國
立
交
通
大
學
機 械 工 程 學 系
碩 士 論 文
放置可移動擾動銅粒子在一水平加熱銅板上
對 FC-72 池沸騰熱傳增強研究
Enhancement of Subcooled FC-72 Pool Boiling Heat
Transfer by Movable Copper Particles on a
Horizontal Plate
研 究 生:薛 正 宏
指 導 老 師:林 清 發 教授
中 華 民 國 102 年 7 月
放置可移動擾動銅粒子在一水平加熱銅板上
對次冷態 FC-72 池沸騰熱傳增強研究
Enhancement of Subcooled FC-72 Pool Boiling Heat
Transfer by Movable Copper Particles on a
Horizontal Plate
研 究 生 : 薛 正 宏 Student:Cheng-Hung Hsueh
指導教授 : 林 清 發 Advisor:Prof. Tsing-Fa Lin
國立交通大學
機械工程學系
碩士論文
A ThesisSubmitted to Department of Mechanical Engineering College of Engineering
National Chiao Tung University In partial Fulfillment of the Requirements
For the Degree of Master of Science
In
Mechanical Engineering July 2013
放置可移動擾動粒子在依水平加熱銅板上對 FC-72 持
沸騰熱傳增強研究
研究生: 薛 正 宏 指導老師:林 清 發 教授
國立交通大學機械工程學系
摘要
本論文乃針對放置可移動的擾動銅粒子在一沉浸於次冷態 FC-72 中的加熱 銅板之池沸騰熱傳增強研究。在本實驗中,我們探討了流體次冷度、擾動粒子的 直徑、擾動粒子的數目,以及所施加之熱通量之間的關係。其中,次冷度範圍從 5℃到 20℃,輸入熱通量 q 從 0.1 到 6W/cm²,銅粒子的直徑分別有 1.0 和 1.5mm 兩種,在小粒徑時數量從 100 至 1800 顆,而大粒徑時數量從 100 到 800 顆。 實驗結果分別以沸騰曲線和 h-T 圖表示,並且把加上擾動粒子的結果和光滑 銅表面作相互比較。實驗結果發現,當我們在銅板上加上了擾動粒子,熱傳效果 在低和中熱通量時,會有明顯的增強效果,而隨著放置於加熱銅板上的粒子量越 多,熱傳效果會變得越來越好。在本實驗中,最好的一組熱傳效果大約產生相較 於光滑表面之 400%的提升,而熱傳效果也會因為參數的相互組合不同而有所變 化。另外,在高熱通量的情形下,熱傳效果會有明顯的下降趨勢,這個效果主要 歸因於擾動粒子對於氣泡的脫離產生了阻擋的負面效果。在本實驗中,熱傳降低 的幅度最大約光滑表面的 20%。而理想的熱傳效果,必須搭配選用適當的擾動粒 子粒徑、數目、以及流體次冷度才能達到。Enhancement of Subcooled FC-72 Pool Boiling Heat
Transfer by Movable Copper Particles on a
Horizontal Plate
Student: Cheng-Hung Hsueh Advisor: Prof. Tsing-Fa Lin
National Chiao Tung University
ABSTRACT
An experiment is carried out here to investigate how subcooled pool boiling heat transfer of liquid FC-72 over a horizontal heated copper plate is affected by placing a large number of copper particles above the plate surface, intending to explore the possible pool boiling heat transfer enhancement by the moving particles. During the experiment, the copper particles are freely placed above the heated plate with a rectangular acryl fence surrounding the plate so that the particles can be moved by the force induced by the boiling flow without been blown away from the heating plate. In the experiment the liquid subcooling ranges from 5℃ to 20℃ and the imposed heat flux is varied from 0.1 to 6W/cm2 for the diameter of the moving metallic particles fixed at 1.0 and 1.5 mm. Besides, the total particle number placed on the plate ranges from 100 to 1800 and from 200 to 800 respectively for the small and large particles. The measured data are presented in terms of boiling curves and boiling heat transfer coefficients for the heating surface with the presence and absence of the particles. The experimental parameters include the liquid subcooling, imposed heat flux level, and the size and number of the particles.
FC-72 show that placing the movable copper particles can significantly increase the pool boiling heat transfer at low liquid subcooling for ∆𝑇𝑠𝑢𝑏≤10℃. For the small
copper particles at liquid subcooling ∆𝑇𝑠𝑢𝑏=10℃ and 𝑁𝑝=1600, the enhancement can be up to 200% over that for a bare surface for a certain combination of the experimental parameters. The best enhancement in this study can be as high as 300% for the small copper particles at the liquid subcooling of 5℃ and 𝑁𝑝=1400 & 1800.
Even when more than one layer of particles are placed on the plate, relatively significant boiling heat transfer enhancement can be obtained. However, the boiling heat transfer enhancement varies nonmonotonically with the liquid subcooling, particle size and number, and the heat flux applied, reflecting the complex mutual influences of the movable particles and bubble motion near the heated surface. We also note that at higher liquid subcooling, the copper particles are less effective in augmenting the boiling heat transfer. For the high ∆𝑇𝑠𝑢𝑏 of 20℃ the boiling heat
transfer is retarded by the copper particles especially when a large number of the particles are placed on the plate. Besides, the wall superheat for the incipient boiling can be substantially reduced by the moving metallic particles in some cases for 𝑁𝑝
𝑁𝑝𝑓
⁄ ≥ 1.0 and ∆𝑇𝑠𝑢𝑏≤ 10℃. However, at high heat flux (wall superheat) placing
the particles on the plate can substantially reduce the boiling heat transfer especially for the large particles.
The results from the visualization of the boiling flow over the copper plate indicate that placing the movable particles above the plate produce two opposite effects of enhancing and retarding the boiling heat transfer. At high heat flux the retarding effect is strong and boiling heat transfer is impeded by the particles.
TABLE OF CONTENTS
ABSTRACT (ENGLISH) i
TABLE OF CONTENTS iii
LIST OF TABLE v
LIST OF FIGURES vi
NOMENCLATURE xvi
CHAPTER 1 INTRODUCTION 1
1.1 Motive of the Present Study 1
1.2 Literature Review 3
1.3 Objective of Present Study 9
CHAPTER 2 EXPERIMENTAL APPARATUS AND PROCEDURES 10
2.1 Main Test Chamber 10
2.2 Test Heater Assembly 11
2.3 Confinement of Particles and Experimental Parameters 12
2.4 DC Power Supply 13
2.5 Data Acquisition 13
2.6 Optical Measurement Technique 13
2.7 Experimental Procedures 14
CHAPTER 3 DATA REDUCTION 23
3.1 Boiling Heat Transfer Coefficient 23
3.2 Uncertainty Analysis 25
CHAPTER 4 POSSIBLE POOL BOILING HEAT TRANSFER ENHANCEMENT OF FC-72 OVER HEATED COPPER SURFACE 32
4.1 Single-phase Natural Convection Heat Transfer 33
4.4 Effect of Moving Copper Particles on Boiling Heat Transfer 34
4.5 Effects of Subcooling Degree in the Bulk Liquid 37
4.6 Interactions between Particles and Boiling Flow
38
4.7 Proposed correlations
40
CHAPTER 5 CONCLUDING REMARKS. 125
LIST OF TABLES
Table 2.1 Thermophysical properties of FC-72 16
Table 2.2 Cases covered in present study for 1.0 mm copper particle 17
Table 2.3 Cases covered in present study for 1.5 mm copper particle 17
Table 3.1 Summary of the results from the uncertainty analysis 29
Table 4.1 Wall superheats at onset of nuclear boiling for 1.0 mm copper particles 41
LIST OF FIGURES
Experimental Apparatus
Fig. 2.1 Schematic diagram of the test apparatus. ---18 Fig. 2.2 Schematic diagram of the test heater assembly (not to scale). ---19 Fig. 2.3 Locations of three thermocouples in the copper block and one thermocouple
below the heater (not to scale). ---20 Fig. 2.4 Schematic diagram of placing strings on heating plate (not to scale).---21 Fig. 2.5 Schematic diagram of placing movable particles on heating surface with
acryl rectangular enclosure (not to scale). ---22
Data Reduction
Fig. 3.1 Schematic diagram of six main directions of the heat loss. ---30 Fig. 3.2 Schematic diagram of T'5 and T'6. ---31
Subcooled Pool Boiling Heat Transfer
Fig. 4.1 Comparison of the present single-phase natural convection data with the empirical correlation of Radziemska and Lewandowski (2005).---43 Fig. 4.2 Comparison of the present apparatus of saturated nucleate boiling heat
transfer data for bare surface with Rainy and You (2000).---44 Fig. 4.3 Effects of surface aging on subcooled pool boiling curves (a) and boiling
heat transfer coefficients (b) for = 5 for the baresurface.---45 Fig. 4.4 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and .---46 Fig. 4.5 Effects of copper particle diameter and number on subcooled pool boiling
=1.0 mm and . ---47 Fig. 4.6 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and . ---48 Fig. 4.7 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and . ---49 Fig. 4.8 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and .--- ---50 Fig. 4.9 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and . ---51 Fig. 4.10 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and . ---52 Fig. 4.11 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and . ---53 Fig. 4.12 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and . ---54 Fig. 4.13 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and .--- ---55
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and . ---56 Fig. 4.15 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and . ---57 Fig. 4.16 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and .---58 Fig. 4.17 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and . ---59 Fig. 4.18 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.0 mm and . ---60 Fig. 4.19 Variations of ℎ ⁄ with wall superheat for various copper particle ℎ
numbers at =1.0 mm and =5 ---61 Fig. 4.20 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.0 mm and . ---62 Fig. 4.21 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.0 mm and .---63 Fig. 4.22 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.0 mm and . ---64
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.0 mm and . ---65 Fig. 4.24 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.0 mm and .---66 Fig. 4.25 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.0 mm and .. ---67 Fig. 4.26 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.0 mm and . ---68 Fig. 4.27 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.0 mm and .---69 Fig. 4.28 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.0 mm and . ---70 Fig. 4.29 Variations of ℎ ⁄ with wall superheat for various total copper particle ℎ
numbers at =1.0 mm and =10 . ---71 Fig. 4.30 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 15 at =1.0 mm and . ---72 Fig. 4.31 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 15 at =1.0 mm and .---73
curves (a) and boiling heat transfer coefficients (b) for = 15 at =1.0 mm and . ---74 Fig. 4.33 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 15 at =1.0 mm and . ---75 Fig. 4.34 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 15 at =1.0 mm and . ---76 Fig. 4.35 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 20 at =1.0 mm and . ---77 Fig. 4.36 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 20 at =1.0 mm and .---78 Fig. 4.37 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.5 mm and .---79 Fig. 4.38 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.5 mm and .---80 Fig. 4.39 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 5 at =1.5 mm and .--- ---81 Fig. 4.40 Effects of copper particle diameter and number on subcooled pool boiling
Fig. 4.41 Effects of copper particle diameter and number on subcooled pool boiling curves (a) and boiling heat transfer coefficients (b) for = 5 at
=1.5 mm and . ---83 Fig. 4.42 Variations of ℎ ⁄ with wall superheat for total various copper particle ℎ
numbers at =1.5 mm and =5 .---84 Fig. 4.43 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.5 mm and . ---85 Fig. 4.44 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.5 mm and . ---86 Fig. 4.45 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.5 mm and . ---87 Fig. 4.46 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 10 at =1.5 mm and . ---88 Fig. 4.47 Variations of ℎ ⁄ with wall superheat for various total copper particle ℎ numbers at =1.5 mm and =10 .---89 Fig. 4.48 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 15 at =1.5 mm and .---90 Fig. 4.49 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 15 at =1.5 mm and . ---91
curves (a) and boiling heat transfer coefficients (b) for = 15 at =1.5 mm and .---92 Fig. 4.51 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 15 at =1.5 mm and .---93 Fig. 4.52 Variations of ℎ ⁄ with wall superheat for various total copper particle ℎ
numbers at =1.5 mm and =15 .---94 Fig. 4.53 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 20 at =1.5 mm and .---95 Fig. 4.54 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 20 at =1.5 mm and . ---96 Fig. 4.55 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 20 at =1.5 mm and .---97 Fig. 4.56 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 20 at =1.5 mm and .---98 Fig. 4.57 Variations of ℎ ⁄ with wall superheat for various total copper particle ℎ
numbers at =1.0 mm and =20 .---99 Fig. 4.58 Variations of ℎ with wall superheat for various liquid subcoolings at
=1.0 mm and =800.. ---100 Fig. 4.59 Variations of ℎ with wall superheat for various liquid subcoolings at
=1.5 mm and =400. ---102 Fig. 4.61 Variations of ℎ with wall superheat for various liquid subcoolings at
=1.5 mm and =600.. ---103 Fig. 4.62 Variations of ℎ ⁄ with wall superheat for various liquid subcoolings at ℎ
=1.0 mm and =800.. ---104 Fig. 4.63 Variations of ℎ ⁄ with wall superheat for various liquid subcoolings at ℎ
=1.0 mm and =1200.---105 Fig. 4.64 Variations of ℎ ⁄ with wall superheat for various liquid subcoolings at ℎ
=1.5 mm and =400.---106 Fig. 4.65 Variations of ℎ ⁄ with wall superheat for various liquid subcoolings at ℎ
=1.5 mm and =600.---107 Fig. 4.66 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 15 at =0.5 mm and . ---108 Fig. 4.67 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 15 at =0.5 mm and .. ---109 Fig. 4.68 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 20 at =0.5 mm and .---110 Fig. 4.69 Effects of copper particle diameter and number on subcooled pool boiling
curves (a) and boiling heat transfer coefficients (b) for = 20 at =0.5 mm and .---111 Fig. 4.70 Boundaries for boiling heat transfer augmentation and retardation for
Fig. 4.71 Boundaries for boiling heat transfer augmentation and retardation for copper particles with = 10 and different 𝑑 and based on (a) q vs. / 𝑓 and (b) 𝑤 vs. / 𝑓.--- 113 Fig. 4.72 Boundaries for boiling heat transfer augmentation and retardation for
copper particles with = 15 and different 𝑑 and based on (a) q vs. / 𝑓 and (b) 𝑤 vs. / 𝑓.--- ---114 Fig. 4.73 Boundaries for boiling heat transfer augmentation and retardation for
copper particles with = 20 and different 𝑑 and based on (a) q vs. / 𝑓 and (b) 𝑤 vs. / 𝑓.---115
Fig. 4.74 Photos taken from side view of subcooled boiling flow for =5 at selected time instants for q= 0.78 W/ cm2 with copper particles on heated surface at =1.0 mm and .---116 Fig. 4.75 Photos taken from side view of subcooled boiling flow for =5 at
selected time instants for q= 2.2 W/ cm2 with copper particles on heated surface at =1.0 mm and .---117 Fig. 4.76 Photos taken from side view of subcooled boiling flow for =5 at
selected time instants for q= 3.1 W/ cm2 with copper particles on heated surface at =1.0 mm and .---118 Fig. 4.77 Photos taken from side view of subcooled boiling flow for =5 at
selected time instants for q= 1.3 W/ cm2 with copper particles on heated surface at =1.0 mm and .---119 Fig. 4.78 Photos taken from side view of subcooled boiling flow for =10 at
selected time instants for q= 1.3 W/ cm2 with copper particles on heated surface at =1.0 mm and .---120 Fig. 4.79 Photos taken from side view of subcooled boiling flow for =15 at
surface at =1.0 mm and .---121 Fig. 4.80 Photos taken from side view of subcooled boiling flow for =20 at
selected time instants for q= 1.3 W/ cm2 with copper particles on heated surface at =1.0 mm and ---122 Fig. 4.81 Schematic illustration of particle-bubble interactions in boiling flow on
heated surface at (a) low and medium flux and (b) high flux( t ≈
. sec.)---123 Fig. 4.82 Schematic illustration of retarding bubble growth and departure by
NOMENCLATURE
A area, mm2dp diameters of particles, mm
Np numbers of particles
h heat transfer coefficient, W/m2∙K
I measured current from DC power supply, A V measured voltage from DC power supply, V k thermal conductivity, W/m∙K L characteristic length, m NuL Nusselt number, k hL NuL
P system pressure, kPa
Q heat transfer rate, W
qn net wall heat flux, W/cm2
Ra Rayleigh number T temperature, C t time, sec W plate width, cm Cp specific heat, J/kg∙C 𝜌𝐶𝑢 copper density (𝜌𝑐𝑢=8989.9), kg/m3 ∆𝑇𝑠𝑢𝑏 subcooling degree, ∆𝑇𝑠𝑢𝑏= 𝑇𝑠𝑎𝑡− 𝑇𝑏𝑢𝑙𝑘, K ∆𝑇𝑤 wall superheat, ∆𝑇𝑤= 𝑇𝑤 − 𝑇𝑏𝑢𝑙𝑘, K Greek Symbols kinematic viscosity, m2/ s liquid density, kg/m3
absolute viscosity, kg/m∙s
coefficient of expansion, /C
surface tension, N/m
the distance between the thermocouple tips and the upper surface of the copper plate, m
Subscripts
Cu copper
CHAPTER 1
INTRODUCTION
1.1 Motive of the Present Study
Considering the enormous and still increasing needs for electronic products in recent years, the electronics industry rapidly develop tiny integrate circuits including nano components to improve product performance. As a consequence, relatively large amount of heat is generated in the integrate circuits during the device operation. How to effectively remove this large amount of the dissipating heat from the micro processors poses a great challenge to heat transfer research community. In order to transfer the large quantity of the dissipating heat from the chips with an ultra-high microelectronic component density, highly efficient heat transfer methods are required to control their temperatures at allowable level. Although air cooling has been used most commonly over a long period of time, this method has reached its upper performance limit and is unable to handle the huge amount of dissipating heat encountered in the current electronics industry [1]. Therefore, we need a better heat transfer method to solve the problem confronted. Cooling methods based on liquid convection and liquid-vapor phase-change heat transfer have been considered. Among these, boiling heat transfer is regarded as one of the most effective methods in electronics cooling comparing with the methods based on single-phase heat transfer because of the exchange of latent heat involved in the boiling processes which can take away a great quantity of heat. Besides, larger heat transfer rate can be produced by boiling of subcooled liquid due to the larger temperature difference between the coolant and heat dissipating surface. Furthermore, to meet the future need, methods to augment the boiling heat transfer have received increasing attention in the heat transfer research.
changes in the heating surface structure can enhance the pool boiling heat transfer. Typical methods include adding the micro-structures, micro-pin fins and grooves to the surfaces. Besides, coating the surfaces with particles and covering the surfaces with screens have been shown to be effective. These enhancement methods are based on various forms of extended surface fixed firmly onto the surfaces or directly fabricated on the surfaces. In the present study, enhancement of pool boiling heat transfer by placing movable particles above the heating plate will be explored. The particle motion is driven by the two-phase boiling flow near the plate. The particles are confined in a rectangular enclosure surrounding the heating plate in order to avoid the particles to move away from the plate, that would decrease the particle number density on the plate.
The working fluid FC-72 used here is a dielectric fluorocarbon liquid manufactured by the 3M Company and gains popularity in electronics cooling application. It not only has suitable phase-change temperature for thermal control of I.C. components but also owns the quality that does not foul the boiling surface. Most importantly, FC-72 has less impact on our environment than alternative liquids like chlorofluorocarbons or organic liquids. Copper has properties of better thermal conductivity than most metals and is often considered to be suitable for heat dissipating elements. Thus the heat transfer enhancement characteristics of pool boiling of the dielectric liquid on a copper plate by placing movable particles above the heating surface immersed in FC-72 liquid are explored in the present study. In an earlier attempt [2] Wei in our laboratory obtained significant enhancement in pool boiling heat transfer of saturated FC-72 over a horizontal heated copper plate by placing copper and stainless steel particles on the plate when the, size and number of particles are suitably chosen for low and medium wall superheats. In this study we move further to investigate the possibility of enhancing subcooled pool boiling heat transfer of FC-72 by the movable copper particles.
1.2 Literature Review
In what follows the literature relevant to the present study is briefly reviewed. Pool boiling heat transfer is a process of vigorous heat transfer resulting from latent heat exchange associated with liquid-to-vapor phase change in a quiescent liquid. Nukiyama [3] conducted a pioneering pool boiling experiment in 1934 and arranged the experimental heat transfer data as a form of the wall superheat versus the heat flux, which is known as the "boiling curve" today. After that, the pool boiling heat transfer research has received considerable attention.
The state of the art cooling technologies for handling heat dissipation in microelectronic equipments have been developed extensively over the past 30 years. Several products were released including Air-Cooled Modules, High Thermal Conduction Modules, and Liquid-Cooled Modules, as discussed by Bar-Cohen [4].
In an early attempt to improve pool boiling heat transfer by using a micro-configured surface, Miller et al. [5] found that vapor retention could be a function of the scale and geometry of the micro-configurations.They pointed out that the relation between the stability of the potential nucleation sites and the micro-configuration size and geometry required further investigation, so that the size and the site density of the cavities could be optimized for boiling heat transfer enhancement.
Slightly later a few studies were carried out to examine the influences of the surface fabricated microstructures on the pool boiling heat transfer. These include boiling of FC-72 on micro-porous surfaces with particle coating tested by Chang and You [6] and by Vemuri and Kim[7], adding micro-porous pin-fins along with coating particles to the surface investigated by Rainey and You [8,9], and fabricating micro-pin-fins and submicron-scale roughness on the surfaces by Honda et al. [10] and Wei et al. [11]. The study of Rainey and You [8] concluded that the microporous coating can significantly enhance the boiling heat transfer performance over the pin-finned surfaces. For the subcooled boiling on the micro-porous surface [9],
In examining the pool boiling on the micro-pin-fin surfaces, Honda et al. [10] and Wei et al. [11] noted that the boiling curves were characterized by that a very small increase in the wall superheat could cause a large increase in the heat flux. And increasing the fin height was found to provide better heat transfer in the nucleate boiling regime and resulted in a higher critical heat flux. Nucleation site interaction in pool boiling on an artificial surface was investigated by Zhang and Shoji [12] and by Yu et al. [13]. The hydrodynamic interaction can be also influenced by some factors, such as the liquid properties, subcooling, system pressure. The study of Yu et al. [13] concluded that the critical heat flux was dependent on the cavity density. The evaporation/boiling heat transfer regimes in the capillary wicking structures were identified and discussed by Li et al.[14] and Li and Peterson[15]. Anderson and Mudawar [16] reported that microstructures in the forms of fins, studs, grooves and vapor-trapping cavities on the boiling surface significantly shifted the boiling curve toward lower superheats while increasing the incipience excursion. Their results also suggest that the maximum boiling heat flux is a function of surface geometry and orientation but independent of the initial conditions, surface roughness, or the presence of large artificial cavities. Intending to augment boiling heat transfer, O’Connor and You [17] painted silver flakes on the boiling surface. Their experimental data show that the incipience boiling superheats are 70-85% lower and the nucleate boiling superheats are 70-80% lower than the bare surface. Besides, the critical heat flux is increased by 109%. O’Connor et al. [18] then compared two methods of generating surface microstructures, “spraying” and “painting”, for pool boiling heat transfer enhancement. They noted that for saturated FC-72, the incipient boiling superheat showed 33-55% reduction for the sprayed alumina and 63-85% reduction for the painted diamond. The enhancement in the critical heat flux can be up to 45% for the sprayed alumina and 61% for the painted diamond microstructures. While for the subcooled boiling of FC-72, the critical heat flux was increased about 101% and 87% for the diamond paint and sprayed alumina microstructures,
diamond particles on the pool boiling heat transfer performances. They classified the coating thickness into two groups. For coatings thinner than 100 μm, increasing the coating thickness would generate a higher active nucleation density. But for coatings thicker than 100 μm, a further increase in the coating thickness does not always enhance the pool boiling heat transfer. They attributed this result to higher impedance for liquid-vapor exchange channels and higher thermal resistance for the thicker coating. Jung and Kwak [20] investigated the effects of submicron-scale roughness on the subcooled boiling heat transfer over a boiling surface anodized in DMF (dimethylforamide) and HF (hydrofluoric acid). Both surface treatments were found to increase the effective boiling area and served for increasing the nucleation sites and hence showed considerable enhancement in the boiling heat transfer. The critical heat flux also increases linearly. Honda and Wei [21] reviewed recent advances in enhancing boiling heat transfer from electronic components immersed in dielectric liquids through the use of surface microstructures. They concluded that most of the surface microstructures were effective in decreasing the wall superheat at the boiling incipience. The nucleate boiling heat transfer also can be improved and the critical heat flux is raised almost linearly with increasing the liquid subcooling for ∆𝑇𝑠𝑢𝑏 in the range of 0 to 40K. Rainey and You [22] and Rainey et al. [23] respectively studied the effects of the orientation and pressure on the pool boiling heat transfer from microporous surface. Their data show that nucleate boiling performance increases slightly for the surface inclined from 0(horizontal) to 45 and then decreases for the inclination angle ranging from 90 to 180. Moreover, for the plain and microporous surfaces increases in boiling performance and critical heat flux and decrease in the incipience wall superheat were noted as the pressure increased.
Chou et al. [24] arranged several grooved patterns on surfaces intending to enhance boiling heat transfer of distilled water. Their experimental data reveal that the radial grooved pattern has the best enhanced boiling heat transfer performance and the spiral or concentric
for the grid or the spotted grooved pattern. All grooved patterns they investigated have better heat transfer performance than the plain surface and the denser groove is better than the sparser one for the same patterns.
Hasegawa et al. [25] covered a heat pipe with a woven screen to investigate the associated boiling characteristics and burnout phenomena. Their results disclose that the additional screen produces two opposite effects of inhibiting and enhancing the boiling heat transfer. Tsay et al. [26] explored pool boiling heat transfer enhancement by covering the boiling surface with a screen in distilled water. They found that the screen coverage could raise bubble generation frequency and enhance the boiling heat transfer. But the screen can also cover some nucleation sites and hence may retard the boiling heat transfer. They also noted that the boiling heat transfer became poorer at lowering the liquid level. They concluded that covering the heated surface with a screen could augment the pool boiling heat transfer if the mesh size was comparable with the bubble departure diameter. In boiling of methanol and HFE-7100, Liu et al. [27] pointed out that placing a fine mesh layer on the boiling surface enhanced nucleate boiling heat transfer at low wall superheat (∆T𝑠𝑎𝑡<8-10K) but an opposite
trend resulted at high superheat (∆T𝑠𝑎𝑡>8-10K). They also reported that the heat transfer in nucleate boiling always became worse with a coarse mesh on the boiling surface. On the other hand, for smooth surface the increase of liquid subcooling results in lower wall superheat which can be considered as enhancement in heat transfer. Watwe et al. [28] also investigate the pressure and subcooling effects from a PPGA chip package. They concluded that the CHF increased linearly with the subcooling for FC-72 at atmospheric pressure. Moreover, Franco et al. [29] used dielectric refrigerant R141b to investigate enhancement in the boiling heat transfer performance by covering the heated surface with wire meshes. The boiling heat transfer coefficient was noted to increase significantly, especially at relatively low heat fluxes. They also found that the wire mesh coverage on the heating surface resulted in slower
layer covering on boiling heat transfer, Kurihara and Myers [30] tested several working fluids including water, acetone, n-hexane, carbon tetrachloride, and carbon disulfide. They found that active nucleation sites on the heating plate increased due to the mesh covering and the boiling heat transfer coefficient was proportional to the one-third power of the bubble column numbers at high numbers.
Pool boiling heat transfer in liquid saturated particle bed and fluidized bed of distilled water was investigated by Shi et al. [31]. The tests were conducted for glass beads, steel balls, fine sand and 𝐴𝑙2𝑂3 particles. They showed that boiling heat transfer could be enhanced greatly by adding the solid particles into the liquid whether in fixed particle bed or in fluidized particle bed. The boiling heat transfer enhancement is closely related to the particle size (𝑑𝑝=0.5, 1.0 and 2.0 mm), initial bed depth (𝐻𝑝=3.0, 6.5, 9.5 and 13.4 mm) and heat flux
applied. The best heat transfer enhancement is 120% for the particle diameter 𝑑𝑝=1.0 mm and bed height 𝐻𝑝=9.5 mm. A similar study was conducted by Matijevic et al. [32] using lead
spheres to cover a heating surface. The spheres were packed as closely as possible into a single layer. They noted that boiling heat transfer from the heating surface to water could be enhanced substantially by the metallic spheres (d=3.0, 3.5, 3.6, 4.0 and 4.5 mm), and the smaller spheres resulted in a better enhancement of boiling heat transfer.
Mohamed et al. [33] carried out a series of experiments to examine boiling of subcooled HFE-7100 fluid. He found that compared to the saturated state, a higher degree of liquid subcooling caused obviously higher critical heat flux (CHF) and lower surface superheat to initiate boiling on the porous graphite surface and smooth flat copper surface. For the case of the saturated liquid on the smooth flat copper surface, the critical heat flux and surface superheat to initial boiling for saturation state are respectively 21.5 W/cm2 and 10.9 K. While at a subcooling of 30℃ the CHF and initial boiling temperature are individually 37.3W/cm² and 5 K, an increase of more than 73% for CHF and a decrease of 54% for the ONB
Recently, Coulibaly et al. [34] examined bubble coalescence during subcooled nucleate pool boiling of FC-72. They showed that the coalesced bubble moved and oscillated on the heater surface with significant heat transfer variations prior to departure. Bubble departure size and departure frequency decreased as the subcooling increased. Harada et al. [35] also studied bubble behavior in subcooled boiling. Their results showed that when bubbles were lifted-off the heated surface in subcooled liquid, the life time of bubbles was significantly shorten because the bubbles collapsed rapidly due to vapor condensation.
Heat transfer enhancement by the usage of nanofluids has become very popular recently. In nanofluids a very large number of nano particles (diameters smaller than 100 nm) are added into a working fluid which is considered to significantly increase thermal conductivity of the fluid. Wen and Ding [36] reported an enhancement of boiling heat transfer coefficient for about 40% with alumina water based nanofluids. On the other hand, by using the same nanoparticles in the same fluid, Bang and Chang [37] found that the boiling heat transfer coefficient deteriorated for about 20% when the nanoparticles are added.
Some active techniques to enhance boiling heat transfer were also proposed in the literature. Jeong and Kwon [38] found that the CHF augmentation in pool boiling of water due to ultrasonic vibration was closely related to its effects on increasing bubble generation and its departure. They noted that the rate of increase in CHF for downward facing surface ranged from 87~126% as the water subcooling varied from 5 to 40℃. When ultrasonic wave is applied, the rate of CHF augmentation increased as the water subcooling increases. This is caused by an increase in cavitation bubble population, which contributed to fluid mixing, for an increase in subcooling. Cipriani et al. [39] imposed electric field on pool boiling of FC-72 over a heated platinum wire (d=0.1 and 0.2 mm)and found that the boiling heat transfer was strongly influenced by the presence of the electric field at a low wire superheat. An increase of the boiling heat transfer coefficient up to 400% was encountered with the maximum applied
heated surface vibration, Navruzov et al. [40] demonstrated that boiling heat transfer of ethanol could be substantially enhanced at low imposed heat flux. The amplitude of the surface vibration is found to be a governing parameter for heat transfer enhancement at low-frequency vibrations. Besides, the vibration of the heat transfer surface significantly alters the heat transfer process both in subcooled boiling and in free convection. The single-phase heat transfer curves are 70-80% above the basic curve at increasing heat loads.
1.3 Objective of Present Study
Literature review conducted above clearly discloses that considerable works have been carried out in the past to investigate the enhancement in the pool boiling heat transfer over a surface by passive methods through fabricating surface microstructures such as roughness and micro-pin-fins and by covering the surface with mesh screens and particle coating. All these microstructures are fixed firmly onto the boiling surface. Besides, some effective active heat transfer augmentation methods such as vibrating or rotating heating surface and/or fluid and applying electric field to vibrate a heating surface have been suggested. Following the previous work on the enhancement of saturated pool boiling heat transfer [2], an experiment is conducted here to explore the possible enhancement in the subcooled FC-72 pool boiling heat transfer by placing movable copper particles on the boiling surface. The vigorous motion of the bubbles in the boiling flow can cause violent movement of the particles. Meanwhile, this violently moving particles can significantly affect the bubble dynamics near the surface. Thus we expect the boiling heat transfer from the surface can be enhanced. The method proposed here is passive in nature. However, it behaves like an active heat transfer enhancement method.
10
CHAPTER 2
EXPERIMENTAL APPARATUS AND PROCEDURES
A schematic arrangement of the experimental apparatus for the present investigation of the subcooled pool boiling heat transfer enhancement by movable metallic particles driven by the boiling flow is similar to that employed in the previous study [2] and is shown in Fig. 2.1. The experimental system includes a main test chamber, a test heater assembly, and other auxiliary parts such as a D.C. power supply, a data acquisition unit and a high-speed photographic unit. The working fluid, FC-72, is a highly wetting dielectric fluorocarbon liquid produced by 3M Industrial Chemical Products Division, which has been considered as a good candidate fluid for liquid immersion cooling applications. It is chemically stable, dielectric, and has a relatively low boiling point (Tsat=56C at atmospheric pressure). Some
thermophysical properties of FC-72 are given in Table 2.1.
2.1 Main Test Chamber
The main test chamber is a hermetic stainless steel pressure vessel of 205 mm in height and 216 mm in diameter. An internal water condenser is installed inside the chamber and connects with a thermostat (LAUDA RK20) to maintain the bulk temperature of the working fluid in the chamber at the preset level. The maximum cooling power of the thermostat is 180W (at 20C). We further use an external temperature controller (FENWAL MYSPEC Digital Temperature Controller) to control the bulk temperature of FC-72 in the test chamber with an accuracy of 0.1C. Besides, a cartridge heater is located near the bottom of the test chamber to provide additional heating during the degassing process. In order to prevent the heat
11
loss from the vessel to the ambient, a superlon layer of 10-mm thick is wrapped around the chamber. Moreover, a pressure transducer with an operating range of 0-200 kPa is located at the gate valve to measure the pressure of the work fluid. Meanwhile, the working fluid temperature is measured by two resistance temperature detectors (RTDs) located at the gate valve and at a selected location 5 cm above the bottom surface of the chamber with a calibrated accuracy of 0.1C. An auxiliary tank of 10-liter liquid FC-72 is placed right above the test vessel and it is only used for the subcooled pool boiling experiment to prevent regassing of the working fluid after degassing. A pressure transducer and a RTD are placed in the auxiliary tank to measure the internal gas pressure and liquid temperature. In addition, a test heater assembly is mounted to a stainless steel shelf to fix the PEEK (Polyether Ether Ketone) substrate. The working fluid is maintained at approximately 80 mm above the heated surface in the experiment.
2.2 Test Heater Assembly
A schematic of the test heater assembly is shown in Fig. 2.2. The assembly consists mainly of a film heater and it is adhered to the lower surface of a square copper plate by epoxy Omegabond 200. The plate is 10-mm thick with 30x30 𝑚𝑚2 in surface area. The heater supplies the required power input to the copper plate. The copper plate is flush mounted onto a much larger PEEK block. Liquid FC-72 boils on the upper surface of the copper plate. More specifically, the copper plate is heated by D.C. current delivered from a D.C. power supply to the film heater. Besides, three calibrated copper-constantan thermocouples (T-type) with a calibrated accuracy of 0.2C are installed at selected locations in the copper plate right below the boiling surface. They are used for the control and determination of the boiling surface
12
temperature. The detailed locations of the thermocouples in the copper plate are shown in Fig. 2.3. Note that the whole copper plate is inserted into a PEEK block which serves as a heat insulator (kT 0.25W/mK), intending to reduce the heat loss from the lateral and bottom surfaces of the plate to the ambient. Besides, the locations of thermocouples in the PEEK block which installed for the estimation of heat loss are shown in Fig. 2.4.
2.3 Confinement of Particles and Experimental Parameters
Solid particles of the same material and uniform size are placed freely on the upper surface of the copper plate, as schematically shown in Fig. 2.5. In order to insure that the particles would not be blown away by the vigorous motion of the bubbles, we install an acryl fence of 2-cm high and 1-cm thick around the edges of the heating copper plate. In the present study tests will be conducted for copper particles. The density of copper is measured before the experiment with 𝜌𝑐𝑢= 8990 𝑘𝑔 𝑚⁄ 3. The copper particle is chosen here because the copper have much higher density than liquid FC-72 and is used widely in the industry for its excellent conductivity which may enhance the thermal conduction from the plate. Besides, the chosen particles should not be too small so that they float in the liquid above the plate and do not contact the heating surface. Moreover, they should not be too large and cannot be moved by the boiling flow. Here, the particle diameter is selected to be 1.0 and 1.5 mm. On the other hand, the liquid FC-72 subcooling is varied from 5℃ to 20℃. More specifically, four different liquid subcoolings at ∆𝑇𝑠𝑢𝑏=5℃, 10℃, 15℃ and 20℃ are tested. The chosen particle size and number for the cases covered here are summarized in Table 2.2. The measured data expressed in terms of boiling curves and boiling heat transfer coefficients will be compared with that of a bare heating surface.
13
2.4 DC Power Supply
The power generated in the film heater in the test heater assembly is provided by a programmable D.C. power supply (Gpc 3030D). It offers a maximum D.C. power of 180W for an output voltage of 60V and an output current of 3A. The power input to the copper block is transmitted through a GPIB interface to a personal computer. In order to measure the D.C. current, a precision ammeter (KYORITSU A.C./D.C. DIGITAL CLAMP METER) is arranged in series connection with the electric circuit. Besides, a YOKOGAWA data recorder is used to measure the voltage drop across the test heater assembly. All the voltage, current and power measurement devices are calibrated by a YOKOGAWA WT200 power meter according to the Center of Measurement Standards in Industrial Technology Research Institute of Taiwan.
2.5 Data Acquisition
A 20-channel YOKOGAWA data recorder (MX-100) combined with a personal computer is used to acquire and process the data from various transducers. All signals detected from the T-type thermocouples, RTDs, pressure transducer, ammeter, data recorders and power meter are all collected and converted by the internal calibration equations in the computer during the data acquisition.
2.6 Optical Measurement Technique
A high-speed camera along with a microscope is installed in front of the observation window to observe the boiling activity in the flow. The photographic apparatus consists mainly of a high speed digital video camera (IDT High-speed
14
CMOS Camera), a micro-lens (Optem Zoom 16), and a three-dimensional positioning mechanism. The high-speed motion analyzer can take photographs up to 143,307 frames/sec. In the present experiment the recording rate is 1000 frames/sec. After the experimental system reaches a statistical state, we start capturing the images of the particles and bubble in the boiling flow. Besides, we store and display the images in the personal computer through an image-capturing software.
2.7 Experimental Procedures
Before the experiment,
t
he boiling surface is polished by fine sand paper (Number 3000, 2000 and 1000) and cleaned by ethyl alcohol. In each test, we need to remove non-condensable gases existing in the empty test chamber by running a vacuum pump for about 15 minutes and then fill the FC-72 liquid into the chamber until the liquid level is higher than the heating plate for about 80 mm. Next, the FC-72 liquid in the test chamber is heated to 65℃ and boiled vigorously for about 1 hour to further remove the dissolved non-condensable gases in the dielectric liquid. During the process, the temperature in the chamber is detected and maintained by a digital temperature controller. After the working fluid pressure and temperature stabilize to one atmosphere and at the preset subcooled state, we turn on the test heater. The imposed heat flux on the boiling surface is adjusted by controlling the electric current delivered to the heater from the D.C. power supply. Upon reaching the statistical state, we begin collecting the required heat transfer data and visualizing the boiling activity. After the experiment for the case of bare surface is finished, we put the chosen number and size of the copper particles on the copper plate and repeat the procedure described above. In order to keep the particles on the copper plate, we also place an acrylic rectangular enclosure onto the PEEK block around the edge of copper plate.15
Effects of the particle size, number and subcooling of the working fluid on the possible boiling heat transfer enhancement will be investigated in the experiment.
16
Table 2.1 Thermophysical properties of FC-72.
Properties at 25C FC-72
Appearance Clear, colorless
Average Molecular Weight 338
Boiling Point (1atm) 56C
Pour Point (1atm) -90C
Estimated Critical Temperature 449K
Estimated Critical Pressure 1.83 × 106 Pa
Vapor Pressure 3.09 × 104 Pa
Latent Heat of Vaporization hfg
(at normal boiling point)
88 J/g
Liquid Density 1680 kg/m3
Absolute Viscosity 6.4× 10-3 poises ; 6.4× 10-4 kg/m∙s Kinematic Viscosity 3.8 × 10-3 stokes ; 3.8 × 10-7 m2/ s Liquid Specific Heat cp 1100 J/kg∙C
Liquid Thermal Conductivity k 0.057 W/m∙C
Coefficient of Expansion 0.00156 /C
Material Subcooling Degrees 𝑁𝑝
Copper
(1mm)
5℃
100 1000 200 1100 300 1200 400 1300 500 1400 600 1500 700 1600 800 1700 900 180010℃
200 1200 400 1400 600 1600 800 1800 100015℃
200 800 400 1200 60020℃
800 1200Material Subcooling Degrees 𝑁𝑝
Copper
(1.5mm)
5℃
200 600 400 80010℃
200 600 400 80015℃
200 600 400 80020℃
200 600 400 800Table 2.2 Cases covered in present study for 1.0 mm copper particle
Fig. 2.1 Schematic diagram of the test apparatus. Liquid Level
P
Condenser Coil Observation WindowTo Degassing Tank and Drain
Computer GPIB MX100 Data Acquisition Heater Boiling Surface FC-72 Digital Temperature Controller Shelf RTD Condenser Test Heater Assembly Observation Window Electric Cord Signal Cord Programmable D.C. Power Supply Liquid Level
P
Condenser Coil Observation WindowTo Degassing Tank and Drain
Computer GPIB MX100 Data Acquisition Heater Boiling Surface FC-72 Digital Temperature Controller Shelf RTD Condenser Test Heater Assembly Test Heater Assembly Observation Window Electric Cord Signal Cord Programmable D.C. Power Supply
Fig. 2.2 Schematic diagram of the test heater assembly (not to scale).
30
30 7
100
Embedded Copper Plate
Electric Film Heater
Perspective view
Front view
Top view
PEEK substrate
PEEK substrate(unit:mm)
Fig. 2.3 Locations of three thermocouples in the copper plate and one thermocouple below the heater (not to scale).
Front view
Top view
(unit:mm)
Perspective view
#3,5 #3 #3 #1,8 #1,8 #1 #4 #2 #5 #2,4 #8 #5 #4 #2 1 5 5 30 30Fig. 2.4 Locations of two thermocouples in the PEEK (not to scale).
(unit:mm)
Perspective view
PEEK
substrate
#7 #6Front view
3.5 #6 #7 12Top view
Copper Surface
#7 #6Copper Plate
Copper Plate
31Fig. 2.5 Schematic diagram of placing movable particles on heating surface with acryl rectangular enclosure (not to scale).
Perspective view
Top view
PEEK substrate PEEK Surface(unit:mm)
Right view
CHAPTER 3
DATA REDUCTION
3.1 Boiling Heat Transfer Coefficient
The space-average natural convection and boiling heat transfer coefficients over the upper surface of the heated square copper plate when the flow is at a statistical state are both defined as
h = 𝑞𝑛
∆𝑇𝑤
⁄ (3.1) where qn is the net heat flux imposed on the upper surface and ∆Tw is the wall
superheat defined as the difference between the average surface temperature and the bulk liquid temperature of FC-72 which can be written as:
∆𝑇𝑤 = 𝑇𝑤 − 𝑇𝑏 (3.2)
The average heated surface temperature 𝑇𝑤 is estimated from the measured average temperature from the thermocouples installed at different locations near the upper surface of the copper plate according to the steady-state one-dimensional conduction heat transfer. Specifically,
Cu n Cu w k δ q T T (3.3) where
TCu = the average measured temperature from the thermocouples installed in
the copper plate (C)
kCu = the thermal conductivity of copper (W/m∙K)
= the vertical distance between the thermocouple tips and the upper surface of the copper plate (m)
The total power input Qt to the copper plate can be obtained from the
measured voltage drop across the film heater in the test heater assembly and the current passing through it,
V I
Qt (3.4)
where
Qt = total power input to the upper surface of the copper plate (W)
I = electric current passing through the film heater (Amp.) V = voltage drop across the film heater (Volts)
The substrate of the test section is made from PEEK, which have a much lower thermal conductivity (kT 0.25W/mK) than the copper (k 386W/mK). In evaluating total heat loss from the heater assembly, we focus on heat transfer from the heater and copper plate surface to the PEEK. Figures 2.3 and 2.4 are the schematic diagrams of the thermocouples buried in the copper plate and PEEK. The heat dissipation model used to estimate the heat loss is shown in Fig. 3.1, and the total heat loss can be estimated as follows:
Q
loss= k
p∙
(T8−T7) L1∙ A
1+ 4 ∙ k
p∙
(Tcu−T6) L2∙ A
2+
2π∙kp∙L3∙(Tcu−T6) ln( r6 rcu,2)+
2π∙kp∙L4∙(Tcu−T6) ln( r6 rcu,3)+k
p∙
(Tcu−T′5) L5∙ A
5+k
p∙
(Tcu−T′6) L6∙ A
6 whereT6 , T7 , T8 : the average measured temperatures from the thermocouples inside the
PEEK insulator, as schematically shown in Figs. 2.3 & 2.4
𝐿 1, 𝐿2 , 𝐿 3 , 𝐿 4 , 𝐿 5 , 𝐿 6: shortest distances between locations No.1~No.6 and the
film heater or copper plate (m)
A1 , A2, A3, A4, A5, A6 : bottom and lateral surface areas of the copper plate
T'5 , T'6 : these two temperatures are calculated by using interpolation method based
on 𝑇6, as schematically shown in Fig. 3.2
Finally, the net imposed input heat flux to the upper surface of copper plate can be evaluated from the relation
Cu loss t n A Q Q q (3.6)
where ACu is the area of the upper surface of the copper plate.
3.2 Uncertainty Analysis
An uncertainty analysis is carried out here to estimate the uncertainty levels in the experiment. Kline and McClintock [41] proposed a formula for evaluating the uncertainty in the result F as a function of independent variables, X1, X2, X3∙∙∙∙∙∙∙∙∙∙∙∙Xn,
F=F (X1 ,X2, X3∙∙∙∙∙∙∙∙∙∙∙∙Xn) (3.7)
The absolute uncertainty of F is expressed as
2 1 2 2 3 3 2 2 2 2 1 1 n n X X F X X F X X F X X F F (3.8)
and the relative uncertainty of F is
2 1 2 2 3 3 3 2 2 2 2 2 1 1 1 n n n X X nX nF X X nX nF X X nX nF X X nX nF F F (3.9) If 1 2 3... c b a X X X
2 1 2 3 3 2 2 2 2 1 1 X X c X X b X X a F F (3.10) where i X F
and Xi are, respectively, the sensitivity coefficient and uncertainty
level associated with the variableX . The values of the uncertainty intervalsi Xi are obtained by a root-mean-square combination of the precision uncertainty of the instruments and the unsteadiness uncertainty, as recommended by Moffat [42]. The choice of the variableX to be included in the calculation of the total uncertainty i
level of the result F depends on the purpose of the analysis.
The uncertainties of the parameters in the present study are calculated as follows: (1) Uncertainty of temperature difference, Tw=Tw-Tb
2 1 2 2 2 1 2 2 2 1 2 2 ) ( ) ( b w b b w w b b b w b w w b w w b b b b w w w w b w b w b w T T T T T T T T T T T T T T T T T T nT T T n T T nT T T n T T T T (3.11) (2) Uncertainty of total power input, QtV I Qt (3.4) and 2 1 2 2 V V I I Q Q t t (3.12)
Cu loss t n A Q Q q (3.6) and 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 1 loss t loss loss t t Cu Cu loss loss loss t loss t t loss t t Cu Cu loss loss loss n t t t n Cu Cu Cu n n n Q Q Q Q Q Q A A Q Q Q Q Q Q Q Q Q Q A A Q Q nQ nq Q Q nQ nq A A nA nq q q (3.13) Where
Q
loss= k
p∙
(T8−T7) L1∙ A
1+ 4 ∙ k
p∙
(Tcu−T6) L2∙ A
2+
2π∙kp∙L3∙(Tcu−T6) ln(rcu,2r6 )+
2π∙kp∙L4∙(Tcu−T6) ln(rcu,3r6 )+k
p∙
(Tcu−T′5) L5∙ A
5+k
p∙
(Tcu−T′6) L6∙ A
6 (3.5) (4) Uncertainty of space-average heat transfer coefficient, hw n T q h Δ (3.1) And
2 1 2 2 2 1 2 2 2 1 2 2 ) ( ) ( 1 1 b w b w n n b w b w n n b w b w b w n n n T T T T q q T T T T q q T T T T T T n nh q q nq nh h h (3.13)A summary of the results from the present uncertaintly analysis is given in Table 3.1.
Table 3.1 Summary of the results from the uncertainty analysis.
Parameter Uncertainty
Geometry Length & thickness (%)
Area (%) Particle diameter (%) Particle density(%) 0.167% 0.334% 10.0% 13.4% Parameter measurement Temperature, T (C) Temperature difference, ∆𝑇𝑤 (C) System pressure, P (kPa)
0.05 0.36
0.5 Boiling heat transfer on the copper flat plate Total power input, Qt (%)
Imposed net heat flux, 𝑞𝑛(%) Heat transfer coefficient, h(%)
5.9% 8.3% 11.0%
Fig. 3.1 Schematic diagram of six main directions of the heat loss. 2 3 4 5 6 1 Copper block
Fig. 3.2 Schematic diagram of T'5 and T'6
Film heater
Copper block
T′5 T′6