Download ANALYSIS OF UNIFORM SEMI-POROUS HEAT SINK MEDIAS

ANALYSIS OF UNIFORM SEMI-POROUS HEAT SINK MEDIAS WITH FREE
CONVECTION
by
Eric R. Savery
A Project submitted in partial fulfillment of the
requirements for the degree of
Masters of Engineering
Rensselaer Polytechnic Institute
2011
Approved by ___________________________________________________
Ernesto Guiteerez-Mirravette, Engineering Project Advisor
Rensselaer Polytechnic Institute
Hartford, Connecticut
December, 2011
i
Table of Contents:
List of Tables .................................................................................................................... iii
List of Figures ................................................................................................................... iv
Nomenclature .................................................................................................................... v
Acknowledgement ............................................................................................................ vi
1. Abstract .................................................................................................................... vii
2. Introduction ............................................................................................................... 1
4. Methodology/Approach ............................................................................................ 3
4.1.
Assumption ........................................................................................................ 3
4.2.
Theory ................................................................................................................ 4
4.3.
Modeling ............................................................................................................ 8
5. Results and Discussion............................................................................................ 11
6. Conclusion ............................................................................................................... 22
7. Appendix 1 ............................................................................................................... 24
8. Appendix 2 ............................................................................................................... 25
9. Appendix 3 ............................................................................................................... 26
10.
Reference ............................................................................................................. 27
ii
List of Tables
Table 1: Temperature vs Density ........................................................................................ 5
Table 2: Porous Heat Sink Characteristics.......................................................................... 8
Table 3: Block Form .......................................................................................................... 9
Table 4: Control Block Heat Sink Results ....................................................................... 11
Table 5: Porous Heat Sink Results................................................................................... 13
iii
List of Figures
Figure 1: Fin Heat Sink ....................................................................................................... 1
Figure 2: Assumptions ....................................................................................................... 3
Figure 3: Porosity............................................................................................................... 6
Figure 4: Permeability........................................................................................................ 6
Figure 5: No Heat Sink Mesh .......................................................................................... 10
Figure 6: Solid Block Mesh ............................................................................................. 10
Figure 7: Porous Block Mesh .......................................................................................... 10
Figure 8: No Heat Sink T-V............................................................................................. 12
Figure 9: Solid Heat Sink T-V ......................................................................................... 12
Figure 10: Porosity Affect on Heat Transfer ................................................................... 14
Figure 11: Permeability Affect on Heat Transfer ............................................................ 15
Figure 12: Permeability Affect on Velocity..................................................................... 16
Figure 13:Affect Of Increasing Permeability on Total Heat Flux .................................... 17
Figure 14: Affect Of Increasing Permeability on Volume Flow Rate ............................. 18
Figure 15: Porous Heat Sink T-V .................................................................................... 19
Figure 11: Porous Heat Sink P-V .................................................................................... 19
Figure 17: Mesh Affect on Total Flux .............................................................................. 20
Figure 18: Mesh Affect on Volume Flow Rate ............................................................... 21
iv
Nomenclature
Symbols
Cp
=
K
=
ρ
=
ε
=
q
=
P
=
T
=
K
=
u
=
g
=
Heat Capacity at Constant Pressure
Permeability
Density
Porosity
Heat Flux
Pressure
Temperature
Thermal Conductivity
Fluid Velocity Field
Gravity
Subscripts
Air
=
AL
=
c
=
eq
=
0
=
Air
Aluminum Heat sink
Initial/Cold Temperature
Equivalent
Initial
v
Acknowledgement
vi
1. Abstract
This work investigates what affects the use of metallic porous materials has when
used as a heat sink. Specifically a comparison of how differences in the porous
material characteristics affect the performance of a heat sink while comparing it to a
traditional block heat sink and no heat sink at all. The modeled heat sinks will use the
same volume mass of material, material thermal conductivity (ie Material) and have
the same dimensional footprint. The boundary chip is held at a constant temperature
and by varying the heat sinks porosity and permeability the total heat flux of the chip
will be calculated. The results of the each heat sink are then compared and analyzed
against each other to determine the affect of porous material as a heat sink.
vii
2. Introduction
Since the discovery of the microprocessor computing power is becoming more
powerful and consequently the chips have been creating more heat. The heat in
which more powerful processors create is required to be dissipated else the processor
will become less reliable or fail1. For every 10ºc that you are able to reduce a
transistors temperature the failure of the electronic component is halved1. Therefore
the more heat that is able to be removed from the transistor the greater the reliability
is. To transfer the waste heat from the transistor to the environment requires the use
of a heat sink. A heat sink is a device which dissipates energy from a component to
the ambient environment by use of natural or forced convection. The heat sink’s
ability to dissipate the heat energy is a function of the material properties, geometry
and the environmental conditions2. Increasing the amount of heat energy which is
dissipated by the heat sink will allow for higher processing speeds at a lower temp.
Below is an example of a simple fin heat sink that would be used on a typical
integrated circuit.
Figure 1: Fin Heat Sink
This paper looks at how the use of semi-porous media with a significant amount of
surface area affects the efficiency of a heat sink to dissipate heat energy from a
computer chip. With the use of comsol modeling this paper will compare the
efficiency of a block heat sink against a heat sink that uses a semi-porous material.
1
3. Problem Description
The design of a heat sink is dependant on the physical space, cooling needs and cost
of the component. In a semiconductor application increasing capabilities results in the
need for additional cooling, increase cooling requires a larger heat sink and as a result
increases the overall size and cost of the final component. For portable electronics the
goal is to provide the most capability, in the smallest package for the lowest cost. Using
a semi-porous material for a heat-sink may provide increased cooling per cubic inch of
space resulting in a smaller and more capable device at a lower cost when compared to a
traditional fin heat sink. To determine the most efficient porous material heat sink a
comparison of the porous material characteristics is required in addition to comparing the
porous material heat sink to the control case.
2
4. Methodology/Approach
A systematic approach is used to build and analyze 2 different heat sinks and a flat
plate. The heat sinks are be made of the same base material and have the following
physics; porous and non-porous blocks. Each heat sink is made from the same base
material to ensure that the differences in the results are not due to material thermal
properties. The solid block heat sink and no heat sink are control cases while the porous
block heat sink are subjected to differing porous material characteristics to see there
effects on the heat sinks ability transfer heat at a standard temperature.
4.1. Assumption
To effectively analyze the affects of using porous material as a heat sink the following
diagram should be referenced:
Open Boundary
Insulated Wall
Heat Sink
Air
Insulated Wall
Open Boundary at Tc
Figure 2: Assumptions
In addition the following assumptions should be used:

Bounded area is 50mm by 50mm.

No single side of the heat sink can be larger than 10mm.

Air inlet temperature is Tc. Tc is 293.15 K.
3
Insulated Wall
Wall with
Temperatur
e of Th

Wall has a constant temperature Th. Th is 310
4.2. Theory
Heat Transfer: There are three different modes of heat transfer conduction, convection
and radiation. In the case of the model without a heat sink the heat transfer of interest is
pure convection. In addition to convection the porous and non porous material goes
under conduction. The system without a heat sink results in a pure convection process
where heat from the wall transfers directly into the fluid without an intermediate step.
When a heat sink is used an intermediate step is present where the energy from the wall
must pass through the block under conduction and then into the liquid via convection.
Equation 1 is the governing equation for conduction and equation 2 is the governing
equation for convection for non-porous material heat transfer.
Qcond  kA
T
x
Equation 1:Conduction
Qconv  hAs T 
Equation 2: Convection
One might think that adding an addition heat transfer step might decrease the efficiency
of removing heat from a chip or heat source but the exact opposite true. The advantage
of the intermediate step is that the block will increase the surface area in which
convective heat transfer is able to occur. Increasing the surface area in which convection
can occur can have a substantial increase in the rate in which heat can be transferred from
a heat source.
Buoyancy: Natural circulation is a function of the buoyancy of the cooling fluid. In
cases where there isn’t a fan or another motive force to circulate coolant a natural force
known as buoyancy causes the fluid to circulate. This fluid movement is consequence of
the density gradient caused by the differing temperatures between the incoming air and
the air which has been heated. As the air is heated the density of the fluid decreases
causing an upward force opposite of gravity, this is also known as buoyancy force. The
4
forces cause an upward velocity of the cooling fluid. For modeling this phenomenon the
following equation is used to determine the volume force.
F  g(  0 )
Equation 3
The equation 3 shows that as the density of a point decreases below the initial density a
force is created. This density is directly proportional to the temperature of the cooling
fluid at a particular point. Table 1 below show how density of air changes as a function
of air.
Temperature
(degrees C)
35
30
25
20
15
10
5
0
-5
-10
-15
-20
-25
Density
(kg/m^3)
1.1455
1.1644
1.1839
1.2041
1.225
1.2466
1.269
1.292
1.3163
1.3413
1.3673
1.3943
1.4224
Table 1: Temperature vs Density3
Porous Material Characteristics: There are two characteristics of significant
importance when analyzing porous heat sinks. Those characteristics are porosity and
permeability. Permeability (kappa) is the measure of the ability of a material to transmit
fluid though itself. Porosity (epsilon) is also known as void fraction, this is the measure
of voids or spaces in a material. This is defined in terms of a fraction of the total volume
of the material. An increase in porosity means the heat sink is more air than the base
material. See Figure 3 for an example of the difference of porosity and Figure 4 for an
explanation of permeability.
5
Figure 3: Porosity
Figure 4 shows the porosity of the block on the left is 4 time the porosity of the block on
the right. Permeability of both of the blocks is approximately the same because only one
hole passes all the way through the blocks. Assuming that the each hole equates to a
tenth of the total area of the block, the block on the left has a porosity of .4 while the
block on the right has a porosity of .1. Below is an example and explanation of
permeability.
Figure 4: Permeability
Figure 4 demonstrates how two blocks could have the same porosity of approximately .4
but have two completely different permeability’s. The block on the left has one small
hole passing through the entire way, while the block on the right has a large hole passing
all the way through. Therefore the ability to pass fluid through the block on the right is
much easier than passing fluid through the block on the left. This mean the permeability
of the block on the right is greater than the block on the left.
Heat Transfer in Porous Media: Heat transfer through a porous material is similar to
heat transfer through a solid block. A heat equation similar to that used for heat transfer
through a solid block heat sink is used to calculate heat transfer through the porous block.
Equation 4 is the heat transfer equation that is used for the porous block heat sink:
 * Cp eq T   * Cp * u *  * T   * k eq *  * T   Q
t
Equation 4
6
4
The difference between the simple heat equation and the heat equation for porous
material are the corresponding affect of the volumetric heat capacity and thermal
conductivity. In the case of the porous material both volumetric heat capacity and
thermal conductivity is a function of the material porosity. As the material becomes
more porous the composition of both the thermal conductivity and the volumetric heat
capacity becomes more like the cooling fluid. Alternatively as the porosity nears zero the
conductivity and volumetric heat capacity becomes more like that of the base material.
Below equation 5 are the equation to determine the equivalent thermal conductivity and
volumetric heat capacity.
keq   p k p   F k F
 * Cp eq   p  pCp p   F  F Cp F
 p F  1
Equation 5
It should be noted equation 5 shows how the fraction of porous base material and fraction
of cooling fluid must add up to 1.
Free and Porous Media Flow: Since in porous material the cooling fluid is able to
move through the heat sink, a way to model the flow of liquid through it is required. For
a pure porous system flow the Darcy-Brinkman equation is the accepted method of
approximating the flow through the media. Since the system modeled has both free and
porous flow the interactions between the porous media and the free flow region must be
taken into account. For this reason a modified Darcy-Brinkman equation is need. The
modified equation mixes the Strokes-Darcy equation as described in Reference 5. The
mixed equation for modeling the Stroke-Darcy is equation 6.

  

 
u 

2
T


u *       pl 
u  u  
 * u t   
  F u  Qbr u  F
 p 
 p 
p
3 p

  kbr



Equation 6
7
It should be noted that equation 6 is affected by both permeability and porosity of the
heat sink material. This equation is used to model all cases where a porous heat sinks is
used.
4.3. Modeling
Using Comsol a heat sink is modeled to be 10 mm by 10 mm in a 50mm by 50 mm
system. The heat sink sits on a wall that is heated to 310K. This wall mimics a computer
chip in that it provides a heat flux that must be dissipated. The chip is design to run only
at 310K so depending on the efficiency of the heat the speed of the chip will be
determined. The faster the chip is able to operate the higher the heat flux will be. The
heat sink will consist of two forms; a porous block, a solid block and a third condition
with no heat sink at all. The porous heat sinks will consist of different characteristics; 10
different porosities and 3 different permeabilities for a total of 30 different porous heat
sink options. In addition one solid block heat sink and one system without a heat sink
will be analyzed for a total of 32 different cases all of which are provided below in Table
2 (Porous Heat Sink) and Table 3 (Block Heat Sink).
Table 2: Porous Heat Sink Characteristics
Form
Porosity
1a
1b
1c
1d
1e
1f
1g
1h
1i
1j
2a
2b
2c
2d
2e
2f
2g
2h
2i
2j
Permeability
0.05
0.1544
0.2589
0.3633
0.4678
0.5722
0.6767
0.7811
0.8856
0.99
0.05
0.1544
0.2589
0.3633
0.4678
0.5722
0.6767
0.7811
0.8856
0.99
8
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
3a
3b
3c
3d
3e
3f
3g
3h
3i
3j
0.05
0.1544
0.2589
0.3633
0.4678
0.5722
0.6767
0.7811
0.8856
0.99
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
Table 3: Block Form
Form
Depth (mm)
5-a
0
5-b
10
The characteristics chosen above for the porous heat sink are those that easily show the
affect of permeability and porosity to heat transfer. The porous material characteristics
analyzed may not be producible in the real world but they provide a useful understanding
of the affect of porous materials has when used as a heat sink. Each heat sink will be
made of the same base material in addition each system will utilize the same cooling fluid
(air). The models will be subjected to the same wall temperature or 310K. The models
are analyzed to determine the total heat flux that is able to be dissipated for the prescribed
wall temperature. In addition plots of the flow path and temperature gradients will be
produced. Using the resulting data it is then determined which heat sink has the potential
of transferring the most heat.
In addition mesh control can significantly affect the results of the analysis. To ensure
that meshing is controlled in the same manner between all of the models the same mesh
setting are used. For all three systems the mesh will be a physic-controlled mesh with
normal sized element. This set up allows Comsol to optimize the number elements, the
mesh size and the mesh geometry. This optimization is based on the geometry of the
model and studies which are being completed. Figures 5, 6 and 7 below are the meshes
in which Comsol has determined to be the most effective meshes based on the system
geometry.
9
Figure 5: No Heat Sink Mesh
Figure 6: Solid Block Mesh
Figure 7: Porous Block Mesh
10
5. Results and Discussion
Control Cases: The first analysis that was completed was the comparison of the use of
no heat sink and use of a solid block heat sink. Table 4: Control Block Heat Sink
Results below provides the important data from the model analysis. Table 4 provides the
corresponding heat flux associated with a non-porous block and the model with no heat
sink.
Table 4: Control Block Heat Sink Results
Trial
Depth (mm)
No Heat Sink
Solid Heat Sink
0
10
Heat Flux (W/m)
1.513
2.9278
Mass Flow Rate
(m^2/sec)
0.0012
0.001
As expected the heat flux out of the chip with the solid heat sink is larger than the case
without any heat sink. This is due to the fact that there is a greater amount of surface area
for heat to transfer to occur between the source and the cooling fluid. Figure 8 shows
how the block heat sink has a large area of material at the 310K temperature.
Alternatively Figure 7 shows that the wall is the only location where the temperature is
310K. If the block was to have a smaller width dimension the heat flux would be less
than that of the 10mm block but more than the system without a heat sink.
The associated mass flow rate of the model without the heat sink is greater than that of
the model with the block heat sink. The mass flow rate is a function of the buoyancy
force and the drag caused by the heat sink. Increasing the heat flux results in a greater
buoyancy force therefore increase the flow rate. Alternatively the larger the block is the
greater the drag force acting on the fluid moving by it. As can be seen in figure 8 the
flow path for the model with the block heat sink requires the fluid to flow around the heat
sink while figure 7 shows how with no heat sink flows right across the chip without a
disruption in the flow path.
11
Figure 8: No Heat Sink T-V
Figure 9: Solid Heat Sink T-V
Porous Heat Sink: The second analysis compared porous heat sinks with differing
permeabilities and porosities. Table 5: Porous Heat Sink Results below provide the data
from the model analysis of porous material heat sinks. Specific data of interest is the
total heat flux and volumetric flow rate of the systems.
12
Table 5: Porous Heat Sink Results
Form
1a
1b
1c
1d
1e
1f
1g
1h
1i
1j
2a
2b
2c
2d
2e
2f
2g
2h
2i
2j
3a
3b
3c
3d
3e
3f
3g
3h
3i
3j
Porosity
Permeability
0.05
0.1544
0.2589
0.3633
0.4678
0.5722
0.6767
0.7811
0.8856
0.99
0.05
0.1544
0.2589
0.3633
0.4678
0.5722
0.6767
0.7811
0.8856
0.99
0.05
0.1544
0.2589
0.3633
0.4678
0.5722
0.6767
0.7811
0.8856
0.99
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
1.00E-08
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
5.05E-07
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
1.00E-06
Total Heat Flux
Volumetric Flow
(W/m)
Rate (m^2/s)
3.1391
3.1443
3.1456
3.1452
3.1443
3.1429
3.1406
3.1361
3.1233
2.8752
7.6455
11.5721
10.6431
10.04
9.7644
9.6461
9.585
9.5285
9.4072
7.5302
7.9756
14.0391
14.9183
15.1979
15.1892
15.0854
14.9662
14.8254
14.543
10.7887
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.0011
0.001
0.002
0.0027
0.0025
0.0024
0.0024
0.0024
0.0024
0.0024
0.0023
0.0021
0.002
0.0031
0.0033
0.0033
0.0033
0.0033
0.0033
0.0033
0.0033
0.0028
For ease of analysis the affect of porosity on the heat sinks performance will be compared
independent of permeability. Figure 6 was created from the data in Table 4 for the
differing permeability’s. By fluctuating the porosity the affect of porosities between 0
and 1 the corresponding heat flux is plotted.
13
Porosity Affect on Heat Transfer
16
14
Total Heat Flux (W/m)
12
10
kappa = 1e-8
kappa = 5.05e-7
kappa =1e-6
8
6
4
2
0
0
0.2
0.4
0.6
0.8
1
1.2
Porosity (epsilon)
Figure 10: Porosity Affect on Heat Transfer
From Figure 10 the affect of porosity can be analyzed independent of permeability. At
the extremes of porosity (ie 0-.1 and .9-1) a detrimental affect on the performance of the
heat sink is seen. By looking at appendix 2 flow models, it is obvious why the extreme
cases cause a decrease in the heat sinks ability to transfer heat. In those cases where the
porosity is large the flow path of the coolant is similar to that of block heat sink case
where fluid does not flow through the heat sink. This is also simlar to the case where the
heat sink has a low permeability. As flow through the heat sink diminishes until the heat
sink act as a boundary and no longer allows flow though it the advantage of being a
porous media is lost.
On the other hand looking at the temperature plots in appendix 2 it is apparent that when
the porosity is increases above .9 the propagation of heat through the heat sink is not as
uniformed when compared with material with less porosity. From the governing
equation for heat conduction through a porous media it is apparent that once porosity
becomes too large the equivalent conductivity becomes more like the cooling fluid than
the base material. This causes heat not to propagate though the heat sink as readily. This
14
diminishment of heat propagation results in the decrease in the overall heat flux being
dissipated.
The second characteristic that was of importance for heat transfer in a porous material is
the materials permeability. Figure 11 was created from the results in Table 4 for 5. By
fluctuating the permeability the corresponding heat flux is able to be compared between
each other.
Permeability Affect on Heat Transfer
16
14
Total Heat Flux (W/m)
12
10
Porosity 0.6
Porosity 0.795
Porosity 0.99
Wall
Block
8
6
4
2
0
0.00E+00
2.00E-07
4.00E-07
6.00E-07
8.00E-07
1.00E-06
1.20E-06
Permeability (1/m^2)
Figure 11: Permeability Affect on Heat Transfer
From Figure 11 it is determined that increasing permeability will increase the
performance of the heat sink. By looking at Appendix 1 plots of flow it is apparent that
increasing the permeability causes the flow to be similar to that of the control case with
no heat sink at all. The increase heat flux is due to the ability of the fluid to flow through
the heat sink, while the heat sink thermal conductivity is unaffected. This differs from
decreasing porosity in that the optimum flow pattern is able to be achieved without
changing the thermal conductivity of the heat sink. That flow pattern contributes to the
volumetric flow rate being so high.
15
As presented in Figure 12 the permeability and porosity also affect the volumetric flow
rate as well as the heat transfer. The higher the permeability is will result is a higher
coolant flow rate.
Permeability Affect on Velocity
0.0035
0.003
Velorcity (m/sec)
0.0025
Porosity 0.6
Porosity 0.99
Porosity 0.795
Block
No Heatsink
0.002
0.0015
0.001
0.0005
0
1.00E-08
5.05E-07
1.00E-06
Permeability (1/m^2)
Figure 12: Permeability Affect on Velocity
The reason for the increase of flow rate due to the increase of permeability can be easily
seen in appendix 1 flow rate plots. The greater the permeability is results in less flow
being diverted around the heat sinks. The less diverting of flow results in less drag and
an increase in the volumetric flow rate. For the same amount of buoyancy force a system
with no drag due to a block will have more flow rate than one with a block in its flow
path.
On the other hand an increase of porosity decreases the volumetric flow rate. This is due
to the fact that flow is a function of buoyancy force. Buoyancy force is a function of heat
flux since the force is a comparison of incoming density to a point density, and density at
a point in the system is dependant on temperature. An increase in heat flux will
correspond to an increase in temperature, therefore increase the buoyancy force. Since a
16
low porosity has a negative affect on heat flux it will also have a negative affect on
velocity.
It should also be noted that there is a diminishing affect on the heat sinks ability to
transfer heat once the flow is able to pass through the heat sink with out being disturbed.
Figure 13 and Figure 14 below show how once permeability gets above a certain point
increasing it further does not has as large of an affect. At the point where neither velocity
nor heat flux increase with respect to permeability is where the flow path is similar to that
of the control condition with no heat sink. This is due to the fact that once flow of the
coolant become unobstructed there is no increase in its velocity. Since velocity doesn’t
increase heat transfer will not increase either.
Figure 13:Affect Of Increasing Permeability on Total Heat Flux
17
Figure 14: Affect Of Increasing Permeability on Volume Flow Rate
Comparison of Porous and Control Conditions:
From the analysis above it is evident that the porous heat sinks have a district advantage
over the non-porous heat sink when comparing heat dissipation. This was expected due
to the ability of the cooling fluid to flow through the heat sink in addition to the increased
surface area between the cooling fluid and the heat sink. The characteristic of the flow
through the system without a heat sink can be seen in figure 8 and appendix 3 which
shows the fluid flowing straight through the system heating up as it passes the chip.
Figure 9 and Appendix 2 show the fluid flow of the block heat sink and how the fluid
rises from the inlet with cool air continues to flow around the heat sink while the fluids
temperature rises until it exist from the top of the system. Alternatively in Figure 15, 16
and Appendix 1 the cooling air flows through as the heat sink. In addition Figure 12:
Permeability Affect on Velocity and Tables 4 and 5 show how the fluid volumetric flow
rate is increased with porosity.
This increase in volumetric flow rate is due to two reasons. First the drag produced by
the porous material versus the solid block is less. Since the air can pass through the block
instead of around it the volume can pass with less pressure drop. Secondly the increased
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buoyancy force due to a greater heat flux results in a greater volume force, increasing
velocity and therefore increasing the volumetric flow rate.
v
Figure 15: Porous Heat Sink T-V
Figure 16: Porous Heat Sink P-V
How does meshing Affect the Results:
As described in prior sections it was determined to use a normal mesh setting for analysis
of the systems. This helped to ensure that the models were able to achieve a result in a
reasonable amount of time while achieving results of significance. To ensure that the
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results are of significance Figures 17 and 18 are provided below to compare the results of
a system with a coarser mesh a normal mesh, a finer mesh and an extremely fine mesh.
Mesh Affect on Total Energy Flux
12
Total Energy Flux (W/m)
10
8
6
4
2
0
Coarser
Normal
Finer
Mesh
Mesh Affect on Total Energy Flux
Figure 17: Mesh Affect on Total Flux
20
Extremely Fine
Affect of Mesh On Volume Flow Rate
0.0026
0.0025
Volume Flow Rate
0.0024
0.0023
0.0022
0.0021
0.002
0.0019
Coarser
Normal
Finer
Extremely Fine
Mesh
Epsilon .9 Kappa 5.05e-7
Figure 18: Mesh Affect on Volume Flow Rate
It is determined that the results using a mesh setting of normal is numerically significant.
The results of normal mesh setting and the extremely fine setting are within 10% of each
other. For the purpose of this analysis that is close enough. In addition the graphs show
that the results begin to flatten out right past the normal mesh criteria. Therefore the
results determined in this analysis are considered to be of significance.
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6. Conclusion
The comparison between the use of porous and non-porous heat sinks confirmed the
hypothesis that there is a substantial benefit of using porous material in lieu of nonporous material for heat sinks. The benefit between porous and non-porous material heat
sinks is only relevant to the initial efficiency of the heat sink. Over time fouling and
material degradation may have a greater affect on the porous material versus the nonporous heat sink. In addition neither a cost comparison nor material availability research
has been completed which may diminish the porous material overall advantage.
To compare the advantage of porous material versus non-porous, an analysis of the
affects of permeability and porosity characteristics was evaluated. Unlike the simple
comparison between porous and non-porous material, the evaluation of the porous
material characteristics a more complicated result ensued. The first characteristic
analyzed was permeability, which is the ease in which fluid can pass through the heat
sink. It was determined that the more permeability the porous media is the more efficient
the heat sink becomes. Although the increase of permeability helped only so much, once
there was little resistance for the cooling fluid to pass through the heat sink there was
little advantage to increase the permeability. At that point increasing and decreasing
porosity had a greater affect.
The second material characteristic that was analyzed was the affect of porosity to the
performance of the porous heat sink. It was determined that if the porosity is too high or
too low there performance of the heat sink is adversely affected. Performance of the heat
sink diminishes with increase of porosity due to the fact that the equivalent thermal
conductivity of the heat sink diminishes to be close to the thermal conductivity of the
cooling fluid. On the other hand, decreasing the porosity too much causes surface area
for heat transfer to occur to diminish. Once porosity is diminished enough its flow path
become similar to that of a solid block.
Overall it has been determined a heat sink with high permeability and a porosity not near
the extremes of the porosity range would perform best. This analysis looked at the
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hypothetical cases for material porosity and permeability, therefore the ability to make
the material analyzed may not be possible. For future analysis it would be beneficial to
look at the possible porous materials that are able to be created and to perform actual
testing of the material.
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7. Appendix 1
Data from Porous Material Analysis
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8. Appendix 2
Data from Block Analysis
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9. Appendix 3
Data from No Heat Sink Analysis
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26
10. Reference
1
Fundamentals of Thermal-Fluid Sciences; Second Edition, Yunus A. Cengel & Robert H. Turner, © 2005
http://en.wikipedia.org/wiki/Heat_sink
3
Medal Foam and Finned Metal Foam Heat Sinks for Electronic Cooling in Buoyancy-Induced
Convection. A. Bhattacharya & R.L Mahajan, © 2006
4
An analytical study of local thermal equilibrium in porous heat sinks using fin theory. Tzer-Ming Jeng,
Sheng-Chung Tzeng, Ying-Huei Hung; © January 10, 2006
3
http://en.wikipedia.org/wiki/Density_of_air
4
Comsol
5
Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy
solidification. M. Le Bars and M. GRAE Worster, ©8 August 2005.
2
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