TRANSIENT SIMULATION OF HEAT TRANSFER ABOUT AN LED LAMP

TRANSIENT SIMULATION OF HEAT TRANSFER ABOUT AN LED LAMP by KRISTEN BROUWER Submitted in partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical and Aerospace Engineering CASE WESTERN RESERVE UNIVERSITY January, 2017

CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis of Kristen Brouwer Candidate for the degree of Master of Science*: Committee Chair Paul Barnhart, Ph.D. Committee Member Joseph Prahl, Ph.D. Committee Member Yasuhiro Kamotani, Ph.D. Date of Defense December 2, 2016 *We also certify that written approval has been obtained for any proprietary material contained therein. i

Acknowledgements I would like to thank my adviser, Dr. Paul Barnhart, for his technical guidance throughout the course of my thesis work. I would not have been able to complete this thesis without his constant support and motivation. I want to thank my committee members, Dr. Joseph Prahl and Dr. Yasuhiro Kamotani for reviewing my thesis. I d also like to thank General Electric for allowing me to take the necessary time to complete my work and supporting me throughout my graduate education. ii

Table of Contents Acknowledgements... ii List of Figures... vi List of Tables... ix List of Symbols... x List of Acronyms... xii Abstract... xiii Chapter 1 Introduction... 1 Chapter 2 Analysis and Methodology... 4 2.1 Problem Description... 4 2.2 Problem Simplifications... 10 2.2.1 One-dimensional analysis problem simplifications... 11 2.2.2 Two-dimensional analysis problem simplifications... 12 2.2.3 Geometrical Simplifications... 13 2.3 Thermal Resistance Model... 15 2.3.1 Convection and Conduction... 15 2.3.2 Radiation... 19 2.4 Free Convection Vertical Plates... 21 iii

2.5 One-dimensional Heat Flow... 22 2.6 Two-dimensional Heat Flow... 24 2.7 Unsteady Calculations... 26 2.8 MATLAB Analysis Model... 29 Chapter 3 Experiment... 31 3.1 Heat Sink Prototype... 31 3.2 Setup... 32 3.3 Instrumentation... 35 3.3.1 Omega Thermocouples... 35 3.3.2 Agilent Technologies DC Power Supply... 36 3.3.3 Graphtec midi Logger... 38 Chapter 4 Results and Discussion... 40 4.1 Experimental Results... 40 4.2 Model Results... 42 4.3 Discussion... 44 4.3.1 Convection Coefficient Uncertainty... 64 4.3.2 Measurement Equipment Uncertainty... 66 Chapter 5 Conclusion... 68 Appendix A... 71 Engineering Drawings... 71 Experimental Data... 74 iv

Simulation Results... 84 Appendix B Solving Systems on Equations... 89 Newton Rapson Method... 89 LU Decomposition... 91 Bibliography... 94 v

List of Figures Figure 1.1: GE High Output Multi-Vapor Quartz Metal Halide BT56 [1]... 1 Figure 2.1: LED Replacement Lamp with Outward Facing Fins [2]... 5 Figure 2.2: LED Replacement Lamp with Inward Facing Fins... 6 Figure 2.3: Highbay HID Lamp Application [3]... 7 Figure 2.4: ANSI Dimensions for BT56 Bulb [1]... 8 Figure 2.5: LED Junction Temperature... 9 Figure 2.6: Junction Temperature Effects on Useful LED Life [4]... 10 Figure 2.7: Small Section of Heatsink... 14 Figure 2.8: Cross section Simplification... 15 Figure 2.9: Analogy between thermal and electrical resistance concepts [5]... 16 Figure 2.10: The thermal resistance network for heat transfer through a two-layer plane wall subjected to convection on both sides. [5]... 18 Figure 2.11: Small Surface inside a large isothermal enclosure [7]... 19 Figure 2.12: One Dimensional Thermal Resistance Model... 23 Figure 2.13: Two Dimensional Thermal Resistance Model... 25 Figure 3.1: NTI Lab Thermal Test Cage... 31 Figure 3.2: Test Setup... 33 Figure 3.3: Experimental Thermocouple Locations... 34 Figure 3.4: OMEGA Copper-Constantan Type T Thermocouples... 36 Figure 3.5: Agilent N5772A DC Power Supply... 37 vi

Figure 3.6: Graphtec midi Logger GL820... 39 Figure 4.1: Experimental Pad Temperature vs. Time at 0.5A... 41 Figure 4.2: Simulation Pad Temperature vs. Time at 0.5A... 43 Figure 4.3: 0.5A Top: LED Pad Temperature vs. Time... 46 Figure 4.4: 0.5A Top: % Error... 46 Figure 4.5: 0.5A Bottom: LED Pad Temperature vs. Time... 47 Figure 4.6: 0.5A Bottom: % Error... 47 Figure 4.7: 0.5A Middle: LED Pad Temperature vs. Time... 48 Figure 4.8: 0.5A Middle: % Error... 48 Figure 4.9: 0.75A Top: LED Pad Temperature vs. Time... 49 Figure 4.10: 0.75A Top: % Error... 50 Figure 4.11: 0.75A Bottom: LED Pad Temperature vs. Time... 50 Figure 4.12: 0.75A Bottom: % Error... 51 Figure 4.13: 0.75A Middle: LED Pad Temperature vs. Time... 51 Figure 4.14: 0.75A Middle: % Error... 52 Figure 4.15: 1.0A Top: LED Pad Temperature vs. Time... 53 Figure 4.16: 1.0A Top: % Error... 53 Figure 4.17: 1.0A Bottom: LED Pad Temperature vs. Time... 54 Figure 4.18: 1.0A Bottom: % Error... 54 Figure 4.19: 1.0A Middle: LED Pad Temperature vs. Time... 55 Figure 4.20: 1.0A Middle: % Error... 55 Figure 4.21: 1.25A Top: LED Pad Temperature vs. Time... 56 Figure 4.22: 1.25A Top: % Error... 57 Figure 4.23: 1.25A Bottom: LED Pad Temperature vs. Time... 57 Figure 4.24: 1.25A Bottom: % Error... 58 vii

Figure 4.25: 1.25A Middle: LED Pad Temperature vs. Time... 58 Figure 4.26: 1.25A Middle: % Error... 59 Figure 4.27: 1.5A Top: LED Pad Temperature vs. Time... 60 Figure 4.28: 1.5A Top: % Error... 61 Figure 4.29: 1.5A Bottom: LED Pad Temperature vs. Time... 61 Figure 4.30: 1.5A Bottom: % Error... 62 Figure 4.31: 1.5A Middle: LED Pad Temperature vs. Time... 62 Figure 4.32: 1.5A Middle: % Error... 63 viii

List of Tables Table 2.1: Temperature distribution and heat transfer rate for uniform cross section fins... 22 Table 2.2: One Dimensional Thermal Resistance Model Equations... 23 Table 2.3: Two Dimensional Thermal Resistance Model Equations... 26 Table 2.4: MATLAB Model Constants... 30 Table 3.1: Test Matrix... 35 Table 4.1: Experimental Data Steady State Temperature Summary... 40 Table 4.2: Theoretical Data Steady State Temperature Summary... 42 Table 4.3: % Error Summary... 45 Table 4.4: Steady State Pad Temperature Simulation Accuracy... 64 Table 4.5: Convection Coefficient % Difference... 64 Table 4.6: Rayleigh Number for each Input Current... 65 ix

List of Symbols A c E g h H i k L m Nu Pr q Q R Ra T V x, y, z r, θ Area Specific heat Emissive power Acceleration due to gravity Average heat-transfer coefficient Irradiation Electric current Thermal conductivity Length Mass Average nusselt number Prandtl number Heat flux Heat transfer rate Resistance Rayleigh number Temperature Voltage Cartesian coordinates Cylindrical coordinates Greek Symbols α β Absorptivity or thermal diffusivity Thermal expansion coefficient β = 1 ; T T mean = T s + T mean 2 x

σ μ ν Stefan-Boltzmann constant Dynamic viscosity Kinematic viscosity Subscripts b Blackbody or base c Cross-sectional cond Conduction conv Convection e Electrical j Junction L Length rad Radiation s Surface s1 Surface 1 (x = 0) s2 Surface 2 (x = L) th Thermal wall Along the wall Ambient xi

List of Acronyms Acronym ANSI CFD HID LED NTI PCBA Definition American National Standards Institute Computational Fluid Dynamics High Intensity Discharge Light Emitting Diode New Technology Introduction Printed Circuit Board Assembly xii

Transient Simulation of Heat Transfer about an LED Lamp Abstract By KRISTEN BROUWER A transient method for estimating heat transfer about an LED lamp has been developed to estimate the LED pad temperature and has been validated with an experiment. The simulation applies the user defined power and ambient temperature to the predefined system networking the conductive, convective, and radiative heat transfer based on LED lamp geometry and material. The simulation calculates the LED pad temperature and how it changes with time and space. The maximum error of the model when compared to the experimental data is 0.69%. This simulation allows for more time effective design iterations than CFD and more time and cost effective design iterations than building and testing experimental prototypes. xiii

Chapter 1 Introduction Figure 1.1: GE High Output Multi-Vapor Quartz Metal Halide BT56 [1] The first practical Incandescent lamp was invented by Thomas Edison in 1879. Following the Incandescent lamp was the Fluorescent lamp in 1938, the Halogen lamp in 1959, the High Intensity Discharge lamp (HID) and the Visible Light Emitting Diode (LED) in 1962. 1

Historically, the HID lamp has been widely used in commercial spaces that have high installation costs and risks, such as highways and stadiums, due to its long life and high efficiency compared to the other commercially available lighting products. In the past decade, as the LED has become more commercially viable, lamp designers have been working to come up with LED replacement options for the core (Incandescent, Halogen, Fluorescent, and HID) historical technology products seen in the marketplace. The last of these core technologies yet to be replaced is the HID lamp due to its ability to compete with LED products from a life performance standpoint and beat LED from a product cost perspective. As LED technology has gained commercial popularity in the marketplace, its costs have dropped to the point where is considered competitive with comparable HID products. The main benefits of LED technology over HID technology are simple: LED lamps do not contain Mercury like HID lamps and therefore are non-hazardous when broken and do not require costly waste disposal methods at the end of a lamp s life. Additionally, LED lamps maintain color much better than HID lamps over their lifespan making them more appealing in commercial spaces where products are being displayed or in roadway settings where law enforcement needs to be able to accurately see colors of cars. Finally, in what may be the strongest argument for LED technology over HID technology, is that LED lamps are instant on where HID lamps can take up to 15mins to reach full brightness after being turned on. While LEDs are largely competitive with HIDs, LEDs do not perform well in high temperatures; conversely, HID technology thrives in high temperature situations. Until the HID lamp, engineers and designers have been able to replace all core technology lamps with basic passive heat transfer methods. The lamps and fixtures that have been replaced to date have had one thing in common, a low amount of power per unit surface area. LED replacement lamps have all either had small amounts of power in small spaces (i.e. replacement of a 60W Incandescent A19 lamp is only ~10W) or large amounts of area with large amounts of power 2

(i.e. a 4ft x 2ft fluorescent fixture replacement is ~100W). Lamp designers are now faced with the issue of replacing a HID lamp, which requires large amounts of power in small spaces. For example, a 1,000W HID lamp used in high bay and highway applications is being replace with a ~400W LED lamp that is roughly the size of a football. Even by optimizing the thermal efficiency of the lamp design, lamp designers can t dissipate enough heat through natural convection to keep the LEDs cool enough to maintain a long life. 3

Chapter 2 Analysis and Methodology 2.1 Problem Description To date, Computational Fluid Dynamics programs, or CFD, have been the primary tool used to test effectiveness of a heat sink design. Depending on the complexity of the design, a typical CFD simulation on a single design takes ~8-12 hours. The typical lamp design lifecycle to take the concept through to a fully launched commercially available product is roughly a half a year. Due to the lengthy time and high computing power required to run thermal simulations in CFD, it is often not feasible to fully optimize a heat sink design in a reasonable amount of time given the short overall project timeline. The goal of this analysis is to closely duplicate experimental results for a heat sink with inward facing vertical fins using a stacked nodal twodimensional model. A quick and accurate way of estimating heat sink temperatures in lieu of experimental and CFD results is desirable because it allows for a more refined and effective heat sink designs to be developed in less time. Using this technique could allow multiple design permutations to be quickly evaluated from an efficiency perspective. If further analysis was required, CFD could be run on the designs showing the most promise in a method that significantly reduces the design time for a new lamp. 4

Fins are used to enhance heat transfer by increasing convection surface area. Generally, there are two ways commonly used to incorporate fins into a LED replacement lamp design, the fins either face outward on the external surface of the lamp as seen in Figure 2.1 or inward towards the center of the lamp as seen in Figure 2.2. Internal fins we chosen for this particular application rather than outward facing fins because outward facing fins would pose a negative effect on the efficiency of the lamp. Outward facing fins would reduce the optical efficiency of the lamp by blocking and absorbing some of the light output from the LEDs. A reduction in optical efficiency would require the LEDs to be run at higher driver currents in order to create the same desired light output, which would increase the amount of heat needing to be dissipated. Failure to effectively dissipate this heat has the ability to shorten the LEDs effective life. Figure 2.1: LED Replacement Lamp with Outward Facing Fins [2] 5

Figure 2.2: LED Replacement Lamp with Inward Facing Fins Fin orientation is particularly important in this application. This system will primarily be in a vertical orientation. Vertical fins will be more effective that horizontal fins because they will allow for more natural convection during normal operating scenarios. 6

Figure 2.3: Highbay HID Lamp Application [3] The majority of HID lamps are used in high bay ceiling applications where the lamp is hung vertically with the base of the lamp facing up towards the ceiling so that the non-base end with unobstructed light is facing down towards the working floor. Figure 2.3 above shows an example the application of HID lamps. Heat sinks for this particular application must remain within the standard geometrical envelope of a HID lamp. Standard 1,000W HID lamps conform to a BT56 bulb type, where BT stands for the blub shape, blown tubular, and 56 represents the total eighths of an inch make up the maximum diameter of the bulb. Per American National Standards Institute (ANSI) specifications, the LED replacement lamp for a 1,000W HID lamp must fit into a blown tubular 7

envelope shape with a 7-inch maximum diameter, these parameters are depicted in Figure 2.4 below. Figure 2.4: ANSI Dimensions for BT56 Bulb [1] 8

LEDs are semiconductors with light-emitting diode junctions designed to use lowvoltage, constant current DC power to produce light. Figure 2.5: LED Junction Temperature In a typical LED lamp system, LEDs are subjected to various stresses, such as electrical and thermal. Temperature affects the reliability of LEDs and is one of the main cause of failure. Unlike in historical lighting where failure is defined as a catastrophic failure that prevents the lamp from generating light, failure in LED lamp systems is defined as when the light has degraded past the acceptable light output limit for the customer or application. The light output from an LED light source decreases with increasing LED die junction temperature (T j), defined in Figure 2.5 above. As seen in Figure 2.6 below, Higher LED die 9

junction temperatures, resulting from increased power dissipation or changes in ambient temperature, can have a significant effect on light output. Figure 2.6: Junction Temperature Effects on Useful LED Life [4] 2.2 Problem Simplifications In order to make this problem one that can be handled without using Computational Fluid Dynamics (CFD), certain simplifications and assumptions must be made. These simplifications differ depending on the complexity of the analysis. Geometric simplifications are made depending on if the material is moving a relatively small amount of heat in comparison to 10

the amount of mathematical effort and complexity that that component or feature would add to the model. Heat movement assumptions and simplifications are made based on knowledge of substrate material characteristics and how it performs in comparison to the other materials in the overall thermal system. The logic is to simplify and ignore items that only increase accuracy slightly, but increase processing effort significantly. 2.2.1 One-dimensional analysis problem simplifications A one dimensional simplification looks at one small dy section of the entire system and assumes that the small dy section is representative of the entire system. Below are the assumptions and simplifications to the HID LED replacement lamp to begin the problem definition for a one-dimensional analysis: 1. Plastic cap on top dissipate an insignificant amount of heat. For the one dimensional thermal estimation, the plastic cap on the top and bottom of the lamp are insignificant when comparing their length to the overall length of the heat sink. By ignoring this component of the overall system, the results will be less accurate, but not by much because the majority of the heat transfer effects come from the aluminum heatsink and PCBA, which dominate the percentage of the overall system length. 2. Heat dissipated by individual LEDs can be averaged over the outer surface area of the heat sink. Directly beneath the LED pad is a continuous copper substrate connecting all of the LED pads together. Due to copper s very high thermal conductivity, it can be 11

assumed that the power and heat from each individual LED will be dispersed and spread out evenly with a constant flux across the outer PCBA layer of the lamp. 3. Amount of power dissipated as heat from LEDs varies based on current inputted to the LEDs Power is a function of current and voltage. The input voltage is held relatively constant because it is dictated by the LED circuit. This means that the total power of lamp varies based on the amount of current applied to the LEDs. The power dissipated as heat from the LED is a percentage of the total power. 4. One small cross section of the heat sink is representative of the entire heat sink performance After the entire lamp reaches steady state, the temperature across the lamp will be uniform. By ignoring the thermal inertia between each dy and dr segment, the results will not be as accurate. 2.2.2 Two-dimensional analysis problem simplifications A two dimensional simplification stacks the small dy sections discussed above to build the entire system. Below are the assumptions and simplifications to the HID LED replacement lamp to begin the problem definition for a two-dimensional analysis: 1. Heat dissipated by each individual LEDs can be averaged over the outer surface area of the heat sink due to copper substrate Directly beneath the LED pad is a continuous copper substrate connecting all of the LED pads together. Due to copper s very high thermal conductivity, it can be 12

assumed that the power and heat from each individual LED will be dispersed and spread out evenly with a constant flux across the outer PCBA layer of the lamp. 2. Amount of heat dissipated from LEDs varies based on current run through/ inputted to LEDs Power is a function of current and voltage. The input voltage is held relatively constant because it is dictated by the LED circuit. This means that the total power of lamp varies based on the amount of current applied to the LEDs. The power dissipated as heat from the LED is a percentage of the total power. 3. The small vertical cross sections of the heat sink interact thermally with their neighboring cross sections In addition to the conduction between each material substrate, there is also heat flowing up and down the y-axis of the lamp system. Rather than adding the complexity of having the heat as a function of y, a node approach can be applied where there is conduction between each dy stacked section. 2.2.3 Geometrical Simplifications By looking at a small section (dr, dθ, and dy) of the heat sink, the curvature in dr can be assumed to be insignificant. The section can now be analyzed, as seen below in Figure 2.7, in terms on dx and dy: 13

Figure 2.7: Small Section of Heatsink By assuming thermal symmetry because of electrical and geometrical symmetry, we can analyze the smallest symmetrical section rather than the entire cylindrical cross section. Figure 2.8 below shows this simplification. 14

Figure 2.8: Cross section Simplification 2.3 Thermal Resistance Model 2.3.1 Convection and Conduction An electric circuit analogy can be applied to the governing heat transfer equations. i = V R e (2.1) Q = T R th (2.2) where the electric current i is analogous to the heat transfer rate Q, the voltage difference V is analogous to the temperature difference T, and the electrical resistancer e is analogous to the 15

thermal resistance R th. Figure 2.9 shows the visual comparison between equations (2.1) and (2.2). Figure 2.9: Analogy between thermal and electrical resistance concepts [5] The one-dimensional, steady state solution for constant conduction heat transfer rate through a wall is given by: Q cond(x) = ka L (T s1 T s2 ) (2.3) where subscripts s1 and s2 denotes surface 1 (x = 0) and surface 2 (x = L), respectively, k is the thermal conductivity, and A is the area perpendicular to the direction of heat transfer. Fourier s law governs conduction heat transfer in solids and stagnant fluids, it also applies within the fluid immediately adjacent to the wall, the one-dimensional, steady state solution for convection heat transfer rate is given by: 16

Q conv = k f dt dy wall (2.4) where k f is the fluid thermal conductivity and dt/dy wall is the temperature gradient of the fluid along the wall. The empirical rate law frequently adopted to describe convection heat transfer is: Q conv = h conv (T s T ) (2.5) where h conv is the heat-transfer coefficient averaged over the surface are A, T s is the surface temperature, and T is the average fluid temperature far away from the wall or ambient temperature. Applying equation 2.2 to equation 2.3 it can be shown that the thermal resistance for plane wall conduction is R th,plane wall = L ka (2.6) Applying equation 2.2 to equation 2.5, it can be shown that the thermal resistance for convection is R th,conv = 1 h conv A (2.7) Combining knowledge of circuits with thermal resistance is particularly useful for analyzing systems where a surface temperature is unknown. As seen in Figure 2.10, one can use 17

an equivalent resistance using series and parallel resistance, found via circuit summation equations, to determine surface temperature [6]. Figure 2.10: The thermal resistance network for heat transfer through a two-layer plane wall subjected to convection on both sides. [5] 18

2.3.2 Radiation This thermal resistance model can be further expanded to some cases of radiative heat transfer. If we consider a radiation exchange from a gray or black surface to a very large isothermal surface, like that seen in Figure 2.11, one can approximate a radiative thermal resistance. Figure 2.11: Small Surface inside a large isothermal enclosure [7] The energy balance for a radiative surface can be expressed by: q = q emission q absorption = E αh (2.8) 19

where q is heat flux, E is emissive power, α is absorptivity, and H is the irradiation [7]. Assuming that the surface is a gray surface, then the emissivity ε is equal to the absorptance α and irradiation is approximated by emission from a blackbody, H = σt 4 (2.9) the heat transfer rate can be rewritten as: Q rad = AεE b (T s ) AαH = Aεσ(T s 4 T 4 ) (2.10) where σ is the Stefan-Boltzmann constant. By defining the radiative heat transfer coefficient as: h rad = εσ(t s + T )(T s 2 + T 2 ) (2.11) Equation 2.10 can be rewritten as: Q rad = h rad A(T s T ) (2.12) By combining equation 2.2 with equation 2.12, the radiative thermal resistance can be defined as: R rad = 1 h rad A (2.13) 20

2.4 Free Convection Vertical Plates To determine the heat dissipated from the vertical plates by convection in this model, we must first accurately estimate the terms governing laminar convection. Based on equation 2.5, the average heat-transfer coefficient must be determined. The average heat transfer coefficient can be expressed in terms of Nusselt number, Nu L, characteristic length, L, and convection coefficient, k [5]. h = Nu Lk L (2.14) An expression for the Nusselt number developed specifically for laminar flow vertical plates is: Nu L = 0.68 + 0.670Ra L 1 4 4 [1 + ( 0.492 9 9 Pr ) 16 ] Ra L 10 9 (2.15) Where the Rayleigh number, Ra L, is defined as Ra L = gβ(t s T )L 3 να (2.16) And Prandtl number, Pr, is defined as Pr = c pμ k 0.7(for air) (2.17) The heat transfer rate from fins with a uniform cross section can be further defined by applying equations 2.3 and 2.4, boundary conditions, and geometry of the fin to the general form of the energy equation for and extended surface 21

d 2 T dx 2 + ( 1 da c A c dx ) dt dx ( 1 h da s A c k dx ) (T T ) = 0 (2.18) Table 2.1 below shows the results further defining equation 2.18 for fins where the tip conditions are convection heat transfer, adiabatic, and a prescribed temperature. This model uses case A with convective heat transfer from the fin tip. Case Tip Condition (x = L) Temperature Distribution, θ θ b Fin Heat Transfer Rate, q f A Convection heat transfer: hθ(l) = kdθ /dx x=l cosh m(l x) + ( h ) sinh m(l x) mk cosh ml + ( h M ) sinh ml mk sinh ml + ( h ) cosh ml mk cosh ml + ( h ) sinh ml mk B Adiabatic: dθ/dx x=l = 0 cosh m(l x) cosh ml M tanh ml C Prescribed temperature: θ(l) = θ L ( θ L θ b ) sinh mx + sinh m(l x) sinh ml (cosh ml θ L θ ) M b sinh ml θ = T T θ b = θ(0) = T b T m 2 = hp ka c M = hpka c θ b Table 2.1: Temperature distribution and heat transfer rate for uniform cross section fins 2.5 One-dimensional Heat Flow By combining the concepts discussed in sections 2.3 and 2.4, a mathematical model for the simplified one dimensional heat sink discussed in section 2.2 can be developed. Figure 2.12 22

below shows a visual representation of the thermal resistance model of the one-dimensional heatsink. Figure 2.12: One Dimensional Thermal Resistance Model Each thermal resistance depicted in Figure 2.12 is defined below in Table 2.2. Resistance R rad R conv,heat Sink R cond,mcpcb R cond,heat Sink R conv,heat Sink Base R long fin R short fins Equation 1 h rad A 1 ha t L MCPCB k MCPCB A L Heat Sink k MCPCB A 1 h(a t A t,long fin A t,short fin ) θ b q f, see table 2.1 θ b q f, see table 2.1 Table 2.2: One Dimensional Thermal Resistance Model Equations 23

By applying basic circuits knowledge an equation representing the total thermal resistance for the one dimensional heatsink seen in Figure 2.12 and Table 2.2 can be developed, R total = R rad + R cond,mcpcb + R cond,heat Sink 1 + ( + R conv,heat Sink Base 1 R long fin + 1 1 (2.19) ) R short fin 2.6 Two-dimensional Heat Flow In order to model the full length of the heat sink, equation 2.19 for a small dy cross section of the heat sink must be stacked vertically in a nodal network. Figure 2.13 below shows a visual representation of the thermal resistance model seen in Figure 2.12 stacked to represent the two-dimensional heatsink. 24

Figure 2.13: Two Dimensional Thermal Resistance Model Equation 2.19 can still be used to represent each dy radial cross section of heat transfer. An additional conductive thermal resistance must be added to represent the vertical conductive heat transfer that occurs between each small dy cross section of the heat sink. Each thermal resistance depicted in Figure 2.13 is defined below in Table 2.3. Resistance R rad R conv,heat Sink R cond,mcpcb Equation 1 h rad A 1 ha t L MCPCB k MCPCB A 25

R cond,heat Sink R conv,heat Sink Base L Heat Sink k MCPCB A 1 h(a t A t,long fin A t,short fin ) R long fin θ b q f, see table 2.1 R short fins R cond,dy θ b q f, see table 2.1 dy k heatsink A vert Table 2.3: Two Dimensional Thermal Resistance Model Equations 2.7 Unsteady Calculations In addition to temperature varying in multiple space dimensions, this model can be further expanded to include thermal inertia and vary with time. Transient conduction is a heat transfer process for which the temperature varies with time, as well as location within a solid. Transient conduction originates whenever a system experiences a change in operating conditions and proceeds until the system reaches steady state, which is also described as thermal equilibrium. An approach called the lumped capacitance method is a common method used to evaluated transient conduction. The lumped capacitance method is based on the assumption that the temperature gradient across the media is small and is used when the internal temperature of a body remains relatively constant with respect to distance. Consider a body of arbitrary shape and mass initially at temperature T i @ t = 0 is placed into a medium of temperature T. During the time differential dt, the temperature of the body will rise a differential temperature dt. Knowing this, and energy balance for the control 26

volume of the body can be written, stating that the rate of heat loss at the surface must be equal and opposite to the rate of internal energy change. ha s (T T)dt = mcdt (2.20) Where T is the temperature of the body at a given time, T = T(t) [8]. Applying this methodology to this specific model, the energy balance becomes: Q = mc dt(t) dt = q cond q conv (2.21) Where q conv can be derived from Equation 2.5 as: q conv = ha s (T i T ) (2.22) And q cond can be derived from Equation 2.3 as: q cond = T i T i+1 L ka (2.23) And dt/dt can be estimated as: 27

T i n T i n 1 t dt(t) dt (2.24) Where n is the current time step and i is the LED position indicator. Applying Equations 2.22, 2.23, and 2.24 to Equation 2.21, and expression for change in temperature with respect to some small time step can be defined. T = t mc [ha s(t n i T ) ( T i n n T i+1 )] = T L n n 1 i T (2.25) i ka Where c is the average specific heat for the materials comprising mass m. This method for solving for the incremental change in temperature with an incremental change can be applied to the two dimensional model developed in Section 2.6. Allowing this model to be further expanded from multi-dimensional, to time and space dependent. T i n T i n 1 t mc + Q rad + Q cond + Q conv = Q in (2.26) Equation 2.26 incorporates the thermal inertia from the LEDs and the conduction heat transfer from the end caps of the configuration to the radiation, conduction, and convection terms from the main heat sink configuration developed in section 2.6 to define a full power balance of the system. 28

2.8 MATLAB Analysis Model The theories developed in the sections above were combined into a series of functions and programs in MATLAB. A power balance function was written to calculate a pad temperature based on the thermal resistances defined in Sections 2.5 and 2.6 and a given wattage input. That power balance function is then applied to each stacked section discussed in sections 2.2 and 2.6 in a function defining the temperature matrix. The temperature matrix estimates the pad temperature for each dy section and takes temperature inputs from the nodes above and below each particular section, representing conduction between each dy section. Finally, this temperature matrix function is iterated in a Multi-Variable Newton Raphson iteration in order to solve for the pad temperature of each dy section simultaneously. The Multi-Variable Newton Raphson iteration program also iterates the initial guess for the input LED pad temperature using the unsteady heat transfer concepts discussed in Section 2.7 to calculate how the pad temperature changes with time. After the theoretical equations were developed into a model in MATLAB, constants had to be defined based on the geometric and material properties of the test lamp. The table below summarizes the constants used to define the test lamp. All geometric lengths are further defined in Appendix A. Constant Value Units Definition L MCPCB 0.0016 m L MCPCB is the length heat is conducted through the MCPCB. h MCPCB 0.0068 m k MCPCB 0.5 29 W mk L Heat Sink 0.002 m k Heat Sink 210 W mk h MCPCB is the height of the MCPCB in which heat is conducted through. k MCPCB is the thermal conductivity of the MCPCB material. [9] L Heat Sink is the length heat is conducted through the heat sink. k Heat Sink is the thermal conductivity of the heat sink

h calculated from Equations 2.14 2.17 W m 2 K A t A t = W c h Heat Sink m 2 W c 0.0208 m h Heat Sink 0.0068 m A t,long fin A t,long fin = h Heat Sink t fin,long m 2 A t,short fin A t,short fin = 2 h Heat Sink t fin,short t fin,long 0.002 m t fin,short 0.001 m P fin,long P fin,long = 2(L fin t fin,long ) m m 2 h is the convection coefficient. A t is the cross sectional convective heat sink area. W c is the width of the heat sink being examined h Heat Sink is the height of the heat sink in which heat is conducted through. A t,long fin is the cross sectional long fin convective area. A t,short fin is the cross sectional convective area of the two short fins in the section being examined. t fin,long is the thickness of the long fin. t fin,short is the thickness of the short fin. P fin,long is the perimeter of a long fin. P fin,short P fin,short = 2 (2(L fin t fin,short )) m L fin 0.0075 m q f Varies, Total Power q f = ( # of LEDs ) 2 LED section % Power as heat dy 0.0075 m W P fin,short is the perimeter of the two short fins in the small section being examined. L fin is the height of the fin in which heat is conducted through. q f is the input thermal power per section being examined. dy is the total height of each section being stacked vertically. A vert A vert = L MCPCB W c m 2 A vert is the vertical cross sectional area between each vertical stack. *Geometrical dimensions are blacked out, hisgagh, by request of General Electric Table 2.4: MATLAB Model Constants 30

Chapter 3 Experiment 3.1 Heat Sink Prototype Figure 3.1: NTI Lab Thermal Test Cage 31

The objective of the experimental work is to validate the analysis methodology described in Chapter 2 by testing a prototype heat sink. The test is a thermal study on a heat sink with inward facing heat sinking fins with LED PCBAs covering the outside diameter of the heatsink. The results are compared to the results obtained from the MATLAB analysis that combines two dimensional heat flow analysis with unsteady heat flow methodology. The experimental research was performed and collected at Nela Park in East Cleveland in the New Technology Introduction (NTI) Lab. The NTI lab is not a temperature controlled lab. The basic experiment setup included attaching thermocouples to representative LEDs at their junction points, (shown in Figure 2.5), as well as a control spot on the outer edge of the test apparatus to track the ambient temperature. After the prototype unit has been hung inside of the test cage (shown in Figure 3.1), power is applied to the unit via the DC power supply. Applying a constant power to the unit, it is left to reach steady state while the logger records the temperature data from each thermocouple as a function of time. 3.2 Setup The fully assembled test setup is shown in Figure 3.2. The test cage was constructed specifically for this test setup and was designed to hold the test lamp in a vertical base up orientation with the wiring for the power supply entering the cage from the top mogul base. The blue Plexiglas surrounding the lamp is meant to shield the light coming out of the fixture so that the operator doesn t get blinded when the test is started and the lamp is lit. The opening door allows the engineer to access the test lamp and acts as a path for the thermocouples to exit the test cage to plug into the thermal data collector. The Plexiglas housing is open at the bottom, 32

is not sealed at the seams, and is large enough that the walls are very far away from the boundary layer of the lamp and therefore does not affect the ambient temperature assumption. Figure 3.2: Test Setup In this experiment, the test lamp was first prepped with thermocouples. Thermocouples were glued to the junction temperature measurement points (see Figure 2.5) of three representative LEDs, their locations can be seen in Figure 3.3. Based on fundamentals of natural convection, a LED in on the bottom, middle, and top of the test lamp were selected to represent the average junction temperature of the test lamp. An additional thermocouple was hung over the door in the top corner of the test cage to measure the ambient temperature seen by the test lamp. 33

Figure 3.3: Experimental Thermocouple Locations The test lamp was then hung from the screw in mogul base in the test cage. An additional thermocouple was hung inside the test cage away from the test lamp in order to log a baseline ambient temperature. Once the lamp and control thermocouple are securely hung, the thermocouples were then connected to the temperature data logger. The temperature data logger was turned on and began recording data. The test cage door was then closed and the power supply was turned on. Finally, the test was set to a constant power input and the test was left on to thermally stabilize for roughly an hour. The test matrix for this experiment is shown in Table 3.1. 34

Date Start Time Input Current (A) Duration 4/24/2015 10:49:30AM 0.5 130 minutes 4/24/2015 1:05:00 PM 0.75 60 minutes 4/24/2015 2:05:00 PM 1.0 60 minutes 4/24/2015 3:06:00 PM 1.25 56 minutes 4/24/2015 4:02:00 PM 1.5 60 minutes Table 3.1: Test Matrix 3.3 Instrumentation 3.3.1 Omega Thermocouples Omega Copper-Constantan Type T 30AWG 0.01 diameter thermocouples are important to the test setup because they are the components used to transfer the junction temperature of the LED to the thermal data logger. Omega Copper-Constantan Type T 30AWG 0.01 diameter thermocouples were chosen for this application because of their technical specifications and capabilities. 35

Figure 3.4: OMEGA Copper-Constantan Type T Thermocouples Omega Copper-Constantan Type T 30AWG 0.01 diameter thermocouples have a maximum temperature of 150 C and an accuracy of 1.0 C or 0.75% [10]. The upper limits of the junction temperature for the LEDs are 120 C (393.15K). 3.3.2 Agilent Technologies DC Power Supply The Agilent Technologies DC power supply is important to the setup because it provides stable output power. The DC power supply is also the instrument we use in the setup to measure the electrical performance of the test unit because it has the built-in functionality to 36

measure voltage and current. The specific DC power supply being used is the Agilent Technologies N5772A, which has a maximum output voltage of 600V, a maximum output current of 2.6A, and a maximum output wattage of 1500W. This test lamp has a target wattage of 350W using an input voltage of ~233V and an input current of 1.5A. These programming targets are well within the limits of what the Agilent Technologies N5772A DC power supply can deliver. Figure 3.5: Agilent N5772A DC Power Supply The measurement accuracy for the N5772A DC power supply is 0.1% or 600mV for the voltage and 0.1% or 7.8mA for the current. The programming accuracy for the N5772A DC 37

power supply is 0.05% or 300mV for the voltage and 0.1% or 2.6mA for the current [11]. The measurement and programming accuracy on this power supply are deemed acceptable. 3.3.3 Graphtec midi Logger The Graphtec midi Logger is the instrument used to receive, translate, and record the thermal data being measured by the Omega thermocouples. The Graphtec midi Logger GL820 was chosen for this application because it contains an isolated input system which ensures that signals are not corrupted by inputs to other channels. In addition to high accuracy compared to other temperature loggers available on the market, the Graphtec midi Logger GL820has 2-GB of internal memory, this is important to the experimental setup because historically it is known that LED replacement lamps take approximately an hour to thermally stabilize so having an abundance of data storage space is necessary. 38

Figure 3.6: Graphtec midi Logger GL820 The accuracy of the Graphtec midi Logger when used with Type T thermocouples is ±0.1% of reading plus 0.5 C. The range of the Graphtec midi Logger when used with Type T thermocouples is -100 C to 400 C [12]. 39

Chapter 4 Results and Discussion 4.1 Experimental Results The experiment discussed in Chapter 3 was repeated for six different input currents. The initial input current was 0.5A and was increased by 0.25A for each new current setting until the final measurement at 1.5A. After setting each input current, the test lamp was left for approximately one hour so that the LED pad temperature could reach steady state for the new setting. Temperature data from the thermocouples was collected on the Graphtec midi Logger every five seconds for the duration of the test. Table 4.1 below summarizes the steady state pad temperature results for each given input current. Date Start Time I in (A) V in (V) Power (W) Steady State T pad (K) Top Middle Bottom 4/24/2015 10:49:30AM 0.5 226 113 319.1 319.2 319.0 4/24/2015 1:05:00 PM 0.75 227.1 170.3 328.0 328.0 327.8 4/24/2015 2:05:00 PM 1.0 229.4 229.1 335.6 336.1 335.6 4/24/2015 3:06:00 PM 1.25 231.4 289.3 343.6 344.1 343.3 4/24/2015 4:02:00 PM 1.5 233 349.5 352.5 353.2 352.3 Table 4.1: Experimental Data Steady State Temperature Summary Figure 4.1 below is a graphical representation of top, middle, and bottom pad temperatures over time for 0.5A input current. The same graph for the remaining 4 input currents can be found in Appendix A. 40

Figure 4.1: Experimental Pad Temperature vs. Time at 0.5A 41

4.2 Model Results The theoretical analysis developed in Chapter 2 was repeated five times for five different input currents used to collect the experimental data. The initial input current was 0.5A and was increased by 0.25A for each new current setting until the final analysis at 1.5A. The model developed in Chapter 2 and visualized in Figure 2.13 requires a input power for each node, q in. This total power is first calculated using, P = IV (4.1) The total power is then divided by the 480 nodes receiving power and multiplied by 66%, the percent of power dissipated as heat. Based on research done by General Electric and Cree,Inc., the amount of total power dissipated as heat is between 50% and 75% [13] [14]. After many simulations and performing a sensitivity analysis, it was determined that 66% total power dissipated to heat best matched the steady state portion of the experimental data. q in = ( P 480 ) % power as heat (4.2) Table 4.2 below summarizes the theoretical steady state pad temperature results for each given input current, assuming an ambient temperature of 25 O C or 298.15K. I in (A) V in (V) Total Power (W) q in (W) Steady State T pad (K) Top Middle Bottom 0.5 226 113 0.16 318.0 318.0 318.0 0.75 227.1 170.3 0.23 328.1 328.1 328.1 1.0 229.4 229.1 0.32 336.2 336.2 336.2 1.25 231.4 289.3 0.40 343.6 343.6 343.6 1.5 233 349.5 0.48 353.6 353.6 353.6 Table 4.2: Theoretical Data Steady State Temperature Summary 42

Figure 4.2 below is a graphical representation of top, middle, and bottom pad temperatures over time for 0.5A input current. The same graph for the remaining 4 input currents can be found in Appendix A. Figure 4.2: Simulation Pad Temperature vs. Time at 0.5A 43

4.3 Discussion To examine the results of the transient heat transfer simulation developed for a LED lamp, five different power levels were tested until they reached steady state temperature. These five different experimental results were compared to five different transient MATLAB simulations that mimicked the geometry, material properties, and input power of the experimental lamp test setup. Each power level took roughly one hour to reach steady state in the experimental setup, versus a few seconds for the transient MATLAB simulation to run. The simulation estimated LED pad temperatures for all twenty stacks of LEDs that made up the simulated lamp. The experiment measured LED pad temperature for 3 of the 960 LEDs, all of which were in the same dr section, one of which was at the top of the LED stack, one was in the middle of the LED stack, and one was at the bottom of the LED stack. Just those 3 LEDs were selected from the simulation results to compare to the experimental data. Figures 4.3 through Figure 4.32 compare the experimental data and the results from the model and the % error the model data has from the experimental data for a top, middle, and bottom LED for the five different input currents being studied. The model results do not align exactly with the experimental data. Table 4.3 summarizes the minimum and maximum percent error the simulation temperatures has from the experimental data and the minimum and maximum difference in the simulation temperature and the experimental data. Input Current LED Pad Location % Error (Absolute Temperature) % Error (Celsius) T (Kelvin) Minimum Maximum Minimum Maximum Minimum Maximum 0.5A Bottom 0.001% 0.541% 0.008% 4.495% 0.00 1.70 Top 0.002% 0.478% 0.013% 3.647% 0.01 1.50 Middle 0.010% 0.690% 0.069% 5.346% 0.03 2.17 0.75A Bottom 0.001% 0.170% 0.003% 1.101% 0.00 0.55 Top 0.000% 0.180% 0.001% 1.213% 0.00 0.58 Middle 0.001% 0.213% 0.006% 1.310% 0.00 0.70 44

1.0A Bottom 0.000% 0.394% 0.001% 2.280% 0.00 1.30 Top 0.000% 0.428% 0.001% 2.493% 0.00 1.41 Middle 0.001% 0.218% 0.003% 1.165% 0.00 0.73 1.25A Bottom 0.000% 0.456% 0.002% 2.197% 0.00 1.57 Top 0.000% 0.375% 0.002% 1.806% 0.00 1.29 Middle 0.001% 0.300% 0.002% 1.560% 0.00 1.02 1.5A Bottom 0.000% 0.644% 0.001% 2.833% 0.00 2.38 Top 0.000% 0.565% 0.002% 2.483% 0.00 2.00 Middle 0.000% 0.403% 0.002% 1.772% 0.00 1.63 Table 4.3: % Error Summary Figures 4.3 and 4.4 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the top LED location and an input current of 0.5A. Figures 4.5 and 4.6 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the bottom LED location and an input current of 0.5A. Figures 4.7 and 4.8 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the middle LED location and an input current of 0.5A. The discrepancies between the simulation results and the experimental data during the initial temperature rise can be attributed to error in the material properties, standard manufacturing variation from part to part in the PCBA and LEDs causing not every LED to see the same input current, and standard manufacturing variation from part to part of the LED causing some LEDs to convert more or less power to light. As the experimental data reaches steady state, the data starts to oscillate. It could be attributed to fluctuations in the ambient room temperature fluctuating. Further examining this cause, the experimental data and ambient temperature for 0.5A input current graphed in Appendix A shows that the ambient temperature fluctuates in a similar pattern as the LED pad temperature. 45

Figure 4.3: 0.5A Top: LED Pad Temperature vs. Time Figure 4.4: 0.5A Top: % Error 46

Figure 4.5: 0.5A Bottom: LED Pad Temperature vs. Time Figure 4.6: 0.5A Bottom: % Error 47

Figure 4.7: 0.5A Middle: LED Pad Temperature vs. Time Figure 4.8: 0.5A Middle: % Error 48

Figures 4.9 and 4.10 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the top LED location and an input current of 0.75A. Figures 4.11 and 4.12 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the bottom LED location and an input current of 0.75A. Figures 4.13 and 4.14 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the middle LED location and an input current of 0.75A. For the top and bottom points, the simulation agrees very well with the experimental data. The middle point simulation predicts high temperature during the rise and low temperature as the lamp reaches steady state compared to the experimental data. Overall, the highest % error for the 0.75A input current is only 0.213%. Figure 4.9: 0.75A Top: LED Pad Temperature vs. Time 49

Figure 4.10: 0.75A Top: % Error Figure 4.11: 0.75A Bottom: LED Pad Temperature vs. Time 50

Figure 4.12: 0.75A Bottom: % Error Figure 4.13: 0.75A Middle: LED Pad Temperature vs. Time 51

Figure 4.14: 0.75A Middle: % Error Figures 4.15 and 4.16 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the top LED location and an input current of 1.0A. Figures 4.17 and 4.18 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the bottom LED location and an input current of 1.0A. Figures 4.19 and 4.20 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the middle LED location and an input current of 1.0A. The largest error between the simulation results and the experimental data occurs during the temperature rise of the top and bottom LEDs. During the rise of these LEDs, the simulation predicts a slower temperature ramp up than is seen in the experimental data. 52

Figure 4.15: 1.0A Top: LED Pad Temperature vs. Time Figure 4.16: 1.0A Top: % Error 53

Figure 4.17: 1.0A Bottom: LED Pad Temperature vs. Time Figure 4.18: 1.0A Bottom: % Error 54

Figure 4.19: 1.0A Middle: LED Pad Temperature vs. Time Figure 4.20: 1.0A Middle: % Error 55

Figures 4.21 and 4.22 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the top LED location and an input current of 1.25A. Figures 4.23 and 4.24 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the bottom LED location and an input current of 1.25A. Figures 4.25 and 4.26 show the experimental data compared to the simulation results and the % error the simulation results have from the experimental data for the middle LED location and an input current of 1.25A. For all three points, the largest percent error occurs when the simulation reaches steady state. The experimental data drops off rather than leveling out. Further observing the LED pad temperatures and the ambient temperature versus time in Appendix A, no major change in the room temperature that explains the dip seen in the 0.5A input current is seen. This drop may come from drift from the power supply as voltage from the wall going into the power supply is not steady. Figure 4.21: 1.25A Top: LED Pad Temperature vs. Time 56