Conjugate heat transfer from an electronic module package
cooled by air in a rectangular duct
Hideo Yoshinoa , Motoo Fujii b, Xing Zhang b, Takuji Takeuchia, and Souichi Toyomasua
a) Fujitsu Kyushu System Engineering Limited, Fukuoka 814-8589, Japan
b) Institute of Advanced Material Study, Kyushu University, Kasuga 816-8580, Japan
Experimental and numerical studies are carried out for the conjugate heat transfer of an electronic module
package cooled by air. Firstly, the heat conduction experiment was conducted to obtain the surface temperature
profiles and to estimate the total conductive resistance and natural convection heat transfer rate to air from the
outer wall of duct, where the same type two module packages were fixed opposite at the bottom and top inner
walls of duct and glass wool was filled inside the gap. The measured temperature profiles were compared with
those obtained by the corresponding numerical simulations and the heat transfer coefficient at the outer wall of
duct was estimated. Secondly, the convective heat transfer experiment was done for a single module package
attached on the bottom wall of the duct by switching three fans on and off in various combinations. As for the
surface temperature profiles, the numerical results agree well with the experimental ones. When the thermal
conductivity of printed circuit board is varied, however, the heat transfer coefficients based on the conventional
definition could not be summarized with a unique correlation due to the effects of conjugate heat transfer.
Introducing an effective heat transfer area has solved the problems and a unique correlation is proposed.
Numerical simulations also clarified the effect of thermal conductivity ratio on the non-dimensional effective
heat transfer area, and further the heat transfer characteristics when two or more module packages are set in the
same duct.
1. Introduction
Recently, conjugate heat transfer in microelectronic equipment has received considerable attention from heat
transfer researchers, because of rapid increase in power dissipation of LSI chips and downsizing of electronic
devices. Ramadhyani et al. (1985) and Sugavanam et al. (1994) reported the results of numerical analysis on the
conjugate heat transfer from two-dimensional flush-mounted heat sources to laminar flow in the channel.
Incropera et al. (1986) and Ortega et al. (1994) did experiments for two-dimensional flush-mounted heat sources.
Nakayama and Park (1996) did both the numerical simulations and experiments. They concentrated their
attention on the heat transfer from the floor area near the surface-mounted block and discussed how to develop a
specific prediction method of the conjugate heat transfer. Zhang et al. (1999) discussed how to define an
effective heat transfer area to solve the problems of the conjugate heat transfer from small heat sources mounted
on a conductive wall. Fujii et al. (2001) further summarized their experimental results of the conjugate heat
transfer behavior of an electronic chip module cooled by air, based on the effective heat transfer area.
The present paper describes the experimental and numerical studies on the conjugate heat transfer of a printed
circuit board (PCB) with an electronic module packages cooled by air in a rectangular duct. Two experiments,
heat conduction and heat convection, and corresponding numerical simulations with a commercial CFD code
‘CFdesign’ have been performed. For the heat conduction, the surface temperatures of the module package and
heat losses to air from the outer walls of duct were measured. From the corresponding numerical simulations,
was estimated the value of heat transfer coefficient for the outer walls of duct, which could be used as the
boundary conditions for the successive calculations. For the heat convection, the surface temperature profiles
were measured at various heat rates and air velocities. The numerical simulations under the corresponding
conditions agree well with the experiments as for the temperature profiles. The computational code used was
confirmed to be valid, and then several calculations have done with various combinations of thermal
conductivities of PCB and fluid. When the conventional definition of heat transfer coefficient was used, however,
the heat transfer characteristic could not be summarized with a unique correlation. Then, the effective heat
transfer area proposed by Zhang et al. was examined to rearrange the convection heat transfer. After taking into
account the effect of thermal conductivity ratio between PCB and fluid, the heat transfer characteristics can be
summarized with a unique non-dimensional correlation available not only for a single module package but also
for two or more ones. The experimental results can also be summarized with the same correlation as obtained by
numerical simulations.
2. Heat conduction experiments and simulations
2.1 Experimental setup
Figure 1 shows the geometry of the experimental setup. The same type two PCBs with electronic module
packages are fixed opposite at the bottom and top inner walls of duct with 235.0 mm in length, 200 mm in width,
and 10 mm in height shown in the figure. Each PCB (its thermal conductivity λp=0.3 W/m/K) having 110 mm
square and 1.2mm thick is set at the center about 100 mm away from inlet of the duct. The module package
consists of a heat spreader (λhs=398 W/m/K), a heater (λh=45 W/m/K) and a package substrate (λps=16 W/m/K).
The heat spreader is 28 mm square, and 0.5 mm thick, and is attached to the heater with 13.4 mm square and 0.4
mm thick. The heat spreader and the heater are tightly adhered to the package substrate with 45 mm square and
2.4 mm thick. The package substrate is connected with ball grid array to the center of the PCB. Glass wool
(λgw=0.05 W/m/K) was filled inside the gap to prevent natural convection.
Figure 2 shows the location of the thermocouples. Six T-type thermocouples with 50μm diameter are installed
on the module package to measure the surface temperature, Ts. The thermocouples numbered from 1 to 4 are
located on the heat spreader surface, and the other two, No.5 and No.6, are located on the package substrate
surface. A built-in diode is installed in the center of the heater, and enable to measure junction temperature, Td.
The heater is energized with a DC power supply in a variable voltage range and the maximum power dissipation
of the heater is about 5 watts.
235.0
Package substrate Heater
45 x 45 x 2.4
13.4 x 13.4 x 0.4
1-6 :Thermocouple No.
200.0
Package substrate
B
Heat spreader
6
B
4
Heat spreader
28 x 28 x 0.5
Fan
35 x 35 x 5.0
1
Package substrate
(Symmetrical arrangement)
B-B
10.0
Fan
Table
Fig. 1
3 5
PCB
Heat spreader
Package substrate
3.0
PCB
110 x 110 x 1.2
2
1
2
4 6
3 5
PCB
Heater
Fig. 2
Location of six thermocouples
Package substrate
Schematic of module package
2.2 Simulation model
The simulation model has been developed based on the corresponding experimental setup described above. The
dimensions and thermophysical properties of the duct and module package for the present simulations are the
same as the experimental ones. On the other hand, the complicated internal structures of the package substrate
and PCB were simplified and they were replaced with two blocks with uniform but different thermal
conductivities to save computational time. A volumetrically uniform heat generation was assumed in the heater.
Natural convection boundary conditions are employed at the outer surfaces of the duct. The heat transfer
coefficient was estimated to be 7.46 W/m2/K by fitting the surface temperatures obtained numerically with those
measured for various heating rates.
Ts-To [K]
2.3 Heat conduction results
Figure 3 compares the measured temperature
profiles with numerical ones. The temperature
100.0
Experiments
Simulations
profiles for typical heating rates are plotted. The
solid and broken lines represent the results of the
80.0
experiments and the simulations, respectively. The
Qt=2.09 W
ordinate is the temperature difference between Ts
60.0
Qt=1.50 W
and the room temperature, To. The abscissa
indicates the thermocouple number corresponding
40.0
Qt=0.989 W
to the locations shown in Fig. 2. As the results of
2
20.0
setting the heat transfer coefficient 7.46 W/m /K,
Qt=0.506 W
the temperature profiles of the simulation are in
0.0
good agreement with the experimental results
except for the position of package substrate edge
1
2
3
4
5
6
7
(No.6), where the numerical values show higher
Location of thermocouples
than those measured. The temperatures on the
Fig. 3 Temperature profiles
package substrate of the experiments are lower
than those at the heat spreader surface. On the
other hand, the temperatures on the package substrate of the simulations are relatively flat compared with the
experimental results. These slight differences can be attributed to the simplification of the simulation model.
From the results of heat conduction experiments, the heat conducted through the package substrate and PCB, and
convected away from the outer walls of the duct was estimated. The heat conduction rate, Qloss, is proportional to
the temperature difference (Td - To), and can be expressed by
Qloss = 2.79 x 10-2 (Td - To) - 3.71 x 10-2
(1)
Equation (1) can be used to estimate the natural convection heat losses at the same temperature difference, (Td To), for forced convection experiments.
3. Forced convection experiments and simulations
3.1 Experimental setup
The geometry and dimensions of the experimental setup are those used in the same as the heat conduction
experiment except that there are no more the PCB at the top inner wall of duct and glass wool filled inside. The
three fans with 35 mm square and 5.0 mm high are attached on the downstream most of the duct. Switching three
fans on and off in various combinations can change the flow rate. The average velocity at the inlet was measured
with an accurate hot-wire anemometer.
3.2 Simulation model
The simulation model is also almost the same as the heat conduction case except that the convection boundary
conditions inside the duct must be considered. The uniform pressure and the uniform velocity are assumed at the
inlet and the outlet of the duct, respectively.
3.3 Convection heat transfer results
The average velocities at the duct inlet were measured for the three operation modes. The average values were
0.33, 0.66, and 1.0 m/s for one, two, and three fans, respectively. The temperature profiles at the module package
surface were measured at three heat dissipation rates, 1.00, 2.19 and 3.71 W, while the three fans ran together.
Figure 4 shows a comparison of temperature profiles between experiments and simulations at U=1.00 m/s, and
three heat dissipation rates. The temperature profiles obtained from simulations agree well with those measured.
The numerical results for the other two operation modes are also in good agreement with the experimental data
as shown in Fig. 5, where the heat dissipation rate is kept at 1.00 W. These results confirm that the present CFD
code is valid and can be used for the calculations of the conjugate heat transfer with high accuracy.
60.0
Experiments
40.0
30.0
Qt = 2.19 W
20.0
10.0
Experiment
20.0
Qt = 3.71 W
Ts -To [K]
TS-To[K]
50.0
24.0
Simulations
U=1.00 m/s
Simulations
U=0.33 m/s, Qt = 1.00 W
16.0
U=0.66 m/s, Qt = 1.00 W
12.0
8.0
Qt = 1.00 W
0.0
4.0
1
2
3
4
5
6
Location of thermocouples
7
1
Fig. 4 Temperature profiles for
three fans in operation
2
3
4
5
6
Location of thermocouples
7
Fig. 5 Temperature profiles for
single and two fans in operation
4. Parametric study on single module package
Nu ( = h Lhs / λa )
4.1 Non-dimensional correlation with conventional method
Based on the validity of the present simulations,
103
some parametric calculations were carried out with
λp/λa :
various inlet air velocities and thermal conductivities
of PCB. Figure 6 shows the non-dimensional
11.7
relationship between the heat transfer coefficient and
39.0
air velocity. The ordinate and abscissa are the
117.1
102
Nusselt and Reynolds numbers, respectively, which
are defined as:
390.2
(2)
Nu = ht Lhs/λa
780.3
(3)
Re = U DH/νa
Here, U is the average velocity of the duct inlet, and
10
DH is the hydraulic diameter of the duct, and Lhs is
102
103
104
the length of the heat spreader, and νa and λa
Re ( = U DH/ν)
represent the kinematic viscosity and thermal
conductivity of air, respectively. The heat transfer
Fig. 6 Nu number versus Re number
coefficient, ht, in Eq. (2) is defined by following (Based on the conventional heat transfer coefficient)
conventional method as:
(4)
ht = Qnet/Aref/(Tmax-To)
Where, Qnet is the net heat transfer rate, Qt-Qloss. Qt is the total heat dissipated, Qloss is the heat loss convected
away from the outer walls of the duct, Aref is the surface area of the heat spreader, and Tmax represents the
maximum temperature at the heat spreader surface.
As shown in Fig. 6, the Nusselt number in conjugate heat transfer depends not only on the Reynolds number
but also on the thermal conductivity ratio of PCB and air. The numerical results, therefore, could not be
summarized with a unique non-dimensional correlation when the conventional definition of heat transfer
coefficient is used. In the following discussion, the concept of effective heat transfer area is introduced to deal
with such a complicated conjugate heat transfer phenomenon and to derive a unique correlation.
4.2 Non-dimensional correlation with effective heat transfer area
To introduce the effective heat transfer area, a uniform heat flux is assumed as an average even for the
non-uniform heat flux over a heat transfer surface. At first, the convective heat flux at the heat spreader surface
must be defined as
q = Qconv/Aref
(5)
Here, Qconv is the convective heat actually transferred to air from the heat spreader surface, which can only be
obtained from the simulation. The effective heat transfer area is, then, defined as
(6)
Aeff = Qnet/q = (Qnet/ Qconv )Aref
Using effective surface area, the heat transfer coefficient is newly defined as
(7)
h = Qnet/Aeff /(Tmax-To)
0.5
Therefore, the average Nusselt number can be defined with Aeff as the reference length by
Nu = h Aeff0.5 /λa
(8)
Figure 7 shows the relationship between the effective heat transfer area and the thermal conductivity ratio, λp/λa.
For the region of relatively lower thermal conductivity ratio, the non-dimensional heat transfer area increases
with an increase in Reynolds number. This tendency disappears in the region of higher thermal conductivity ratio.
At λp/λa=780, the effective heat transfer area is almost independent of the Reynolds number.
Figure 8 shows the relationship between Nusselt and Reynolds numbers. The numerical results can be expressed
by a unique non-dimensional correlation by introducing another parameter, the thermal conductivity ratio.
(9)
Nu/(λP/λa)0.074 = 1.6 Re 0.4
102
1.0
10
Re number :
253
421
842
1263
1894
102
λP/λa
Fig. 7 Relationship between
Aeff/Aref and λP/λa
103
λp/λa :
11.7
0.074
Nu/(λP/λa)
Aeff/Aref
10.0
0.074
0.4
Nu/(λP/λa)
= 1.6 Re
39.0
117.1
390.2
780.3
Experiments
10
102
103
Re (=U DH/νa)
104
Fig. 8 Nu number versus Re number
based on effective heat transfer area
According to the above definitions, the present experimental results are rearranged. The results agree well with
Eq. (9) as shown with the symbol ■ in Fig. 8. Practically, the effective heat transfer area for a board with
known thermal conductivity can be determined from such numerical results as shown in Fig. 7. Then the Nu can
be calculated by using Eq. (9) for a given inlet velocity and the duct geometry. Further, the heat transfer
coefficient can be obtained from Eq. (8). Finally, the maximum temperature, that is, the most important
parameter for thermal design can be predicted by the definition of heat transfer coefficient Eq. (7). Conclusively,
the present method can provide two important parameters for thermal design, one is the maximum temperature,
Tmax, and the other is the effective surface area. The latter is particularly important for the case of arrangement
with multiple heat sources.
5. Multiple module packages
Further calculations are carried out for the two cases of multiple arrangements of module packages, that is, the
series and parallel arrangements. The concept of the effective heat transfer area can also be applied to these
systems. Figure 9 shows the relationship between Nu and Re for the series arrangement. The heat transfer
characteristic of the upstream package shown by the solid line is almost the same as that for a single module
package, while that of the second package shown by the dashed line is about 20 % lower, due to the thermal
wake effect. Figure 10 is the case of the parallel arrangement where four module packages are considered. When
the thermal conductivity of PCB is high, the heat transfer characteristics of both upstream and downstream
arrays of packages are almost the same as those for the series arrangement as shown by the solid and dashed
lines. The Nusselt numbers become around 10% higher than those when the thermal conductivity is low.
Air
Νu/(λP/λa)0.074
102
λp/λa & position
11.7, Upstream
Lhs
11.7, Downstream
780.3, Upstream
2Lhs
780.3, Downstream
0.074
0.4
Nu/(λP/λa)
= 1.6 Re
0.074
0.4
Nu/(λP/λa)
= 1.3 Re
10
102
103
Re ( = U DH/νa )
Fig. 9
λp/λa & position
11.7, Upstream
Lhs
Air
104
Nu number versus Re number
(Series arrangement)
Νu/(λP/λa)0.074
102
11.7, Downstream
780.3, Upstream
2Lhs
Nu/(λP/λa)
10
102
Fig. 10
780.3, Downstream
0.074
0.4
= 1.6 Re
0.074
0.4
Nu/(λP/λa)
= 1.3 Re
103
Re ( = U DH/νa )
104
Nu number versus Re number
(Parallel arrangement)
6. Conclusions
Both the experiments and simulations for the conjugate heat transfer of an electronic module package cooled by
air have been carried out. The main conclusions are as follows.
1. Experimental results have shown that the present code “CFdesign” can accurately predict the heat transfer
characteristics of the conjugate heat transfer problems.
2. Based on the concept of effective heat transfer area, a unique non-dimensional correlation is proposed, which
can predict the maximum temperature at the module package surface and can estimate the spreading of
surface area. The present method is confirmed to be available for the series and parallel arrangements of
multiple module packages.
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