Proceedings
Proceedings of the ASME 2009 International Mechanical Engineering
Congressof
& IMECE2009
Exposition
ASME International Mechanical Engineering Congress & Expositions
IMECE2009
November
Lake Buena
Florida
November
13-19,13-19,
Lake Buena
Vista, Vista,
Florida,
USA
IMECE2009-12047
atural Patterns Applied to the Design of Microchannel Heat Sinks
Carlos Alberto Rubio-Jimenez
[email protected]
Department of Mechanical Engineering
Universidad de Guanajuato
Road Salamanca-Valle de Santiago km. 3.5+1.8 km.
Community of Palo Blanco, Zip Code 36885
Salamanca, Guanajuato, México
Abel Hernandez-Guerrero
[email protected]
Department of Mechanical Engineering
Universidad de Guanajuato
Road Salamanca-Valle de Santiago km. 3.5+1.8 km.
Community of Palo Blanco, Zip Code 36885
Salamanca, Guanajuato, México
Jose Cuauhtemoc Rubio-Arana
[email protected]
Department of Mechanical Engineering
Universidad de Guanajuato
Road Salamanca-Valle de Santiago km. 3.5+1.8 km.
Community of Palo Blanco, Zip Code 36885
Salamanca, Guanajuato, México
Satish Kandlikar
[email protected]
Rochester Institute of Technology
76 Lomb Memorial Drive Rochester NY 14623
Rochester, New York, United States
alternative to dissipate the large generated heat fluxes inside
electronic devices, mainly computational processors. Many
studies about this kind of heat sinks have been developed. A
large part of studies had used traditional arrangements (heat
sinks formed by a specific number of microchannels placed in
a parallel way.) These channels typically present a specific and
constant cross section area (rectangular form is the most used.)
Studies developed previously had demonstrated that this kind
of heat sinks is able to dissipate high heat fluxes, using water
in the laminar regime and single phase [1-5]. One important
contribution of these studies is to demonstrate that the
convective coefficient present in these micro arrangements in
laminar regime has the same order of magnitude to those
coefficients present in turbulent regimen in convectional
channels [6]. Thus, in a theoretical way, the heat flux
generated by the current computational processors can be
easily dissipated using these devices. These computational
processors have a maximum design temperature around 70°C
[7,8]. Some studies had demonstrated that microchannel heat
sinks with rectangular and constant cross section area can
dissipate heat fluxes near 700 W/cm2 [2, 3]. However, in many
of those works the temperature profile in the electronic
devices to cool presents a non-uniform behavior [9-11]. That
behavior shows a specific pattern: a low temperature at the
zone where the fluid is entering the heat sink, increasing along
the channel longitudinal direction until reaching a maximum
temperature at the outlet zone of the channel. Typically,
microchannel heat sinks are built from a square base of 1 cm2.
Thus, the phenomenon happens around a length of 1 cm with
the single inlet/outlet header arrangement. Therefore, this
ABSTRACT
The present work shows a study developed of the thermal
and hydrodynamic behaviors present in microchannel heat
sinks formed by non-conventional arrangements. These
arrangements are based on patterns that nature presents. There
are two postulates that model natural forms in a mathematical
way: the Allometric Law and the Biomimetic Tendency. Both
theories have been applied in the last few years in different
fields of science and technology. Using both theories, six
models were analyzed (there are three cases proposed and both
theories are applied to each case). Microchannel heat sinks
with split channels are obtained as a result of applying these
theories. Water is the cooling fluid of the system. The inlet
hydraulic diameter is kept in each model in order to have a
reference for comparison. The Reynolds number inside the
heat sink remains below the transition Reynolds number value
published by several researchers for this channel dimensions.
The inlet Reynolds number of the fluid at the channel inlet is
the same for each model. A heat flux is supplied to the bottom
wall of the heat sink. The magnitude of this heat flux is 150
W/cm2. The temperature fields and velocity profiles are
obtained for each case and compared.
KEYWORDS
Branched Microchannel Heat Sinks, Allometric Law,
Biomimetic Tendency.
ITRODUCTIO
In the last century novel techniques for cooling electronic
devices have been proposed. Microchannel heat sinks are an
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Copyright © 2009 by ASME
temperature field may produce thermo-mechanical stresses
which could reduce the lifetime of the system [12].
Based on these antecedents, a question arises: is it possible
to have homogeneous temperature profiles in the electronic
device to cool, using this kind of arrangements in a laminar
regime and single phase? In a theoretical way, the convective
coefficient is inversely proportional to the channel hydraulic
diameter. Based on this principle, if the channel hydraulic
diameter is decreasing the convective coefficient is improved
as a result. Therefore, the temperature field could be made
more uniform. But, under what criterion could the hydraulic
diameter of microchannel heat sinks be decreased? One source
of inspiration to achieve this criterion for decreasing the
hydraulic diameter can be obtained from natural forms. Those
forms present a general appearance: a main channel which
decreases its hydraulic diameter and branches out at a specific
position into two or more channels with smaller hydraulic
diameter. This behavior is repeated a specific number of times.
Figure 1 sketches the way it occurs. Thus, it is possible to
imagine that there is a ratio which is capable to describe those
natural forms.
Large edge
= 1.6180...
Small edge
(1)
Inlet hydraulic diameter, Dinlet
= 1.6180...
Outlet hydraulic diameter, Doutlet
(2)
ϕ=
ϕ=
Another way to obtain a ratio to decrease the hydraulic
diameter can be taken from measurements of branching
systems (i.e. the human circulatory system.) The Allometric
Law is the result obtained to develop a mathematical model of
those measurements (statistical model) [17-19]. This law
presents a ratio capable to express the decrement of ratio that
branching systems present. Equation (3) shows this ratio.
Therefore, it is possible to use this ratio in order to get
microchannel heat sinks with outlet hydraulic diameters
smaller than inlet hydraulic diameters, in the same way that
nature presents.
Allometriclaw =
Inlet hydraulic diameter, Dinlet
= 21 / 3
Outlet hydraulic diameter, Doutlet
(3)
Based on both tendencies (and their respective ratios), it is
possible to create different structure similar to natural forms.
These structures can be manufactured on a silicon substrate in
order to create channel with specific dimensions which can
distribute a specific working fluid in all the substrate.
Theoretically, this way to create microchannel heat sink could
increase the fluid velocity, specifically at the last section of the
channel. With this, it is expected to improve the overall
convective coefficient, distributing more evenly the
temperature profile on the device to cool. Clearly, the most
important generated problem is an increment in the
mechanical power to be supplied into the system in order to
move the working fluid inside the heat sink.
PROBLEM DESCRIPTIO
Figure 2 shows the natural structures considered. This
figure shows a core channel branching out into some small
channels. These channels structures present a specific form.
This general form can be adjusted in order to obtain
arrangements which can be used as microchannel heat sinks.
In this work, three structures are studied. The patter is similar
in all the cases (a main channel which is bifurcated at a
specific position in two or more channel with smaller
hydraulic diameter.) The inlet flow is considered to be at the
largest hydraulic diameter (main channel.) In Figure 2 a) the
structure is formed by the main channel and one bifurcation at
its last third section. In Figure 2 b) the structure presents a
configuration based on the main channel and two bifurcations.
One bifurcation is placed at its last zone and the other one at a
position before (it is placed inside the last third section of the
main channel.) In Figure 2 c) the structure presents a
configuration similar to Figure 2 b). In this configuration a
second bifurcation is added in bifurcated channel placed firstly
from the inlet flow position of the main channel. Figure 3
shows the heat sink arrangements built under the natural forms
presented in Figure 2.
Figure 1. Typical arrangement of nature forms.
In the last years, some areas of investigation have tried to
imitate natural forms. Some parameters have been used in
order to achieve this target. These can reproduce in an exact
way natural forms. This way to reproduce natural forms is
called Biomimetic Tendency. As well as the π number
(3.1416…) and the e number (2.7182…), the φ number
(1.6180…) is a parameter which has been used along the
history. It had a great impact since the Greek culture down to
the Renaissance age. This number is able to describe some
ratios present in natural forms (i.e. it can describe perfectly a
nautilius spiral) [13-16]. Equation (1) expresses the ratio under
this number between two edges of a natural structure (one
edge larger than the other.) Therefore, if this number is used to
get a channel decrement in heat sinks, it will lead to an outlet
hydraulic diameter smaller than the inlet hydraulic diameter,
increasing the fluid velocity in this last section. Equation (2)
shows the ratio to apply in the models to analyze.
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Copyright © 2009 by ASME
a)
b)
c)
Figure 2. Natural configurations taken to design and built the microchannel heat sinks.
for all the arrangements are shown in Tables 1 and 2. The
angles of bifurcation are 37° (most recurrent angle in natural
forms) and 31.71° (value calculated using the Phi number) for
the Allometric Law and the Biomimetic Tendency,
respectively. The level of bifurcation is referred to the position
where the channel is bifurcated i.e. the level of bifurcation B
1 is referred at the first bifurcation that the main channel
presents. Based on the Allometric Law, this position occurs at
9.5344 mm from the inlet flow position. The channel at this
point has a hydraulic diameter of 150.74 µm (width 128.4 µm
and height 207.8 µm.) The level of bifurcation is increased
with each ramification that the channel presents.
a)
Table 1. Dimension of each level of bifurcation based on the
Allometric Law.
Bifurcation
level,
B
1
2
3
4
b)
Hydraulic
diameter
[µm]
158.74
125.99
99.99
79.36
Channel
width
[µm]
128.4
101.4
80.89
64.2
Channel
height
[µm]
207.8
164.9
130.9
103.9
Bifurcation
long
[mm]
9.5344
1.9648
0.3974
---
Table 2. Dimension of each level of bifurcation based on the
Biomimetic Tendency.
Bifurcation
level,
B
1
2
3
4
c)
Figure 3. Arrangements of microchannel heat sinks based on
natural structures. a) Case 1, b) Case 2, c) Case 3.
The dimensions used in each structure are taken from the
two previously mentioned tendencies. The Allometric Law and
the Biomimetic Tendency can be expressed by means of
Equations (2) and (3), respectively. Thus, in the present study
six models of heat sinks are analyzed (three based on the
Allometric Law and other three on the Biomimetic Tendency.)
The inlet hydraulic diameter is similar for all the cases (200
µm) in order to have a point for comparison. The dimensions
Hydraulic
diameter
[µm]
123.60
76.39
47.27
26.12
Channel
width
[µm]
100.00
61.80
38.24
21.13
Channel
height
[µm]
161.80
100.00
61.88
34.19
Bifurcation
long
[mm]
7.4166
2.8328
1.0819
----
The base material to build each arrangement is a silicon
substrate with a thickness of 361.8 µm and a length of 12 mm.
The bottom wall area is larger than 144 mm2. This area is
taken from the area available for the computational processor,
considering a perfect contact between the heat sink and the
Advanced Smart Cache [7] (commonly these cores are covered
by a plate which increases the heat transfer area, making the
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Copyright © 2009 by ASME
computational processor larger.) The heat sink arrangement is
formed by a specific number of structures. These are placed
counterflow wise in order to use the largest area as possible in
the heat sink (Figure 3.) The number of full structures in each
arrangement is varied since the opening angle at each
ramification for each tendency is different. The models have
six structures in the heat sink arrangement when the
Allometric Law is used and four structures for the Biomimetic
Tendency. Thus, the bottom wall area of the heat sink is
varied. It is 156 mm2 (12 x 13 mm) using the Allometric Law
and 162 mm2 (12 x 13.5 mm) when the Biomimetic Tendency
is used.
Due to the symmetry that each arrangement presents, it is
possible to use only a cell of analysis in order to reduce the
computational time to approach the numerical solution. Figure
4 presents one of the cells built and analyzed under the
numerical model.
Governing Equations
The solution of the model requires solving the continuity,
energy and Navier-Stokes equations, to obtain the temperature
distribution at the bottom wall of the heat sink. Under these
model considerations and taking into consideration thermal
properties variations, the governing equations are:
Continuity equation:
∂u ∂v ∂w
+
+
=0
∂x ∂y ∂z
(4)
Momentum equation for the fluid:
 ∂u
∂u
∂u 
ρ f  u + v + w  =
∂y
∂z 
 ∂x
−
dP ∂  ∂u  ∂   ∂v ∂u   ∂   ∂w ∂u  
+  2µ  +
µ +  +  µ +  
dx ∂x 
∂x  ∂y   ∂x ∂y   ∂z   ∂x ∂z  
 ∂u
∂u
∂u 
+v
+ w  =
∂y
∂z 
 ∂x
ρ f  u
−
dP ∂  ∂v  ∂   ∂v ∂u   ∂   ∂w ∂v  
+  2µ  +
µ +  +
µ
+ 
dy ∂y  ∂y  ∂x   ∂x ∂y   ∂z   ∂y ∂z  
(5)
 ∂u
∂u
∂u 
+ v + w  =
∂y
∂z 
 ∂x
ρ f  u
Figure 4. Sketch of a typical cell to analyze of the heat sink.
−
AALYSIS
Considerations
Several authors have demonstrated the large spatial
variation of temperature and velocity along the microchannel,
making it necessary to considerate 3-D variations in the
analysis. Water is the cooling fluid. The conditions assumed
for this model are steady state, laminar incompressible flow,
inlet temperature of the working fluid of 293 K, negligible
radiation heat transfer as well as thermal resistance between
the electronic device and the microchannel heat sink. The fluid
is kept in a laminar regime through the length of the heat sink.
Energy equation for the solid:
∂  ∂T  ∂  ∂T  ∂  ∂T 
 + ks
ks
 + ks
=0
∂x  ∂x  ∂y  ∂y  ∂z  ∂z 
Viscosity, µ
Thermal
conductivity, kf
Density, ρf
Specific heat, cpf
Value or function
Water
-1.717x10-9T3+1.815x10-6T2
-6.4442x10-4T+0.077189
 ∂ 2T ∂ 2T ∂ 2T 
 ∂T
∂T
∂T 
+v
+ w  = k f  2 + 2 + 2 
 ∂x
∂y
∂z 
∂y
∂z 
 ∂x

ρ f cp f  u
2
 ∂u 2  ∂v 2
 
 ∂w 
+ 2µ   +   +   
  ∂x   ∂y   ∂z  


2
2
2
  ∂u ∂v 
 ∂u ∂w   ∂v ∂w  


+ µ   +  +  +
+
+

  ∂y ∂x   ∂z ∂x   ∂z ∂y  


Units
N s/m2
0.6
W/m K
998.3
4.183
kg/m3
kJ/kg K
0.003345T2-2.8325T+696.7
W/m K
2330
0.712
Kg/m3
kJ/kg K
(7)
Boundary Conditions
The boundary conditions for the model are taken in such a
way that the flow interacts with its surroundings. At the inlet
zone of the main channel a constant fluid inlet velocity is used
(a velocity profile is not assumed.) This parameter is adjusted
to have a specific Reynolds number. A constant heat flux is
supplied by the electronic device at around the surface of the
bottom wall of the heat sink (a thermal resistance at this zone
is not considered.) The outlet zones are adjusted to a zero
static pressure in order to observe the water pressure drop. The
walls at the half-cut of the cell also present symmetry
conditions. The walls which are interacting between both
mediums are adjusted as interfaces. The rest of the walls are
adjusted as adiabatic, since they do not present a high
temperature gradient.
Silicon
Thermal
conductivity, ks
Density, ρs
Specific heat, cps
(6)
Energy equation for the fluid:
Table 3. Thermophysical properties for water and silicon.
Property
dP ∂  ∂w  ∂   ∂w ∂u   ∂   ∂w ∂v  
+  2µ  +  µ 
+  +
µ + 
dz ∂z 
∂z  ∂x   ∂x ∂z   ∂y   ∂y ∂z  
One important point of this kind of analysis is the behavior
that the water and silicon properties have with temperature.
Table 3 shows the thermophysical properties for water and
silicon. Some properties are constant while others are
expressed as a function of temperature since they present a
large variation with temperature.
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Copyright © 2009 by ASME
improves. This is mainly due to the fact that there are more
channels, increasing the used heat transfer area. Also, the
zones of turbulence generation and stagnation points are
increased. The area not used is similar to Cases 1-A and 2-A.
A decrement of this area is achieved in Case 2-B due to the
ramifications in the main channel.
Figures 9 and 10 present the temperature profiles obtained
in Cases 3-A and 3-B, respectively. The behavior in both cases
is similar to the behavior found in the last two cases. A better
temperature distribution is not obtained for these cases. The
most important result is that the temperature profile at the
inlet-outlet zones is more homogeneous.
Operational Parameters
The target of this kind of heat sinks is to cool electronic
devices which present large heat generation. This means that it
is necessary to keep their temperature below the design
temperature. For the case of computational processors, the
heat sinks must keep them with a maximum temperature of
343 K. Experimental results from the companies that
manufacture these processors had found that current
processors can generate up to 150 W/cm2. Therefore, this
value of heat flux is used in the analysis. It is important to
mention that the heat flux supplied at each cell is an exact
proportion of the total heat flux supplied at the bottom surface
of the total heat sink. The inlet Reynolds number is adjusted at
500. This value is the average value taken by many
researchers previously. Also, the velocity obtained with this
Reynolds number allows having a fluid laminar regime
throughout the system.
RESULTS
The temperature profiles for the bottom wall of the heat
sink for the six cases under the specified conditions and
operational parameters are shown in Figures 5 to 10. Each
figure presents 3D plots for the temperature profile (x and y
axis vs temperature.) Figures 5 and 6 present the temperature
profile for Case 1 based on the Allometric Law (Case 1-A)
and Biomimetic Tendency (Case 1-B), respectively. It is
possible to observe a non-uniform behavior in both figures.
The temperature at the midpoint is larger than at the edge
where the working fluid is entering and exiting. For Case 1-B,
the temperature at the midpoint (365 K) is larger than the other
case (338 K.) This indicates that the arrangement for Case 1-B
cannot dissipate the heat flux required to keep the electronic
device temperature inside the safe design range. The other
case is able to keep the electronic device temperature inside
the range, but it is very near the limit. One point to take into
consideration is the temperature gradient present in both cases.
Results show that these gradients are extremely large (i.e.
Case 1-A presents a surface temperature variation of around
14 K between the inlet-outlet zone and the midpoint, this is 6.5
mm.) Thus, thermal stresses could appear which could affect
seriously the electronic device and the heat sink, reducing their
lifetime. The largest heat dissipation in the heat sink is located
at the zones where bifurcations are found. This is expected
since in these zones many phenomena are present which affect
the heat dissipation. Some of those effects are turbulence
generation, stagnation points, flow acceleration, etc. In the
figures, it is also possible to observe the amount of area which
is useless for the heat transfer process. In Case 1-A, this area
not used is concentrated in the middle of the heat sink. For the
other case, this area is distributed in the entire surface. This is
an important reason explaining why the temperature gradients
are larger in Case 1-B than in Case 1-A.
Figures 7 and 8 present the temperature profiles obtained
in Cases 2-A and 2-B, respectively. In an overall observation,
the behavior is similar to the previous cases. The temperature
gradients present a light decrement with respect to Cases 1-A
and 1-B, especially at the zones where the number of
bifurcation was increased. This can be better observed in
Figure 8. The temperature profile at the zones where the
channel branches out is more homogeneous than in the
previous case. Therefore, it is important to note that by
increasing the number of bifurcations, the heat dissipation
Figure 5. Temperature contour for Case 1-A,
Allometric Law.
Figure 6. Temperature contour for Case 1-B,
Biomimetic Tendency.
Unfortunately, the thermal results obtained in the six cases
under considerations do not present advances in the heat
dissipation compared with the traditional arrangements. In
fact, the temperature gradients obtained in these cases are
larger than the traditional microchannel heat sinks. This
behavior is mainly due to the fact that the effective heat
transfer area was reduced (the natural structures did not allow
to use the most amount of heat transfer area of the channel
walls.)
Figures 11 to 16 present the fluid velocity profiles along
the channels. Also, each figure presents a sketch of the zones
where the channels are bifurcated and the inlet and outlet
zones. As it was previously mentioned, one aim of this work is
to increase the fluid velocity while this is passing through the
channels. In the figures, it can be observed that the fluid is
accelerated from the section where the channel starts, to the
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Copyright © 2009 by ASME
ending section. Unfortunately, this acceleration is not so large
to improve the heat dissipation.
Figure 10. Temperature contour for the Case 3-B,
Biomimetic Tendency.
Figure 7. Temperature contour for Case 2-A,
Allometric Law.
Figure 8. Temperature contour for the Case 2-B,
Biomimetic Tendency.
Figure 11. Fluid velocity profiles along the branched channel
for Case 1-A.
Figure 9. Temperature contour for the Case 3-A,
Allometric Law.
The fluid velocity profiles at the midpoint of the channel
for Cases 1-A and 1-B are provided in Figures 11 and 12,
respectively. At the main channel inlet zone, the fluid presents
a constant velocity profile (such as it was assumed in the
considerations.) After this zone, the fluid develops, reaching
“full developed profile” fast (at around a tenth of the length of
the main channel.) It is important to mention that the fluid
velocity profile continues changing due to the fluid
acceleration.
Figure 12. Fluid velocity profiles along the branched channel
for Case 1-B.
For Case 1-A, the fluid velocity at the midpoint of the
channel is larger than for Case 1-B. This is an expected result
since the first case has a more considerable hydraulic diameter
decrement than the second case. At the bifurcation zone,
stagnations points can be observed. This is mainly due to the
bifurcations angles used which are so large that the fluid
suffers large energy losses. That is, the fluid has a large
velocity when is going through the main channel, then having
6
Copyright © 2009 by ASME
a drastic variation when it arrives to the bifurcation zone. Here
its mass is divided in three flows. One flow keeps a large part
of the velocity because the channel continues in a right
direction. The other two flows loose energy because they crash
with the channel walls. This generates an increment in the
fluid pressure and a drastic reduction in the fluid velocity.
Fluid instability is another phenomenon occurring at this
bifurcation zone. The addition of these phenomena produce
better heat dissipation in these zones as it is shown in Figures
5 to 10.
and channel length.) Figures 15 and 16 present the velocity
profile at the same mid plane. The behavior is similar in these
last two cases. The most important detail is that in the second
bifurcation of the first branched channel one channel
bifurcates only in two channels. The fluid velocity is almost
kept constant in the right channel, presenting only a minimum
stagnation point. This is caused by the fluid division. This
phenomenon helps the heat dissipation as well as does the
other bifurcations zones.
Figure 15. Fluid velocity profiles along the branched channel
for Case 3-A.
Figure 13. Fluid velocity profiles along the branched channel
for Case 2-A.
Figure 16. Fluid velocity profiles along the branched channel
for Case 3-B.
Figure 14. Fluid velocity profiles along the branched channel
for Case 2-B.
At the fluid outlet zone both in the main channel as well as
in the branched channels, the fluid presents a fully developed
velocity profile. This is also due to decreasing the channel
hydraulic diameter.
Figures 13 and 14 present the velocity profiles for Cases 2A and 2-B. The fluid behavior is similar to the previous two
cases (a constant velocity at the inlet zone, fluid velocity
increments along the channel, stagnation point at the
bifurcation zones, increment of the fluid pressure, etc.) For
these cases, the fluid has an important increment in its velocity
although the channel section length is very short. This is due
to the fact that in the last sections, the hydraulic diameter
decrement is more drastic than in the other sections, mainly in
Case B-1. Unfortunately, for this specific case, the length is
larger than for the other case. Therefore, it is important to
balance these two parameters (hydraulic diameter decrement
7
COCLUSIOS
The thermal and hydrodynamic results obtained in this
study for the proposed microchannel heat sinks based on
natural structures shown that is possible to cool electronic
devices that generate heat fluxes around 150 W/cm2.
Temperature profile obtained on the bottom wall of the heat
sink for all models presented a non-homogeneous distribution.
It is observed a large temperature at midpoint of the surface,
decreasing at the channel edges where are distributed the fluid
inlet/outlet zones. For some cases (Cases 1-A and 1-B) the
temperature at this position was larger than the computational
processor design temperature. For the rest of the cases, the
temperature was below this design parameter. This behavior
was mainly due to the large heat transfer area that was not
used really in the process.
The velocity profiles obtained in all the cases have an
expected behavior. The fluid presents a non-fully developed
behavior at the fluid inlet zones. While the fluid is passing
through the channels, the velocity profile is developing,
researching zones where it may consider as fully developed.
Copyright © 2009 by ASME
[12] Kandlinkar, S., High Flux Heat Removal with
Microchannels – A Roadmap of Challenges and
Opportunities, 3rd International Conference on
Microchannels and Minichannels, June 12-15, 2005.
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Fluid instabilities and velocity losses are presented at the
bifurcation zones, helping to the heat dissipation. These were
expected results.
In an overall observation, Case 2-A presents the best
behavior. This has good heat dissipation, mainly in the fluid
inlet/outlet zones. The temperature at the midpoint on the heat
sink bottom wall is below the design temperature. Also, this
temperature is lower than Cases 1-A, 1-B, 2-B and 3-B and
almost near Case 3-A. For this last case, the fluid has larger
lost energy, requiring more mechanical energy in order to
move the working fluid in the system. This can be observed in
the velocity profiles generated along the channels. In these,
there are zone where the fluid velocity is nearer zero.
The most important observation in these results is that the
fluid velocity can be increased only decreasing the hydraulic
diameter. For this kind of heat sinks, this decrement can
improve the heat dissipation. Therefore, arrangements of
microchannel heat sinks that could generate these phenomena
and use all the available heat transfer area may produce a
better heat dissipation.
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