
Nu
over
predicted
Friction factor
agreement
below Re 8001000,
heat
transfer
coefficient
higher
than
thermally
developing
flow theory
Agreement for
friction factor,
no heat transfer
study
NA
Hydraulic
Diameters
(µm),
Measurement
Verification
69-304, Stylus
surface
profilometer
Flow
rate
Measurement
Apparatus
Fused silicon
microtubes,
single channel
16-30, SEM
Graduated
flask and stop
watch
Etched Silicon
channels,
multiple
channels
Milling copper
plates, multiple
channels
222, SEM
280-3670, NA
Bucci et al., [8]
Microtube,
Single channel
172-520, NA
Hegab et al.,
[9]
Milled
Aluminium
plates, multiple
channels
112-210,
digital
calipers
Mala and Li,
[10]
Fused
silica,
Stainless Steel
microtubes,
single channel
50-254, NA
Flow sensor,
confirmed by
actual
measurement
Yu et al.,
[11]
Microtubes,
single channel
19-102µm,
SEM
NA
Rectangular
channels
machined on
steel substrate,
single channel
133-367, NA
Rotameter
Author
Channel
Details
Hrnjak and Tu,
[3]
Machined
in
PVC substrate,
single channel
Rands et al.,
[4]
Steinke and
Kandlikar, [5],
[6]
Solomon and
Sobhan, [7]
Peng
[12]
et
al.,
Rheotherm®
mass
flow
meter
Flowmeter
dial
flow and heat transfer nature and the physical aspects are
altered.
Mala and Li [10] investigated water flow through tubes of
diameters ranging from 50 to 254µm. The flow characteristics
Friction factor
underpredicted
for
smaller
diameter tubes,
no heat transfer
study.
Friction factor
overpredicted,
no heat transfer
prediction in
laminar
Significant
deviation from
theory for Nu
and
friction
factor
+-3.5% for f
16-29 % for
fRe
3-23%
for
friction factor,
67%
for
Nusselt
number
in
laminar regime
NA
11.9% in fRe
NA
for smaller tubes deviated significantly from the conventional
theory. Material dependence on the friction factors was
observed and the values obtained experimentally were higher
2
Copyright © 2007 by ASME
than the predictions. At lower flow rates the results were in
rough agreement with the theory however, significant
deviations were noted at higher Re flows.
Harms et al., [13] applied the developing flow theory for
both single channel and multiple channel systems to
characterize flow and heat transfer in minichannels. The
channels were 1000µm deep and 251µm wide. They
experimentally observed that the local Nusselt number agreed
well with the classical developing flow theory. However, for
multiple channel design, agreement was reasonably well at
higher flow rates but deviated significantly from theory at low
flow rates. Authors reported this deviation to the flow bypass in
the manifold.
Hegab et al. [9] found that the friction factors values were
consistently lower than values predicted by macroscale
correlations in the transition and the turbulent regime. R-134a
was used as the test fluid for 112-210 µm hydraulic diameter
rectangular channels. For the heat transfer calculations at lower
Reynolds numbers, the uncertainties reported were as high as
67%. Hence the heat transfer predictions in the laminar regime
were not reported.
Hrnjak and Tu [3] investigated fully developed liquid and
vapor flow through rectangular microchannels with hydraulic
diameters of 69 to 304µm. For low surface roughness the flaminar
approached the conventional values for all the channels tested.
No heat transfer studies were performed.
Steinke and Kandlikar [5,6] conducted an exhaustive
survey of literature and experimentally investigated friction
factor and Nusselt number in Silicon microchannels. They used
the simultaneously developing flow condition since the channel
lengths were small, and compared the data with the developing
flow theory. It was reported that the developing flow theory
was in very good agreement with the data. It may be noted that
the individual channel dimensions were measured and were
very close to each other.
It is observed from literature that there are contradictory
findings, especially as related to the applicability of the laminar
flow theory for heat transfer in microchannels. However, there
seems to be an agreement that fluid flow in microchannels in
the laminar regime is not different from macroscale
phenomenon in some of the carefully conducted experiments
with same size channels. Although the continuum assumption is
widely accepted for microchannels, the effect of individual
channel size variations is believed to be a factor responsible for
these deviations in parallel microchannels.
EXPERIMENTAL SETUP AND PROCEDURE:
A schematic of the experimental loop is shown in Fig. 1.
A pressure driven open loop is employed. Water is first
degassed to remove any dissolved gases and stored in a closed
tank. The water tank is allowed to cool down and a pump is
used to drive the flow. Two digital flow meters, one from 0-100
ml/min and the second from 100-1000ml/min range are used to
measure the flow rate. Six microchannels are milled on a
copper block. K type thermocouples are used to measure the
inlet and outlet temperatures of water. The copper block has a
hole in the centre of the block along the length of the
microchannels to house a cartridge heater. Just below the
microchannels, holes are drilled at two different heights for
inserting the thermocouples. The surface heat flux is calculated
using the temperature difference in the normal direction after
subtracting the heat losses. The copper block is covered with
insulation to reduce the heat losses. The inlet and outlet
manifolds are fabricated inside an acrylic transparent cover
plate.
Tin
Test
Section
Tout
∆P
Water
Tank
Receiver
Flow
Meter
Pump
Fig. 1 Schematic diagram of the test setup
A differential pressure sensor (OMEGA PX26 series) is
connected across the inlet and outlet manifolds for measuring
pressure drops up to 689 kPa. The water is then collected into a
receiver. Distilled water is used for all the runs. Readings are
taken after the temperatures stabilize in the system, generally
within about 60-90 minutes after changing the settings.
CHANNEL DIMENSIONS:
The individual channel dimensions were measured using a
KEYENCE Confocal Microscope. Samples were taken at
different locations along the length of the channel for each of
the channels. Table 2 gives the depth and width of each
channel. Surface texture was also measured and all the channels
can be considered as smooth in the flow direction.
Table 2. Channel dimensions
CHANNEL
1
2
3
4
5
6
Depth (µm)
210.8
181.4
201.4
184.5
204.2
200.3
Height (µm)
249.5
247.8
243.7
245.4
247.9
256.0
EXPERIMENTAL UNCERTAINTIES:
The uncertainty is determined by the method of evaluating
the bias and precision errors. The pressure transducer has an
uncertainty of ±0.69 kPa. The temperature reading has an
uncertainty of ±0.1°C. The power supply used to provide input
power within ±0.05 V and current within ±0.005 amps
uncertainty. The flow meter uncertainty in the volumetric flow
3
Copyright © 2007 by ASME
measurement is ±0.0588 cc/min. The power measurement has
an accuracy of ±0.5 Watts. The temperature difference
measurements have an uncertainty of ±0.2°C. The resulting
uncertainties are calculated for the heat transfer coefficient as
8.61%, the pressure drop is 7.19%, and friction factor is 4.80%,
at a median flow case. The major source of error is the
temperature reading. This uncertainty is based on Steinke and
Kandlikar [14] as the instrumentation used is same.
Num , 4 = a.b x .x c
where the constants a, b and c are found to be: a = 1.905, b
= 5.495 and c = -0.319.
The non-dimensional hydrodynamic and thermal entry
lengths are represented by x+ and x* are given by the following
equations:
L
Re .Dh
L
x* =
Re .Dh . Pr
DATA REDUCTION:
x+ =
From the measured flow rate and the pressure drop, the
experimental friction factor is calculated as per Eq. (1).
f app =
∆pe xpt .Dh .ρ . Ac2
(1)
2.m&.L
Based on the total power supplied, inlet and outlet
temperatures of fluid and the surface temperature, heat transfer
coefficient is calculated using Eq. (2). Experimental Num is
then calculated as follows.
havg =
Qe xpt
Aht LMTD
havg Dh
(3)
k
(7)
(8)
Both fapp and Num,3 are the average values, which include
the developing flow as well as the fully developed friction
factor and Nusselt number. Hence these two parameters are
used in the analysis.
The pressure drop was measured across the inlet and outlet
manifold. It includes the losses in the 90° bends and the
expansion and contraction losses.
 A
∆pl =  c
 A p

(2)
Where LMTD is the log mean temperature difference
between the microchannel and the water at the inlet and outlet
sections. The mean Nusselt number is given by:
Nu m =
(6)
2
 &2

 .2 K 90 + K c + K e  m

 2 Ac2 ρ


(9)
The pressure drop ∆pexpt is referenced in this paper
henceforth after deducting the pressure losses from the actual
measured pressure drop and represents the pressure drop in the
microchannels.
UNIFORM FLOW ANALYSIS:
NON-UNIFORM FLOW ANALYSIS:
The developing flow analysis is employed for calculating
the theoretical apparent friction factor fapp,th . The curve-fit
expression for fapp is given by Eq. (4) and the values of the
constants a-f are obtained from [2].
To study the effect of non-uniform flow distribution in the
parallel microchannels, six parallel channels of varying depth
and height are machined on the copper block. Since the cross
sectional area of each channel is different, for the same
measured pressure drop across the inlet and outlet manifold, the
flow rate is not uniform in the parallel channels. Because of
this, the heat removed by the liquid in each channel also varies.
Thus, the analysis based on uniform flow is not applicable to
the channels with different individual cross-sectional
dimensions.
To check the applicability of the developing region
analysis, a reverse analysis is carried out. Since the flow is
developing, theoretical values of fapp and Num,3 are calculated
based on individual channel dimensions. Based on the fapp
estimate and the measured pressure drop across the channels,
mass flow rate in each channel is calculated. This represents the
actual flow in channels if the developing theory was to hold
true in microchannels. Flow through individual channels is
added up to find the total flow rate according to the theory, and
this is compared with the actual measured flow rate in the
experiments.
For heat transfer calculations, the individual channel mass
flow rates calculated above using the developing flow theory,
and the estimated Num,3 are used in calculating the heat
f app Re =
a + cx +
1 + bx +
0.5
0.5
+ ex +
+ dx + + fx +
1.5
(4)
Num,3 represents the average Nusselt number with the
three-sided heating. It is related to the Nusselt number for foursided heating Num,4, which is given by Wibulswas [15] for the
H1 boundary condition by:
Nu m,3 = Nu m, 4 .
Nu fd ,3
Nu fd , 4
(5)
The correction factor Nufd,3/ Nufd,4 is obtained from Phillips
[16]. The tabular values of Num,4 are fitted with the following
curve-fit equation:
4
Copyright © 2007 by ASME
removed by the liquid flowing through each channel. In this
way heat removed by each of the six parallel channels is
calculated and the total heat removed is estimated. This heat
removal rate represents the heat dissipated as per the
developing flow theory. This is compared to the actual heat
removed by the liquid in the experiments. Detailed procedure is
further explained below. In addition, calculations are also
performed using the fully developed and developing flow
theories based on the average channel dimensions. The average
of six channel dimensions is taken and based on the formulae
for friction factor and Nusselt number for fully developed and
developing flow. This will provide a direct comparison in
observing the effect of non-uniform flow distribution.
Guess Re
Eq. (6, 4)
Calculate
x+, fapp
Eq. (1)
Calculate
∆Ptheory
CALCULATION PROCEDURE:
The procedure given below is for calculating mass flow
rate through one channel, which is repeated for all the channels
to find the theoretical mass flow rate through all the parallel
channels.
Fluid Flow Calculations:
1. Guess the Re which would closely represent the flow
through the particular channel.
2. Based on this Re, calculate the theoretical value of non
dimensional hydrodynamic length x+ and the apparent
friction factor fapp using Eqs. (7) and (4).
3. Now, based on the above apparent friction factor for
the assumed flow rate, calculate the theoretical
pressure drop using Eq. (1). This value represents the
pressure drop in that particular channel for the
assumed value of Re and theoretical friction factor,
which is also based on the assumed Re.
No
Is
∆Ptheory=∆Pexpt
Eq. (10)
Calculate
m&ch
Fig. 2 Flow chart for calculating
Compare this theoretical value of pressure drop to the
actual measured pressure drop. Now since the
channels are parallel to each other, pressure drop
across each channel is the same. Hence, change the
guessed value of Re in step 1 such that the theoretical
value of pressure drop equals the measured value of
pressure drop after accounting for the losses.
4.
Re .µ . Ac
Dh
m&ch
Heat Transfer Calculations:
&ch and Re in
1. From the fluid flow calculations, the m
each channel are known.
2. Based on the above mass flow rate, calculate the nondimensional thermal length x* for each channel given
by Eq. (8) and the corresponding mean Nusselt
number by Eq. (5,6).
3. Translate Nu into heat transfer coefficient based on the
channel dimensions from Eq. (3).
The measured inlet and outlet temperatures
represent the average values of temperatures. Since
each channel has different flow rate, the exit
temperature from each channel would be different.
Hence the outlet temperature is calculated for each
channel. This involves an iterative step.
4. Tout is calculated by using Eq. (11). In this equation,
the only unknown is Tout. LMTD is the log mean
temperature difference which is given by Eq. (12).
Surface temperature at the exit and inlet are measured
from the thermocouples at respective locations under
the microchannel. When the iteration is complete, Tout
is found for each channel.
Tout calculated in the above step represents the
theoretical value of exit temperature in each channel
based on the theoretical value of mass flow rate and
the local Nusselt number which is also based on
The value of Re for which the calculated (theoretical)
pressure drop is equal to the measured pressure drop,
represents the mass flow rate through the channel
based on the developing flow theory. Mass flow rate
through each channel is calculated from Re using Eq.
(10).
m&ch =
Yes
(10)
The above steps are repeated for all the six channels, and
the mass flow through each channel is calculated using the
individual channel dimensions. Flow rate through each
channel is added up to find the total flow rate according the
developing flow theory. This is called as the theoretical
mass flow rate, m&theory . Figure 2 gives the flow chart for
&ch .
calculating the m
5
Copyright © 2007 by ASME
thermally developing flow theory. The properties are
evaluated at the mean water temperature.
m&.Cp.(Tout − Tin ) = h. Aht .LMTD
LMTD =
5.
((T
s ,in
− Tin ) − (Ts ,out − Tout ) )
 (Ts ,in − Tin ) 

ln

(
T
−
T
)
s
,
out
out


(11)
(12)
Using Eq. (13) and Tout find the heat removed by that
channel.
Q = m&.C p .(Tout − Tin )
theoretical value of flow rates obtained in these channels based
on the measured pressure drop.
(13)
Repeat the above procedure for all channels and add up the
heat dissipated by each channel to find the total heat removed
by the parallel microchannels. This heat represents the heat
removed based on the thermally developing flow, Qtheory.
Compare Qtheory to the power supplied to the cartridge heater,
Qexptl.
Rm =
m&e xptl
(14)
m&theory
The plot in Fig. 4 shows the variation of Rm with the flow
rates. Re is not chosen as the x axis since Re is different for
different channels because of varying dimensions. The range of
Re for the data set, based on the average channel dimensions, is
from 250-1000. It is seen from the plot that the Rm is very close
to unity, with a mean deviation of 7 percent. However, all the
points lie below the unity line. Value of Rm less than 1 indicates
that the actual flow rate is less than the theoretical flow. Since
the pressure drop is same for the two flow rates, a lower mass
flow rate indicates a higher friction factor compared to the
theoretical prediction. The uniform flow analysis using the
developing flow theory predicts the data closely to theory.
1.2
1
Figure 3 illustrates the procedure for calculating Qch.
Rm
0.8
Get mch
0.6
non uniform flow
analysis
0.4
Eq. (8, 5)
0.2
Calculate
x*, Num,3
Developing flow
Uniform Flow
Analysis
0
0
10
Eq. (3)
Calculate h
20
30
Flow rate (ml/min)
40
50
Fig. 4 Variation of the ratio of experimental to theoretical
mass flow ratio Rm in laminar region
Eq. (11)
1.4
Calculate Tout
1.2
1
Eq. (13)
RQ 0.8
0.6
Calculate Qch
Developing flow
Uniform flow analysis
non uniform flow
analysis
0.4
0.2
0
Fig. 3 Procedure for finding Qch
0
10
20
30
40
50
Flow rate ml/min
RESULTS:
The ratio of m is defined by Eq. (14) and indicates the
experimental flow rate observed in the multiple channels to the
Fig. 5 Variation of the ratio of experimental to theoretical
heat transfer rate ratio RQ in laminar region
6
Copyright © 2007 by ASME
Heat transfer analysis includes finding out a similar ratio
RQ given by Eq. (15). It is the ratio of the total heat removed
experimentally by the microchannels to the theoretical value
based on developing flow theory.
RQ =
Qe xptl
Qtheory
NOMENCLATURE
[15)
Figure 5 depicts the effect of non uniform flow distribution
on heat transfer predictions. The theoretical values are over
predicted by a mean deviation of 12 percent. A ratio of unity
for RQ implies that the heat removed by the channels is the
same as that calculated using the developing flow theory.
The ratio RQ using the developing flow theory with the
average channel dimensions are also shown in Fig. 5. These
predictions are based on the uniform flow assumption through
each channel. It is seen that the uniform flow assumption leads
to a significant deviation at lower flow rates (26 percent), with
an increasing trend at higher flow rates. This trend is not
present in the non-uniform flow analysis results.
ACKNOWLEDGMENT
This work was conducted in the Thermal Analysis and
Microfluidics Laboratory in the Mechanical Engineering
Department at Rochester Institute of Technology.
Cross section area, m2
Heat transfer area, m2
Specific heat, J/kgK
Hydraulic diameter, m
Fanning friction factor, dimensionless
Apparent friction factor, dimensionless
Average heat transfer coefficient, W/mK
Loss coefficient for 90° bends
Contraction loss coefficient
Expansion loss coefficient
Log Mean Temperature Difference
Mass flow rate in individual channels, kg/s
m&exptl
m&theory
Experimental mass flow rate, kg/s
Theoretical mass flow rate, kg/s
Non dimensional Fully developed Nusselt
number for three sided heating
Non dimensional fully developed Nusselt no.
for four sided heating
Nusselt number for three-sided heating
Nusselt number for four-sided heating
Prandtl number
Heat transfer in individual channel, W
Experimental heat transfer rate, W
Theoretical heat transfer rate, W
Dimensionless Reynolds number
Ratio of experimental to theoretical mass
flow rates
Ratio of experimental to theoretical heat
transfer rate
Water inlet temperature, °C
Water outlet temperature, °C
Surface temperature at inlet, °C
Surface temperature at outlet, °C
Dimensionless hydrodynamic entry length
Dimensionless thermal entry length
Differential pressure drop, Pa
Dynamic viscosity, kg/ms
Nufd,3
Nufd,4
Num,3
Num,4
Pr
Qch
Qexptl
Qtheory
Re
Rm
CONCLUSIONS
A careful set of experiments is carried out to study the
effect of non-uniform flow distribution in each channel on the
pressure drop and heat transfer in a parallel set of
microchannels. The pressure drop and the inlet and outlet
temperature measurements are made across the inlet and outlet
manifolds. The developing flow theory equations are used to
compare with the experimental data. The equations based on
Phillips [16] and Wibulswas [15] for rectangular channels are
used. These equations for friction factor and Nusselt number
are the average values and are calculated for the complete
channel length. Since each channel is of different dimensions,
mass flow rate is calculated based on the theoretical value of
friction factor and the measured pressure drop, while the total
heat dissipated per channel is calculated based on the
theoretical value of the average Nusselt number. From this
study following conclusions can be drawn.
1. The friction factor in microchannels can be predicted
using developing flow theory after accounting for the
entry and exit losses.
2. The pressure drop and heat transfer predictions based
on the non-uniform flow distribution resulting from
the channel area variation using the developing flow
theory are in good agreement with the experimental
data to within average deviation of 12 percent. There
is no trend observed in these predicted values as a
function of flow rate (Reynolds number).
3. Channel dimensions need to be measured accurately.
Variations in the individual channel dimensions are
responsible for deviations from the theoretical friction
factor and heat transfer predictions during laminar
flow in smooth microchannels.
Ac
Aht
Cp
Dh
f
fapp
havg
K90
Kc
Ke
LMTD
m&ch
RQ
Tin
Tout
Ts,in
Ts,out
x+
x*
∆p
µ
REFERENCES
[1] Tuckerman, D. B., and Pease, R. F. W., High-Performance
Heat Sinking For VLSI, IEEE Electron Device Letters, vol.
ED-2, no. 5, pp. 126-129, 1981.
[2] Kandlikar, S. G., Garimella, S., Li, D., Colin, S., King, M.
R., Heat Transfer and Fluid Flow in Microchannels and
Minichannels, Elsevier, 2006.
[3] Hrnjak, P., and Tu, X., Single Phase Pressure Drop in
Microchannels, International Journal of Heat and Fluid
Flow, vol. 28, no. 1, pp. 2-14, 2007.
[4] Rands, C., Webb, B. W., Maynes, D., Characterization Of
Transition To Turbulence In Microchannels, International
Journal of Heat and Mass Transfer, v 49, n 17-18, p 29242930, August 2006
[5] Steinke, M., E. and Kandlikar, S., G., Single Phase Liquid
Friction Factors In Microchannels, Proceedings of the 3rd
International
Conference
on
Microchannels
and
Minichannels, 2005, part A, p 291-303, 2005.
7
Copyright © 2007 by ASME
[6] Steinke, M., E. and Kandlikar, S., G., Single Phase Liquid
Heat Transfer In Microchannels, Proceedings of the 3rd
International
Conference
on
Microchannels
and
Minichannels, 2005, part B, p 667-678, 2005.
[7] Solomon, J. T., and Sobhan, C. B., Experimental
Investigations On Fluid Flow And Heat Transfer Through
Rectangular Mini Channels, 2005 ASME Fluids Engineering
Division Summer Meeting, FEDSM2005, Jun 19-23 2005,
vol. 2005, pp. 353-368, 2005.
[8] Bucci, A., Celata, G.P., Cumo, M., Serra, E. and Zummo,G.
Water Single-Phase Fluid Flow And Heat Transfer In
Capillarytubes, International Conference on Microchannels
and Minichannels, Paper # 1037 ASME Publications 1
(2003) 319-326.
[9] Hegab, H. E., Bari, A., and Ameel, T. A., Experimental
Investigation Of Flow And Heat Transfer Characteristics Of
R-134a In Microchannels, Microfluidics and BioMEMS, 2224 Oct. 2001, vol. 4560, pp. 117-25, 2001.
[10] Mala, G. M. and Li, D., Flow Characteristics Of Water In
Microtubes, International Journal of Heat and Fluid Flow,
vol. 20, pp. 142-158, 1999
[11] Yu, D., Warrington, R., and Barron, R., Experimental And
Theoretical Investigation Of Fluid Flow And Heat Transfer
In Microtubes, Proceedings of the 1995 ASME/JSME
Thermal Engineering Joint Conference. Part 1 (of 4), Mar
19-24 1995, vol. 1, pp. 523-530, 1995.
[12] Peng, X. F., Peterson, G. P., and Wang, B. X., Heat
Transfer Characteristics of Water Flowing through
Microchannels, Experimental Heat Transfer, vol. 7, no. 4, pp.
265-83, 1994.
[13] Harms, T. M., Kazmierczak, M. J. and Gerner, F. M.,
Developing Convective Heat Transfer In Deep Rectangular
Microchannels, International Journal of Heat and Fluid
Flow, vol. 20, pp. 149-157, 1999
[14] Steinke, M., E. and Kandlikar, S., G., An Experimental
Investigation of Flow Boiling Characteristics of Water in
Parallel Microchannels, Journal of Heat Transfer, vol. 126,
pp. 518-526, 2004.
[15] Wibulswas, P., Laminar Flow Heat Transfer in NonCircular Ducts, Ph. D. Thesis, London Univ., London, 1966.
[16] Phillips, R. J., Forced convection, Liquid Cooled,
Microchannel Heat Sinks, MS Thesis, Department of
Mechanical Engineering, Massachusetts Institute of
Technology, Cambridge, MA, 1987.
8
Copyright © 2007 by ASME