Transcript Heat Pipe Background

CAMCOS Reports Day
May 17, 2006
Mathematical and
Statistical Analysis
of Heat Pipe Design
Sandy DeSousa
Cuong Dong
Sergio de Ornelas
Michelle Fernelius
Marian Hofer
Tracy Holsclaw
Adam Jennison
Diem Mai
Kim Ninh
Misako van der Poel
All heat pipes and data presented today are purely fictional. Any similarity with any heat pipe, functioning
or not, is purely coincidental.
Modern Day Microchips

Microchips already
contain millions of
transistors

In three decades,
circuit elements will
be the size of a single
atom

40 – 60 °C
Dealing with the Heat

Traditional stacked
heatsink and fan set
up not feasible in a
laptop

Need to separate the
two where you have
more space
Requirements for Cooling

Solid metal rods lose
too much heat to the
environment

Cannot use a
powered cooling
system, too much
power consumption
caused the problem
What is a Heat Pipe?
Kim Ninh
Heat Pipe Background

1800s – A. M. Perkins and J. Perkins developed
Perkins tube

1944 – R. S. Gaugler introduced the use of a
wicking structure

1964 – G. M. Grover published research and
coined the “Heat Pipe” name
Applications of Heat Pipes
Transfer of Heat
Heat Added
Heat Released
Heat Pipe
Heat
*Drawing is not to scale.
Processor
Heat Sink
Heat Transfer within
a Heat Pipe
Heat Absorbed
Container
Heat Released
Wick Structure
Evaporation
Condensation
Wick Structure
Heat Absorbed
*Drawing is not to scale.
Container
Heat Released
Components of a
Heat Pipe
Sergio de Ornelas
Container

Metal Tubing, usually
copper or aluminum.

Provides a medium
with high thermal
conductivity.

Shape of tubing can
be bent or flattened.
Working Fluid

Pure liquids such as helium, water and liquid
silver

Impure solutions cause deposits on the interior
of the heat pipe reducing its overall
performance.

The type of liquid depends on the temperature
range of the application.
Examples of Working Fluid
MEDIUM
MELTING
PT. (° C )
BOILING PT. AT
ATM. PRESSURE
(° C)
Helium
- 271
- 261
-271 to -269
Ammonia
- 78
- 33
-60 to 100
Water
0
100
30 to 200
Silver
960
2212
1800 to 2300
USEFUL
RANGE
(° C)
The Wicking Structure
Axial Groove Wick
Created by carving out grooves on the interior
core of the Heat Pipe.
Screen Mesh Wick
Utilizes multiple wire layers to create a porous
wick.
Sintering can be used.
Sintered Powder Wick
Utilizes densely packed metal spheres.
Sintering must be used to solidify the spheres.
Purpose of the Wick

Transports working fluid from the Condenser to
the Evaporator.

Provides liquid flow even against gravity.
How the Wick Works

Liquid flows in a wick due to capillary action.

Intermolecular forces between the wick and the
fluid are stronger than the forces within the fluid.

A resultant increase in surface tension occurs.
Mathematical Models for Liquid
Flow Through the Wick

Brinkman Equation

Darcy's Law
Permeability


Permeability, K, is a measure of the ability of a
material to transmit fluids and depends on
factors such as the wick diameter, wick
thickness, pore size.
Porosity, φ, and the effective pore radius, R,
contribute to an increase in permeability.
Capillary Limitation

Wick must have minimum pressure difference
between the condenser and the evaporator for
liquid to flow.

Dry-out occurs when there is insufficient
pressure difference.
Evaporator
Misako van der Poel
Evaporator
The evaporator section is enclosed in a copper
block, which is placed on top of the CPU.
What happens in the
Evaporator Section

The working fluid is heated to its boiling point
and converted into a vapor.

Pressure and temperature differences forces the
vapor to flow to the cooler regions of the heat
pipe.
The Thermal Resistance
= F (heat pipe geometry,
evaporator length,
flatness, power input,
wick structure,
working fluid….)
Condenser
Diem Mai
Condenser`s operations
Condensation
Vapor gives up its latent heat of vaporization
 Vapor cools down and returns to its liquid state
 Working fluid then flows back to the evaporator
through the wick.

Pressure governs the
condenser's operations

Capillary pressure at the liquid-vapor interface

Vapor pressure drop

Liquid pressure drop

Pressure drop at the phase transition
Heat Exchanger

Dissipates heat into environment

High Thermal Conductivity

Improve heat exchanger's
performance
 Increase surface area with
more fins
 Include a fan
Thermal resistance θ




Is a mathematical concept
analogous to the electrical
resistance
Is a function of the
temperature difference and
the heat input
Unit: C / W
Reduce all thermal
resistances to prevent heat
loss along the heat pipe
Factors to Consider in Heat
Pipe Design





Wick structure
Pore size
Working fluid
Shape of heat pipes
Liquid Charge





Length
Diameter
Bending angle
Flatness
Material
Data Characteristics
Tracy Holsclaw
The Data

11 heat pipes - 6 test runs each



Minimize response - thermal resistance, Ө
3 factors:




8 combination runs, and 3 baseline runs
Powder Size
Wick Thickness
Liquid Charge
Attempt to improve previous results
1.4
1.2
Ө
1.0
Theta-jamb
1.6
Box Plots
5
7
9
11
13
H eatpipe number
15
17
19
Experimental Design

23 Factorial Design (three factors)
Set up for factor screening
 Replicates only at the center point

Analysis of Variance
(ANOVA)
Sandy DeSousa
ANOVA


A procedure to determine whether
differences exist between group means
Goals:
 Identify the important factors
 If differences exist, identify the
best heat pipe among the given
settings (choose best point of
cube)
ANOVA Findings
Term
P-value
Constant
0.000
PowderSize
0.000
WickThickness
0.467
LiquidCharge
0.000
PowderSize*WickThickness
0.000
PowderSize*LiquidCharge
0.000
WickThickness*LiquidCharge
0.021
PowderSize*WickThickness*LiquidCharge
0.005
Tukey's Comparisons of Treatments
HP
5
13
17
9
19
15
11
7
Mean
1.01
1.06
1.09
1.12
1.22
1.40
1.61
1.62
Individual 95% CIs For Mean
--+---------+---------+---------+----(-*-)
(-*-)
(-*-)
(-*-)
(-*-)
(-*-)
(-*-)
(-*-)
--+---------+---------+---------+----1.00
1.20
1.40
1.60
Regression Analysis
Michelle Fernelius
Regression


Regression analysis is used to model the
relationship between the dependent (response)
and independent variables (factors)
Goal: Optimize the experimental settings within
the scope of the data (search entire cube for
best setting)
Regressio
Equatio
Term
Itercept
PowderSize
WickThickess
LiquidCharge
Coeffi
pciet valu
e
1.8
0.0
7888
000
0.0
0.0
000
4439
0.9
0.0
2143
000
0.0
0.0
Response Surface
The minimum occurs at:
Powder size = 77.2
θ
Wick thickness = 0.65
Liquid charge = 138
Ө = 0.5988
39% Improvement
Further Analysis
&
Recommendations
Marian Hofer
Nested Design


Does variability in the manufacturing process
affect our analysis?
There are 3 heat pipes of “identical” construction
Analysis of Nested Design
Analysis of Variance for θ
Term
Treatment
Heat Pipe (nested within Treatment)
Strong evidence of variability in the
manufacturing process.
P-value
0.016
0.039
Recommendations



Augment the design by adding more
experimental settings at key locations (e.g.
axial-settings)
Ensure testing conditions
are uniform across
experimental settings
Use more than one unit
per experimental setting
Break
Q&A
Partial Differential
Equations
Cuong Dong
Physical Phenomena & PDE's

Heat transfer in the pipe: conduction and convection equation

Vapor flow: Navier-Stokes equations

Liquid flow in wick structure: Brinkman`s equation
Physical Properties & Coupling

Properties such as density, viscosity, pressure changes
with temperature.

Formulae for water and steam properties published by
the International Association for the Properties of Water
and Steam (IAPWS) could be used for better accuracy.

The vapor and water flow decides how much heat is
transferred, which in turn affects the temperature.

Thus, the system of PDE's is highly nonlinear.
Computer
Simulation
Purpose

The system of PDE's is nonlinear and it is
unlikely that it is solvable analytically.

Numerical solution could be done by computer
using Finite Element Method (FEM).

To provide a tool to test and visualize our
theories and enable us to predict performance of
heat pipe at arbitrary conditions.
Assumptions

Stationary analysis: the temperature and the
flows are in equilibrium.

Ignoring radiation: low temperature difference in
heat pipe.

Axial symmetry.

Vapor does not mix with liquid in wick structure.
Geometry

Baseline dimension:
Adiabatic
Evaporator 65 mm
30 mm
Condenser 75 mm
170 mm
Wick thickness .75 mm
Copper thickness .25 mm
PDE and Boundary Condition
No slip
u=0
Axis


p(T) is the saturated vapor pressure at T.
Viscosity and density of vapor change with
temperature.
PDE and Boundary Condition
Slip condition
Axis


Viscosity of water change with temperature.
K (permeability of wick structure) depends of the
porosity and size of sphere.
PDE and Boundary Condition
Natural
Heat flux
Axis
convection
Forced Convection
Parameters

Simulate with different values of parameter while
everything else is kept constant.
 Heat flux
 Temperature at evaporator
 Copper thickness
 Porosity
 Pipe radius

Other parameters
θ vs. Temperature
(ceteris paribus)
Theta
Theta vs. Temperature
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
300
Se
305
310
315
320
Temperature (K)
325
330
335
θ vs. Temperature
Theta vs. Temperature
0.012
0.01
Theta
0.008
Se
0.006
Se
Se
0.004
0.002
0
300
305
310
315
320
Temperature (K)
325
330
335
θ vs. Heat Flux
(ceteris paribus)
Theta vs. Heat Flux
1.2
1
Theta
0.8
0.6
0.4
0.2
0
0
10000
20000
30000
Heat Flux (W/m2)
40000
50000
θ vs. Heat Flux
Theta vs. Heat Flux
0.014
0.012
Theta
0.01
0.008
0.006
0.004
0.002
0
0
10000
20000
30000
Heat Flux (W/m2)
40000
50000
θ vs. Copper Thickness
(ceteris paribus)
Theta vs. Copper Thickness
1.2
1
Theta
0.8
0.6
0.4
0.2
0
0.00E+00
1.00E-04
2.00E-04
3.00E-04
4.00E-04
Copper Thickness
5.00E-04
6.00E-04
θ vs. Copper Thickness
Theta vs. Copper Thickness
0.016
0.014
Theta
0.012
0.01
Serie
0.008
Serie
0.006
Serie
0.004
0.002
0
0.00E+00 1.00E-04 2.00E-04 3.00E-04 4.00E-04 5.00E-04 6.00E-04
Copper Thickness
Hypothesis: Heat pipe with varying copper thickness might be better.
Conclusions and
Future Work
Adam Jennison
Recommendations

Vary a combination of factors

Make a more complete model

Build and test a heat pipe using
specifications from the simulation
We would like to thank
CAMCOS
Intel Corporation
Woodward Foundation
Dr. David Blockus
Dr. Tim Hsu
Brian Kluge
Dr. Sridhar Machiroutu
Dr. Himanshu Pokharna
our family and friends