CAMCOS Reports Day May 17, 2006

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Moris Curtis Malone
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1 CAMCOS Reports Day May 17, 2006

2 Mathematical and Statistical Analysis of Heat Pipe Design Sandy DeSousa Sergio de Ornelas Marian Hofer Adam Jennison Kim Ninh Cuong Dong Michelle Fernelius Tracy Holsclaw Diem Mai 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.

3 Modern Day Microchips Microchips already contain millions of transistors In three decades, circuit elements will be the size of a single atom C

4 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

5 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

6 What is a Heat Pipe? Kim Ninh

7 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 ˆHeat Pipe name

8 Applications of Heat Pipes

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

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

11 Components of a Heat Pipe Sergio de Ornelas

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

13 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.

14 Examples of Working Fluid MEDIUM MELTING PT. ( ( C ) BOILING PT. AT ATM. PRESSURE ( C) USEFUL RANGE ( C) Helium to -269 Ammonia to 100 Water to 200 Silver to 2300

15 The Wicking Structure

16 Axial Groove Wick Created by carving out grooves on the interior core of the Heat Pipe.

17 Screen Mesh Wick Utilizes multiple wire layers to create a porous wick. Sintering can be used.

18 Sintered Powder Wick Utilizes densely packed metal spheres. Sintering must be used to solidify the spheres.

19 Purpose of the Wick Transports working fluid from the Condenser to the Evaporator. Provides liquid flow even against gravity.

20 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.

21 Mathematical Models for Liquid Flow Through the Wick Brinkman Equation Darcy s Law

22 Permeability K = 2 R 2 ϕ fre 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.

23 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.

24 Evaporator Misako van der Poel

25 Evaporator The evaporator section is enclosed in a copper block, which is placed on top of the CPU.

26 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.

27 The Thermal Resistance θ evaporator = T T Block HP Power = F (heat pipe geometry, evaporator length, flatness, power input, wick structure, working fluid.)

28 Condenser Diem Mai

29 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.

30 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

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

32 Thermal resistance θ θ total T = evaporator T P condenser Is a mathematical concept analogous to the electrical resistance Is a function of the temperature difference and the heat input Unit: C C / W Reduce all thermal resistances to prevent heat loss along the heat pipe

33 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

34 Data Characteristics Tracy Holsclaw

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

36 Box Plots Ө Theta-jamb Heatpipe number

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

38 Analysis of Variance (ANOVA) Sandy DeSousa

39 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)

40 ANOVA Findings Constant PowderSize WickThickness LiquidCharge Term PowderSize*WickThickness PowderSize*LiquidCharge WickThickness*LiquidCharge PowderSize*WickThickness WickThickness*LiquidCharge P-value

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

42 Regression Analysis Michelle Fernelius

43 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)

44 PowderSize PowderSize*LiquidCharge LiquidCharge LiquidCharge LiquidCharge PowderSize PowderSize LiquidCharge LiquidCharge WickThickness WickThickness PowderSize PowderSize Intercept Intercept p value value Coefficient Coefficient Term Term Regression Equation Regression Equation

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

46 Further Analysis & Recommendations Marian Hofer

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

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

49 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

50 Break Q&A

51 Partial Differential Equations Cuong Dong

52 Physical Phenomena & Physical Phenomena & PDE s PDE s Heat transfer in the pipe: conduction and convection equation Heat transfer in the pipe: conduction and convection equation Vapor flow: Vapor flow: Navier Navier Stokes equations Stokes equations Liquid flow in wick structure: Liquid flow in wick structure: Brinkman s Brinkman s equation equation T C Q T k t T C = + u ρ ρ ) ( 0 ) ( ) )( 3 2 ( ) ) ( ( ) ( = = + u F Ι u u u Ι u u u 1 ρ ρ κ η η ρ ρ t p t T 0 0 ) ( ) ) ( ( = = + + u F u u u u p K t T η η ρ

53 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.

54 Computer Simulation

55 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.

56 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.

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

58 PDE and Boundary Condition p = p(t ) No slip u = 0 p = p(t ) Axis ρ( u 1 ) u 1 = pι + η( u 1 ( ρu + ( u 1 1 ) ) = 0 T ) 2η ( κ)( u 3 1 ) Ι + F p(t) ) is the saturated vapor pressure at T. Viscosity and density of vapor change with temperature.

59 PDE and Boundary Condition p = 2 p 1 Slip condition Mass balance ρ u = ρwater u vapor 1 2 Axis η( u 2 T η + ( u2) ) ( u K u = p) = 0 Viscosity of water change with temperature. K (permeability of wick structure) depends of the porosity and size of sphere.

60 PDE and Boundary Condition Heat flux Natural convection Forced Convection n ( k T ) = q n ( k T ) = h( T T ) Axis Copper : ( T ) = k copper 0 Vapor flow : ( k T ) = ρcu1 T Water flow : ( k wick T ) = g

61 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

62 θ vs. Temperature (ceteris paribus) Theta vs. Temperature Theta Temperature (K)

63 θ vs. Temperature Theta vs. Temperature Theta Temperature (K)

64 θ vs. Heat Flux (ceteris paribus) Theta vs. Heat Flux Theta Heat Flux (W/m2)

65 θ vs. Heat Flux Theta vs. Heat Flux Theta Heat Flux (W/m2)

66 θ vs. Copper Thickness (ceteris paribus) Theta vs. Copper Thickness Theta E E E E E E E-04 Copper Thickness

67 θ vs. Copper Thickness Theta vs. Copper Thickness Theta E E E E E E E-04 Copper Thickness Hypothesis: Heat pipe with varying copper thickness might be better.

68 Conclusions and Future Work Adam Jennison

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

70 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

NUMERICAL INVESTIGATION OF STEADY STATE AND TRANSIENT THERMAL PERFORMANCE OF A MULTI-CHIP VAPOR CHAMBER MOHAMMAD PARHIZI

NUMERICAL INVESTIGATION OF STEADY STATE AND TRANSIENT THERMAL PERFORMANCE OF A MULTI-CHIP VAPOR CHAMBER by MOHAMMAD PARHIZI Presented to the Faculty of the Graduate School of The University of Texas at