本論文研究目的為計算多熱源之等效面積與平板熱管尺寸對擴散熱阻的影響，比較理論解析與電腦數值模擬結果。主要動機為現今與擴散熱阻相關的文獻多以理論解析為主，主要以傳統金屬材料為探討方向，並以數值模擬與實驗之結果比對。面對現今系統散熱設計，隨著多熱源以及高發熱瓦數晶片在高階電子系統的應用，本文以推導等效熱源面積關係式，探討多熱源散熱模組在設計上所需考慮的參數，配合電腦數值模擬提出改善散熱模組散熱效能的最佳化設計方法，本論文中將設計參數代入無因次等效熱源面積關係式，並將之運用於多熱源熱傳遞的分析，藉由比較熱阻方程式、電腦模擬分析結果與實驗數據之差異，提出建立熱源發熱功率、熱源面積、平板熱管厚度及熱源相對位置之間熱傳導與熱對流熱阻的參數最佳設計區間，並參考Bi數作為瞭解小面積熱源的熱傳遞模式，以為應用平板熱管散熱模組最佳化設計之基礎。
   對於本研究所探討之多熱源平板熱管散熱模組最佳設計，配合多熱源散熱模組之實驗量測，熱源的最高溫度值誤差為3.3%，利用等效熱源關係式以電腦數值模擬的方法可以準確的預測多熱源在平板熱管散熱模組的熱傳機制。

The objective of this thesis is to compute the spreading thermal resistance of multiple heat sources on a vapor chamber module, as well as the surface temperatures and the heat flux distributions at the heating surface. The analytical correlations are expressed in a dimensionless with the governing parameters of the relative distance dimensions between heat sources and dimensionless heat sources size on heat spreader, including a vapor chamber and metal materials evaluation, subject to the influence of multiple heat sources. This study also presents vapor chamber temperature distribution on heat spreader contact surface, and it correlates to heat sources number and distance. Hence, spreading thermal resistance decreases with the increasing lateral length of vapor chamber. There is large difference between spreading and conductive thermal resistance as lateral length is disproportion to heat source heating area. Therefore, spreading thermal resistance is an important factor when design the thermal solution of a high density chipset power, and it caused high temperature in heat sources which embedded a thinner heatsink base, especially. Spreading thermal resistance is disproportion to heat spreader size, material conductivity, then conductive thermal resistance is not the only parameter for vapor chamber module design, it needs to consider the spreading resistance effect of a vapor chamber and multiple heat sources array, Bi number can be fairly understood by imagining the heat flow from small and hot heat sources suddenly immersed in a pool, to the surrounding fluid. Numerical simulation results of the integrated vapor chamber module are carried out with the mathematical model. The computed results are in good agreement with the experiments, and deliver a difference of 3.3% for the maximum heat source temperature rises, and it presents predictable thermal phenomena of a vapor chamber applying on multiple heat sources.

Table of Content
Title Page	 II
Signature page     III
Acknowledgements	 IV
Abstract (Chinese)  V
Abstract (English) VII
Table of Content	 IX
List of Figure	 XII
List of Table      XVIII
Nomenclature       XX
Chapter 1 Introduction 1
1.1  Motivation for research 3
1.2  Literature review 5
Chapter 2  Multiple heat sources in electronics cooling	13
2.1  Heat generating in electronics and present applications 13
2.2  Current cooling technologies 15
2.3  Roadmap for cooling in high power electronics 17
2.4  Manufacture processes of vapor chamber 19
2.4.1  Heat transport limitations 21
2.4.2  Vapor chamber dynamics 22
2.4.3  The working fluid 24
2.4.4  The wick structure 26
Chapter 3  Formula and solution 29
3.1  Spreading thermal resistance 30
3.2  Base thickness design of a vapor chamber	33
3.3  Fins	 35
3.3.1  Fin design parameters 36
3.3.2  Suggestions of fin design 40
3.4  Biot number 40
3.5  Temperature equation 41
3.6  General equation of multiple heat sources 45
3.6.1  Multiple heat sources in circular array 48
3.6.2  Multiple heat sources in matrix array	51
Chapter 4  Experiment 56
4.1  Experimental setup and calibration 56
4.2  Experiment results of dual resources (natural convection) 59
4.3  Thermal resistance measurement for VC performance validation (liquid cooling)	64
4.3.1  Test conditions 64
4.3.2  Test equipment of liquid cooling 64
4.3.3  Thermocouple locations 65
4.3.4  Definition of thermal resistance 66
4.3.5  Test data 66
4.3.4  Definition of thermal resistance 66
4.4  Thermal resistance measurement (wind tunnel) 67
4.5  Experiment setup of quad heat sources (LED natural cooling)	71
Chapter 5  Numerical ayalysis 77
5.1  Overview of thermal modeling in electronics cooling	77
5.2  Simulation setup 79
5.3  Modeling 80
5.4  Fin optimization by simulation	82
5.5  Numerical analysis referred to experimental data 84
5.6  Vapor chamber application on multiple heat sources cooling 91
5.7  Contour plot of response surface optimization 95
5.8  Error correction 99
5.9  Uncertainty analysis 100
Chapter 6  Conclusion and future work 103
6.1  Conclusion 103
6.1.1  Design an optimal geometry heat spreader for multiple heat sources cooling 104
6.1.2  Analysis thermal phenomena of multiple heat sources heat spreading on a vapor chamber 104
6.2  Future work 106
References 107
Appendix I    Introduction of linear regrssion method	115
Appendix II   Thermocouple calibration 120
Appendix III  Thermal conductivity of material property	121
Appendix IV  Vapor chamber orientation test data 122
Appendix V   Reliabilitytest of a vapor chamber 125
Publication list 132

List of Figures
Fig.1.1   Experiment result of thermal resistance and air volume flow	3
Fig.1.2   Heat dissipation path of a chipset package	4
Fig.1.3   The design range by using a vapor chamber to a metal heatsink.	5
Fig.1.4   Illustration of heat flux spreading in base	6
Fig.1.5   Dimensionless geometry variation to heat source temperature	6
Fig.1.6   Temperature map of source plane for heatsink	7
Fig.1.7   Thermal resistance difference by spreader sizes	8
Fig.1.8   Surface temperature distribution at copper base plate thickness of 5mm	9
Fig.1.9   Maximum temperature location at aluminum heatsink base	10
Fig.1.10  Correlation factor to heat source location	10
Fig.1.11  Quad heat sources dimension definition	11
Fig.1.12  Equivalent heat source and thermal resistance with heat source size	12
Fig.1.13  Equivalent heat source and thermal resistance with heat source location	12
Fig.2.1   Chipset array on a print circuit board	14
Fig.2.2   LED array for lighting applications	14
Fig.2.3   Different shapes of vapor chambers	15
Fig.2.4   System on chip power consumption trends	17
Fig.2.5   Vapor chamber configuration	20
Fig.2.6   Vapor chamber manufacture processes	20
Fig.2.7   General working behavior of a vapor chamber	21
Fig.2.8   An operating cycle diagram of a vapor chamber	23
Fig.2.9   Flow chart of a vapor chamber operating phenomena	24
Fig.2.10  Microscope picture of sintered particles	27
Fig.2.11  Sintered wick structure of a vapor chamber	28
Fig.3.1   Schematic diagram of the square base spreader	29
Fig.3.2   Heat source with temperature distribution on a heatsink	31
Fig.3.3   Temperature profiles at the surface of aluminum extrusion	32
Fig.3.4   Temperature profiles at the surface of extrusion with vapor chamber	32
Fig.3.5   Thermal resistance network	33
Fig.3.6   Block resistance with base thickness of the fin attached spreader	34
Fig.3.7   Heat spreader thermal resistance with base thickness	35
Fig.3.8   Fin types by various manufacture processes	36
Fig.3.9   Sketch of fin parameters	37
Fig.3.10  Heat spreader with dual heat sources	42
Fig.3.11  Heat sources locations on heat spreader	42
Fig.3.12  Thermal resistance network of dual heat sources	43
Fig.3.13  Top surface temperature distribution of dual heat sources by Muzychka et al.'s solution	44
Fig.3.14  Top surface temperature distribution of dual heat sources by Yun Ho Kim a, et al.’s solution	44
Fig.3.15  Thermal spreading resistances vs. heat flux	45
Fig.3.16  Flow chart of multiple heat sources design target	46
Fig.3.17  Calculate multiple heat sources from equivalent heat source	47
Fig.3.18  Methodology of multiple heat sources to an equivalent heat source	48
Fig.3.19  Description of multiple heat sources in circular array	49
Fig.3.20  Dimensionless size of a single equivalent heat source	51
Fig.3.21  Multiple heat sources in matrix array	52
Fig.3.22  Zoom in the multiple heat sources in matrix array	52
Fig.3.23  Temperature distribution of matrix array heat sources on heat spreader	54
Fig.3.24  Correlation of equivalent heat source with dimensionless heat source size of heat spreaders	55
Fig.4.1   Thermocouple measured locations	56
Fig.4.2   Experiment equipment description	58
Fig.4.3   Sketch of test piece measured points	58
Fig.4.4   Vapor chamber structure embedded on a heatsink base	59
Fig.4.5   Application of vapor chamber (Lower spreading resistance)	61
Fig.4.6   Aluminum heatsink (Higher spreading resistance)	61
Fig.4.7   Temperature difference comparison of various ambient	62
Fig.4.8   Temperature description of different fin efficiency	63
Fig.4.9   Thermal resistance comparison of various ambient	63
Fig.4.10  Test platform of liquid cooling	64
Fig.4.11  Test piece description	65
Fig.4.12  Thermocouple location on vapor chamber	65
Fig.4.13  Cooling surface area of vapor chamber	65 
Fig.4.14  IR Picture for surface temperature difference comparison	67
Fig.4.15  Air flow direction of test piece	68
Fig.4.16  Wind tunnel for providing system flow and impedance	68
Fig.4.17  Thermal test platform with wind tunnel	69
Fig.4.18  Comparison thermal resistance with vapor chamber and blocked by input power	69
Fig.4.19  Test procedures from heat sources distance 20mm to 50mm	71
Fig.4.20  Test methodology and equipment (natural convection with fin)	72
Fig.4.21  Natural convection chamber	72
Fig.4.22  Reliability of a cool white LED luminous flux efficiency	73
Fig.4.23  Correlation concept of multiple heat sources and equivalent heat source	74
Fig.4.24  Temperature measured point of equivalent heat source	75
Fig.4.25  Test configuration of an equivalent heat source	76
Fig.5.1   Finite difference method for system modeling	78
Fig.5.2   Simulation processes flow chart	80
Fig.5.3   Finite element location design range by minimizing Tjuncton temperature of dual heat sources	82
Fig.5.4   Configuration of a vapor chamber embedded on plat fin heatsink	82
Fig.5.5   Sggested fan-less thermal solution for 4W	83
Fig.5.6   Suggested fan-less thermal solution for 7W	83
Fig.5.7   Design range of fin number 50~60	84
Fig.5.8   Conductivity comparison with vapor chamber and copper plate by increasing input power	86
Fig.5.8   Contour plot of temperature distribution with heat source on a spreader corner	86
Fig.5.9   Material conductivity to thermal resistance by multiple heat sources	87
Fig.5.10  Heat sources temperature by varying power input of multiple heat sources number	87
Fig.5.11  Percentage of spreading thermal resistance on the total thermal resistance by different heat spreader materials	88
Fig.5.12  Dimensionless spreading thermal resistance varies with the distance (h=100)	89
Fig.5.13  Spreading thermal resistance of heat spreaders by multiple heat sources and dimensionless heat source pitch	90
Fig.5.14  Experiment data comparison with numerical result	91
Fig.5.15  Thermal resistance of various dimensionless heat source size and distance (h=100 W/m2C)	92
Fig.5.16  Total thermal resistance vs. convection coefficient (m/l= 0.167)	92
Fig.5.17  Heat conduction inside the body is much faster than the heat conduction away from its surface (m/l= 0.167)	93
Fig.5.18  Thermal resistance compare with Bi number by dimensionless distance (m/l= 0.167)	94
Fig.5.19  Optimal design domain calculated by spreading resistance and dimensionless heat source area	95
Fig.5.20  Optimal response surface temperature of a vapor chamber (d/l=0.25)	96
Fig.5.21  Optimal response surface temperature of a vapor chamber (d/l=0.4)	97
Fig.5.22  Surface temperature distribution along lateral length of a vapor chamber (Thickness = 3.5mm, h>500 W/m2K)	98
Fig.5.23  Optimal design domain with base thickness and convection coefficient of a vapor chamber	 98
Fig.6.1   Concept of advanced vapor chamber heatsink design	106

List of Tables
Table 2.1  Maximum power dissipation of 0.98W/mm2 for a single chip by 2013	18
Table 2.2  Thermal spec of system performance requirement	19
Table 2.3  Properties of considered liquids	25
Table 3.1  Base thickness design range by different materials	35
Table 3.2  Correlation factor of equivalent heat source in circular array.	50
Table 3.3  Correlation factor of equivalent heat source in matrix array	53
Table 4.1  T-type thermocouple calibration data	57
Table 4.2  Temperature differences on various fin orientation and contact wall materials	60
Table 4.3  Experiment data of vapor chamber by liquid cooling	64
Table 4.4  Test data of thermal resistance by liquid cooling	66
Table 4.5  Experiment data of vapor chamber heatsink (wind tunnel)	67
Table 4.6  Thermal resistance measured data of vapor chamber	70
Table 4.7  Vapor chamber application on LED cooling (natural convection)	71
Table 4.8  Cree cool white LED thermal spec and reliability	73
Table 4.9  DOE Energy Star strategy for solid-state lighting general illumination products establishes a transitional approach	73
Table 4.10  Experimental scenarios of quad heat sources thermal test data	 74
Table 4.11  Test data of equivalent heat source	76
Table 5.1   Material properties of simulation models setup	85
Table 5.2   Simulation data of vapor chamber	91
Table 5.3   Experimental error and calculated uncertainty data	102

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