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Transcript
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 Heatpipe 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 Itercept PowderSize WickThickess LiquidCharge Coeffi pciet 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