臺灣博碩士論文加值系統

在本論文研究中，建立了一系列的實驗系統及實驗方法，來探討在水平渠道內空間中高性能散熱座在不同冷卻方法下之熱流特性。冷卻方法分為(一)自然對流與(二)水平渠道內之強制對流兩種。在研究中探討影響自然對流及水平渠道內之強制對流之相關參數分別列之如下：(一)自然對流－穩態格拉雪夫數(GrS)與散熱座高度與渠道高度比(H/HC)。這些參數的探討範圍是GrS=6.42x105~1.64x106與H/HC=0.47~1.0。(二)強制對流－穩態格拉雪夫數(GrS)、散熱座高度與渠道高度比(H/HC)與雷諾數(ReD)。這些參數的探討範圍是GrS=1.66x105~1.05x105，H/HC=0.47~1.0與ReD=7356-30767。
在水平渠道內高性能散熱座之流力特性方面，本研究探討的流力特性包括：局部流速分佈、局部紊流強度分佈與壓降變化。從實驗量測結果顯示：雷諾數對側向無因次化流速分佈之影響並不明顯；針對非高性能散熱座的所有實驗情形，局部紊流強度分佈在0.47�T H/HC �T1.0與1.98m/s<Ui<8.02m/s的範圍內皆小於7.5%。本研究發展出一個理論模式，可以成功的預測散熱座在渠道內有旁通效應下的流速分佈以及壓力降，其預測與實驗量測結果相當吻合。
在無限制及限制空間中高性能散熱座之自然對流熱傳特性方面，分別針對暫態/穩態之局部和平均熱傳特性作探討。研究結果顯示：暫態/穩態之局部和平均紐賽數隨著GrS增加而增大，但其隨著H/HC的增加而減小；研究中亦針對無限制及限制空間中高性能散熱座之自然對流熱傳特性分別提出兩條新的經驗公式。
在水平渠道內高性能散熱座之強制對流熱傳特性方面，本研究先後針對暫態/穩態之局部和平均熱傳特性作探討。研究結果顯示：在相關影響參數的探討中，發現紐賽數會隨著GrS、H/HC與ReD的增加而增大。對於不同材質鰭片和基座所組成的散熱座也可以發現同樣的趨勢。研究中亦針對高性能散熱座在渠道內強制對流之熱傳特性提出新的經驗公式。
根據變異數分析F檢定法，本研究完成實驗相關參數之敏感度分析。經過與實驗數據的比對，確立熱阻與壓力降的反應曲面法二次方模型之準確度。同時，藉由反應曲面法建立了條件限制的分析模型並找出在中央合成設計中影響熱阻與壓力降的關鍵參數；進而應用連續二次規劃法有效的探討各種限制條件下的最佳化設計。最後，研究中亦針對四種不同限制條件情況下得到數值最佳化之結果，與實驗數據比對皆相當吻合。

ABSTRACT

A series of experimental studies on the fluid flow and heat transfer characteristics from non-compact/compact PPF heat sinks at unconfined and confined condition by using different cooling methods have been performed. Two types of cooling methods such as natural convection and forced convection due to channel flow are employed in the present study. The relevant parameters influencing fluid flow and heat transfer performance in natural convection and forced convection studies are listed, respectively. They are: (1) natural convection－the steady-state Grashof number (GrS) and ratio of heat sink height to channel height (H/HC). The ranges of these parameters studied are GrS=6.42x105~1.64x106 and H/HC=0.47-1.0; (2) forced convection－the steady-state Grashof number (GrS), ratio of heat sink height to channel height (H/HC)and Reynolds number (ReD). The ranges of these parameters studied are GrS =1.66x105~1.05x106 (or qC = 2486.56W/m2 ~ 15676.90W/m2), H/HC=0.47~1.0 and ReD=7356~30767. Their effects on fluid flow and heat transfer characteristics in natural convection and forced convection have been systematically explored.
In the hydrodynamic aspect for confined compact heat sinks in channel flow, the fluid flow characteristics including the spanwise velocity distribution, local turbulence intensity distribution, and pressure drop are investigated. From the results, the spanwise dimensionless velocity distributions are not significantly affected by Reynolds number. Besides, for all the cases of non-compact heat sinks, the turbulence intensities at all measuring locations are less than 7.5% for the cases with 0.47<H/HC< 1 and 1.98m/s<Ui<8.02m/s. A theoretical model to effectively predict the velocity and pressure drop for partially-confined heat sinks has been successfully developed. The results show good agreement between the predicted and the experimental data.
For unconfined/confined compact heat sinks in natural convection, the transient/steady-state local and average heat transfer characteristics are studied. The transient/steady-state local and average Nusselt number increases with increasing GrS, but decreasing with H/HC. In addition, two new correlations of steady-state average Nusselt numbers in terms of relevant influencing parameters for unconfined and confined compact PPF heat sinks in natural convection are proposed, respectively.
For confined compact heat sinks in forced convection, the transient/steady-state local and average heat transfer characteristics are successively explored. The transient/steady-state local and average Nusselt numbers increase with increasing GrS, H/HC ratio or ReD. Similar trend can be found for the cases at different heat sink fin and base materials. In addition, a new correlation of steady-state average Nusselt number in terms of relevant influencing parameters for confined compact PPF heat sinks in forced convection is proposed.
According to the results in ANOVA, a sensitivity analysis for the design factors is performed. The accuracies of the quadratic RSM models for both thermal resistance and pressure drop have been verified by comparing the predicted response values to the actual experimental data. The Response Surface Methodology is applied to establish analytical models of the thermal resistance and pressure drop constraints in terms of the key design factors with a CCD experimental design. By employing the Sequential Quadratic Programming technique, a series of constrained optimal designs can be efficiently performed. The numerical optimization results for four cases under different constraints are obtained, and the comparisons between these predicted optimal designs and those measured by the experimental data are made with a satisfactory agreement.

ABSTRACT i
ACKNOWLEDGMENT iv
LIST OF TABLES xiii
LIST OF FIGURES xvi
NOMENCLATURE xxxi

CHAPTER 1 INTRODUCTION AND BACKGROUND 1
1.1 RATIONALE 1
1.2 FUNDAMENTAL MECHANISM OF HEAT SINKS 3
1.2.1 Fluid Flow Characteristics 3
1.2.2 Heat Transfer Characteristics 6
1.3 LITERATURE SURVEY 7
1.3.1 Fluid Flow Characteristics of Heat Sinks 8
1.3.2 Heat Transfer Characteristics of Heat Sinks 9
1.3.3 Optimal Design 12
1.4 RESEARCH TOPICS AND OBJECTIVES 14
1.5 THESIS ORGANIZATION 16

CHAPTER 2 THE EXPERIMENTS 18
2.1 DESCRIPTION OF EXPERIMENTAL FACILTIES 18
2.1.1 Air Supply System 19
2.1.2 Pressure Load Unit 20
2.1.3 Test Section 20
2.1.4 Type of Test Assembly 21
2.1.5 Apparatus and Instrumentation 22
(A) Air Velocity Measurement 22
(B) Pressure Drop Measurement 23
(C) Temperature Measurement 23
(D) Power Input Measurement 24
(E) Heat Flux Measurement 24
(F) Emissivity Measurement of Heat Sinks 25
2.2 DATA ACQUISITION AND CONTROL 25
2.3 EXPERIMENTAL PROCEDURE 26
2.3.1 Start-up Procedure and Operating Procedure 27
2.3.2 Shutdown Procedure 28
2.4 DATA REDUCTION 28
2.5 TEST MATRIX 32
2.5.1 Non-compact Heat Sink 32
2.5.2 Compact Heat Sink 33
2.6 UNCERTAINTY ANALYSIS 33
2.7 SENSITIVITY ANALYSIS 34

CHAPTER 3 METHODOLOGY FOR OPTIMAL DESIGN 84
3.1 DESIGN OF EXPERIMENTS – CENTRAL COMPOSITE DESIGN 84
3.2 RESPONSE SURFACE METHODOLOGY 86
3.3 SEQUENTAL QUADRATIC PROGRAMMING 88

CHAPTER 4 FLUID FLOW CHARACTERISTICS
FOR CONFINED COMPACT HEAT SINKS 92
4.1 EXPERIMENTAL INVESTIGATION 92
4.1.1 Local Mean Spanwise Velocity Distribution 93
4.1.2 Local Turbulence Intensity Distribution 94
4.2 THEORETICAL PREDICTION 94
4.2.1 Bypass Effect in Unconfined Flow 94
4.2.2 Prediction Procedure 97
4.3 RESULTS AND DISCUSSION 101
4.3.1 Velocity Distribution 101
4.3.2 Pressure Drop 102

CHAPTER 5 NATURAL CONVECTIVE HEAT TRANSFER
FOR CONFINED COPACT HEAT SINKS 146
5.1 DEFINITIONS OF HEAT TRANSFER PARAMETERS 147
5.2 TEMPERATURE DISTRIBUTIONS ON HEAT SINK BASE 149
5.3 TRANSIENT HEAT TRANSFER CHARACTERISTICS 150
5.3.1 Transient Heat Flux Distributions of Input Power 150
5.3.2 Transient Convective Heat Flux Distribution 151
(A) Effect of Steady-State Grashof Number 151
(B) Effect of H/HC Ratio 151
5.3.3 Transient Local Heat Transfer Characteristics 153
(A) Effect of Steady-State Grashof Number 153
(B) Effect of H/HC Ratio 155
5.3.4 Transient Average Heat Transfer Characteristics 155
(A) Effect of Steady-State Grashof Number 155
(B) Effect of H/HC Ratio 156
5.4 STEADY-STATE HEAT TRANSFER CHARACTERISTICS 156
5.4.1 Steady-State Local Heat Transfer Performance 157
(A) Effect of Steady-State Grashof Number 157
(B) Effect of H/ H/HC Ratio 157
5.4.2 Steady-State Average Heat Transfer Performance 158
(A) Effect of Steady-State Grashof Number 158
(B) Effect of H/HC Ratio 158
5.4.3 Correlation of Steady-State Average Heat Transfer Characteristics 159

CHAPTER 6 FORCED CONVECTIVE HEAT TRANSFER
FOR CONFINED COMPACT HEAT SINKS 208
6.1 DEFINITIONS OF HEAT TRANSFER PARAMETERS 209
6.2 TEMPERATURE DISTRIBUTIONS ON HEAT SINK BASE 211
6.3 TRANSIENT HEAT TRANSFER CHARACTERISTICS 212
6.3.1 Transient Heat Flux Distributions of Input Power 212
6.3.2 Transient Convective Heat Flux Distribution 213
(A) Effect of Steady-State Grashof Number 213
(B) Effect of H/HC Ratio 214
(C) Effect of Reynolds Number 214
6.3.3 Transient Local Heat Transfer Characteristics 215
(A) Effect of Steady-State Grashof Number 215
(B) Effect of H/HC Ratio 216
(C) Effect of Reynolds Number 217
6.3.4 Transient Average Heat Transfer Characteristics 218
(A) Effect of Steady-State Grashof Number 218
(B) Effect of H/HC Ratio 218
(C) Effect of Reynolds Number 219
6.4 STEADY-STATE HEAT TRANSFER CHARACTERISTICS 219
6.4.1 Steady-State Local Heat Transfer Performance 220
(A) Effect of Steady-State Grashof Number 220
(B) Effect of H/HC Ratio 221
(C) Effect of Reynolds Number 221
6.4.2 Steady-State Average Heat Transfer Performance 222
(A) Effect of Steady-State Grashof Number 222
(B) Effect of H/HC Ratio 222
(C) Effect of Reynolds Number 223
6.4.3 Correlation of Steady-State Average Heat Transfer Characteristics 223

CHAPTER 7 OPTIMAL DESIGN FOR CONFINED COMPACT HEAT SINKS 277
7.1 DESIGN VARIABLES OF COMPACT HEAT SINKS 278
7.2 MODEL ACCURACY EVALUATION 279
7.3 NUMERICAL OPTIMIZATION 280

CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS 319
8.1 CONCLUSIONS 319
8.1.1 Fluid Flow Characteristics for Confined Compact Heat Sinks 320
8.1.2 Natural Convective Heat Transfer for Confined Compact Heat Sinks 321
8.1.3 Forced Convective Heat Transfer for Confined Compact Heat Sinks 322
8.1.4 Optimal Design for Confined Compact Heat Sinks 324
8.2 RECOMMENDATIONS 325

REFERENCES 326
APPENDIX A CALIBRATION OF AIR VELOCITY 330
APPENDIX B EMPIRICAL CORRELATIONS FOR AIR PROPERTIES 335
APPENDIX C RADIATIVE HEAT LOSSES FROM HEAT SINK SURFACE TO SURROUNDINGS 339
APPENDIX D INTERNAL ENERGY CHANGE OF HEAT SINK DURING POWER-ON TRANSIENT PERIOD 344
APPENDIX E UNCERTAINTY ANALYSIS 345
VITA 360
LIST OF PUBLICATIONS 361

REFERENCES

Ashiwake, N., Nakayama, W., Daikoku, T., and Kobaiashi, F., 1983, “Forced Convection Heat Transfer from LSI Packages in an air-cooled wiring card array,” ASME Heat Transfer in Electronic Equipment, HTD-Vol. 28, p.35.
Box, G. E. P. and D. W. Behnken, 1960, “Some New Three Level Designs for the Study of Quantitative Variables,” Technometrics, 2, pp.455-475.
Catharina R. Biber, Christian L.Belady, “Pressure Drop Prediction for Heat Sinks: What Is The Best Method?,” ASME Advances in Electronic Packaging, Vol.2, 1997, pp.1829-1835.
Chen, H. T., Horng, J. T., Chen, P. L., and Hung, Y. H., 2004, “Optimal Design for PPF Heat Sinks in Electronics Cooling Applications,” ASME Journal of Electronic Packaging , May. (In Press)
Ellison, G. N., 1984, Thermal Computations for Electronic Equipment, Van Nostrand Reinhold Company, New York.
Gooding, J. S., Jaeger, R. C., Mackowski, D. W., Fahrner, C. J., and Hingorani, S., 1994, "Optimal Sizing of Planar Thermal Spreaders," ASME Journal of Heat Transfer, Vol.116, pp.296-301
Ishizuka, M., Yokono, Y., and Hisano, K., 1999, "Experimental Study on the Performance of Compact Heat Sink for LSI Packages," Advances in Electronic Packaging, EEP-Vol. 26-1, pp. 713-718.
Jeng, T. M, 2002, “Fluid Flow and Heat Transfer Behavior in Porous Channels,” Ph.D. Thesis, Department of Power Mechanical Engineering, National Tsing Hua University, Taiwan, R.O.C..
Jonsson, H., and Moshfegh, B., 2001, “Modeling of the Thermal and Hydraulic Performance of Plate Fin, Strip Fin, and Pin Fin Heat Sinks—Influence of Flow Bypass, ” IEEE Transactions on Components and Packaging Technologies, Vol. 24, No. 2, June.
Kuo, S. T., 2002, “Fluid Flow And Heat Transfer for Confined Heat Sinks,” Master’s Thesis, Department of Power Mechanical Engineering, National Tsing Hua University, Taiwan, R.O.C..
Kim, S. J., and Kim, D., 1999, “Forced Convection in Microstructures for Electronic Equipment Cooling, “ ASME J. Heat Transfer, Vol. 121, pp. 635-645.
Kraus, A. D., and Bar-Cohen, A., 1995, Design and Analysis of Heat Sinks, John Wiley and Sons, Inc., New York.
Khuri, Andre I., Cornell, John A., 1996, Response surfaces: designs and analyses, second edition, Marcel Dekker.
Linton, R. L., and Agonafer, D., 1995, “Coarse and detailed CFD modeling of a finned heat sink,”IEEE Trans., Comp., Packag., Manufact., Technol. A, Vol. 18,pp517-520, Sep.
Liu, L. K, 2004, “Fluid Flow and Heat Transfer from Heated Extended Surfaces with Confined Slot Jet Impingement,” Ph.D. Thesis, Department of Power Mechanical Engineering, National Tsing Hua University, Taiwan, R.O.C..
Matsushima, H., Yanagida, T., and Kondo, Y., 1992, “Algorithm for Predicting the Thermal Resistance of Finned LSI Packages Mounted on a Circuit Board,” Heat Transfer Japanese Research, Vol. 21, No. 5, pp. 504-517.
Madhusudan, L., and Bar-Cohen, A., 1998, “Optimization of Vertical Pin-Fin Heat Sinks in Natural Convective Heat Transfer,” Heat Transfer, Proceeding of 11 th IHTC, Vol. 3 August 23-26, Kyongju, Korea, pp.501-506.
Mills, A. F., 1999, Basic Heat and Mass Transfer, Prentice-Hall, Inc., New Jersey.
Monthomery, D. C., 2001, Design and Analysis of Experiments, 5rd ed., New York.
Narasimhan, S., Bar-Cohen, A. and Nair, R., 2003, “Flow and Pressure Field Characteristics in the Porous Block Compact Modeling of Parallel Plate Heat Sinks,” IEEE Transactions on Components and Packaging Technologies, vol. 26, No. 1, March.
Raymond H. Myers, Douglas C., 2002, Response surface methodology: process and product optimization using designed experiments, second edition, J. Wiley.
Starner, K. E., and McManus, H. N., Jr., 1963, “An Experimental Investigation of Free Convection Heat Transfer from Rectangular Fin Array,” ASME J. Heat Transfer, Vol. 85, pp. 273-278.
Sparrow, E. M., Baliga, B. R., Patankar, S. V., 1978, "Forced Convection Heat Transfer from a Shrouded Fin Array with and without Tip Clearance," ASME Journal of Heat Transfer, Vol. 100, pp. 572-579.
Sparrow, E. M., and Grannis, V. B., 1990, “Pressure Drop Characteristics of Heat Exchangers Consisting of Arrays of Diamond-Shaped Pin Fins,” Int. J. Heat Transfer. Vol. 34. No. 3, pp.589-600.
Seri, L., 1995, "Optimum Design and Selection of Heat Sinks," IEEE SEMI-THERM Symposium, Eleventh, pp.48-54
You, H. I., and Chang, C. H., 1997, “Numerical Prediction of Heat Transfer Coefficent for a Pin –Fin Channel Flow,” ASME J. Heat Transfer, Vol. 119, pp840-843.
Vanderplaats, G. N., 1993, Numerical Optimization Techniques for Engineering Design, McGraw-Hill, Inc., Singapore
Wirtz, R. A., Chen, W. M., and Zhou, R. H., 1994, "Effect of Flow Bypass on the Performance of Longitudinal Fin Heat Sinks," ASME Journal of Electronic Packaging, Vol. 116, pp. 206-211.
Wu, C. F., and Hamada, M., 2000, Experiments – Planning, Analysis, and Parameter Design Optimization, John Wiley & Sons, Inc., New York.