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 Microchips already contain millions of transistors In three decades, circuit elements will be the size of a single atom In three decades, circuit elements will be the size of a single atom 40 – 60 °C 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 1800s – A. M. Perkins and J. Perkins developed Perkins tube 1944 – R. S. Gaugler introduced the use of a wicking structure 1944 – R. S. Gaugler introduced the use of a wicking structure 1964 – G. M. Grover published research and coined the “Heat Pipe” name 1964 – G. M. Grover published research and coined the “Heat Pipe” name

Applications of Heat Pipes

Heat Transfer of Heat Heat Pipe Heat Sink Processor Heat Added Heat Released *Drawing is not to scale.

EvaporationCondensation Heat Absorbed Heat Released Heat Transfer within a Heat Pipe *Drawing is not to scale. Wick Structure Container

Components of a Heat Pipe Sergio de Ornelas

Container Metal Tubing, usually copper or aluminum. Metal Tubing, usually copper or aluminum. Provides a medium with high thermal conductivity. Provides a medium with high thermal conductivity. Shape of tubing can be bent or flattened. Shape of tubing can be bent or flattened.

Working Fluid Pure liquids such as helium, water and liquid silver Pure liquids such as helium, water and liquid silver Impure solutions cause deposits on the interior of the heat pipe reducing its overall performance. 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. The type of liquid depends on the temperature range of the application.

MEDIUM MELTING PT. (° C ) BOILING PT. AT ATM. PRESSURE (° C) USEFUL RANGE (° C) HeliumAmmoniaWaterSilver to to to to 2300 Examples of Working Fluid

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. Transports working fluid from the Condenser to the Evaporator. Provides liquid flow even against gravity. Provides liquid flow even against gravity.

How the Wick Works Liquid flows in a wick due to capillary action. 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. Intermolecular forces between the wick and the fluid are stronger than the forces within the fluid. A resultant increase in surface tension occurs. A resultant increase in surface tension occurs.

Mathematical Models for Liquid Flow Through the Wick Brinkman Equation Brinkman Equation Darcy's Law 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. 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. 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. 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. 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. 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. Pressure and temperature differences forces the vapor to flow to the cooler regions of the heat pipe.

The Thermal Resistance = F (heat pipe geometry, = F (heat pipe geometry, evaporator length, evaporator length, flatness, power input, flatness, power input, wick structure, wick structure, working fluid….) working fluid….)

Condenser Diem Mai

Condenser`s operations Condensation Vapor gives up its latent heat of vaporization Vapor gives up its latent heat of vaporization Vapor cools down and returns to its liquid state Vapor cools down and returns to its liquid state Working fluid then flows back to the evaporator through the wick. Working fluid then flows back to the evaporator through the wick.

Pressure governs the condenser's operations Capillary pressure at the liquid-vapor interface Capillary pressure at the liquid-vapor interface Vapor pressure drop Vapor pressure drop Liquid pressure drop Liquid pressure drop Pressure drop at the phase transition Pressure drop at the phase transition

Heat Exchanger Dissipates heat into environment Dissipates heat into environment High Thermal Conductivity High Thermal Conductivity Improve heat exchanger's performance Improve heat exchanger's performance Increase surface area with more fins Increase surface area with more fins Include a fan Include a fan

Thermal resistance θ Is a mathematical concept analogous to the electrical resistance Is a mathematical concept analogous to the electrical resistance Is a function of the temperature difference and the heat input Is a function of the temperature difference and the heat input Unit:  C / W Unit:  C / W Reduce all thermal resistances to prevent heat loss along the heat pipe 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 Length Diameter Diameter Bending angle Bending angle Flatness Flatness Material Material

Data Characteristics Tracy Holsclaw

The Data 11 heat pipes - 6 test runs each 11 heat pipes - 6 test runs each 8 combination runs, and 3 baseline runs 8 combination runs, and 3 baseline runs Minimize response - thermal resistance, Ө Minimize response - thermal resistance, Ө 3 factors: 3 factors: Powder Size Powder Size Wick Thickness Wick Thickness Liquid Charge Liquid Charge Attempt to improve previous results Attempt to improve previous results

Box Plots Ө

Experimental Design 2 3 Factorial Design (three factors) 2 3 Factorial Design (three factors) Set up for factor screening Set up for factor screening Replicates only at the center point Replicates only at the center point

Analysis of Variance (ANOVA) Sandy DeSousa

ANOVA A procedure to determine whether differences exist between group means A procedure to determine whether differences exist between group means Goals: Goals: Identify the important factors Identify the important factors If differences exist, identify the If differences exist, identify the best heat pipe among the given settings (choose best point of cube)

ANOVA Findings TermP-value Constant0.000 PowderSize0.000 WickThickness0.467 LiquidCharge0.000 PowderSize*WickThickness0.000 PowderSize*LiquidCharge0.000 WickThickness*LiquidCharge0.021 PowderSize*WickThickness*LiquidCharge0.005

Tukey's Comparisons of Treatments Individual 95% CIs For Mean Individual 95% CIs For Mean HP Mean HP Mean (-*-) (-*-) (-*-) (-*-) (-*-) (-*-) (-*-) (-*-) (-*-) (-*-) (-*-) (-*-) (-*-) (-*-) (-*-) (-*-)

Regression Analysis Michelle Fernelius

Regression Regression analysis is used to model the relationship between the dependent (response) and independent variables (factors) 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) Goal: Optimize the experimental settings within the scope of the data (search entire cube for best setting)

TermCoefficientp-value Intercept PowderSize WickThickness LiquidCharge PowderSize LiquidCharge PowderSize*LiquidCharge Regression Equation

The minimum occurs at: Powder size = 77.2 Wick thickness = 0.65 Liquid charge = 138 Ө = Response Surface 39% Improvement θ

Further Analysis & Recommendations Marian Hofer

Nested Design Does variability in the manufacturing process affect our analysis? Does variability in the manufacturing process affect our analysis? There are 3 heat pipes of “identical” construction There are 3 heat pipes of “identical” construction

Analysis of Nested Design Strong evidence of variability in the manufacturing process. Analysis of Variance for θ Term P-value Treatment Heat Pipe (nested within Treatment) 0.039

Recommendations Augment the design by adding more experimental settings at key locations (e.g. axial-settings) Augment the design by adding more experimental settings at key locations (e.g. axial-settings) Ensure testing conditions Ensure testing conditions are uniform across experimental settings Use more than one unit 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 Heat transfer in the pipe: conduction and convection equation Vapor flow: Navier-Stokes equations Vapor flow: Navier-Stokes equations Liquid flow in wick structure: Brinkman`s equation Liquid flow in wick structure: Brinkman`s equation

Physical Properties & Coupling Properties such as density, viscosity, pressure changes with temperature. 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. 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. 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. 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. 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). 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. 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. Stationary analysis: the temperature and the flows are in equilibrium. Ignoring radiation: low temperature difference in heat pipe. Ignoring radiation: low temperature difference in heat pipe. Axial symmetry. Axial symmetry. Vapor does not mix with liquid in wick structure. Vapor does not mix with liquid in wick structure.

Geometry Baseline dimension: Baseline dimension: 170 mm Evaporator 65 mm Adiabatic 30 mm Condenser 75 mm Wick thickness.75 mm Copper thickness.25 mm

PDE and Boundary Condition Axis p(T) is the saturated vapor pressure at T. p(T) is the saturated vapor pressure at T. Viscosity and density of vapor change with temperature. Viscosity and density of vapor change with temperature. No slip u = 0

PDE and Boundary Condition Axis Viscosity of water change with temperature. Viscosity of water change with temperature. K (permeability of wick structure) depends of the porosity and size of sphere. K (permeability of wick structure) depends of the porosity and size of sphere. Slip condition

PDE and Boundary Condition Axis Heat flux Forced Convection Natural convection

Parameters Simulate with different values of parameter while everything else is kept constant. Simulate with different values of parameter while everything else is kept constant. Heat flux Heat flux Temperature at evaporator Temperature at evaporator Copper thickness Copper thickness Porosity Porosity Pipe radius Pipe radius Other parameters Other parameters

θ vs. Temperature (ceteris paribus)

θ vs. Temperature

θ vs. Heat Flux (ceteris paribus)

θ vs. Heat Flux

θ vs. Copper Thickness (ceteris paribus)

θ vs. Copper Thickness Hypothesis: Heat pipe with varying copper thickness might be better.

Conclusions and Future Work Adam Jennison

Recommendations Vary a combination of factors Vary a combination of factors Make a more complete model Make a more complete model Build and test a heat pipe using specifications from the simulation 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