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微区瞬态吸收钙钛矿
（原创版）
目录
1.微区瞬态吸收的概述
2.钙钛矿的简介
3.微区瞬态吸收在钙钛矿研究中的应用
4.微区瞬态吸收技术的发展前景
正文
1.微区瞬态吸收的概述
微区瞬态吸收是一种在微小区域内研究材料光吸收特性的技术，能够有效地揭示材料的光物理性质和光化学反应过程。
在众多光吸收材料中，钙钛矿因其独特的光电性能而备受关注。
2.钙钛矿的简介
钙钛矿是一类具有特殊晶体结构的材料，其化学式为 ABX3，其中 A、B、X 分别为阳离子、阴离子和卤素离子。
钙钛矿材料在太阳能电池、发光二极管和激光等领域具有广泛的应用前景。
3.微区瞬态吸收在钙钛矿研究中的应用
微区瞬态吸收技术在钙钛矿研究中的应用主要体现在以下几个方面：（1）钙钛矿的光吸收特性：通过微区瞬态吸收技术，可以研究钙钛矿在不同波长下的光吸收特性，从而优化钙钛矿材料的能带结构，提高光电转换效率。
（2）钙钛矿的光激发态寿命：微区瞬态吸收技术可以测量钙钛矿材料的光激发态寿命，为研究钙钛矿材料的光稳定性提供重要依据。
（3）钙钛矿的光生电荷载流子动力学：通过微区瞬态吸收技术，可
以揭示钙钛矿材料中光生电荷载流子的产生、传输和复合过程，从而优化钙钛矿器件的性能。
4.微区瞬态吸收技术的发展前景
随着科学技术的进步，微区瞬态吸收技术在钙钛矿研究中的应用将更加广泛。
未来，微区瞬态吸收技术有望在钙钛矿材料的设计、制备和器件优化等方面发挥更大的作用，推动钙钛矿材料在光电领域的广泛应用。
starccm 耦合电场的固体传热物理模型StarCCM: A Coupled Electric Field and Solid Heat Transfer Physical ModelAbstract:This paper introduces the coupled electric field and solid heat transfer physical model in STAR-CCM+. With this model, electric fields can be included in the heat transfer simulations of solid structures. A simple model is presented and its results are then used to discuss the benefits of using this model. The paper also provides an example of a microscale heat transfer simulation of a solid structure, with electric fields included, using star-CCM+.Introduction:Heat transfer plays an important role in many industries, as it can be used to control the temperature of objects, as well as to model the performance of systems. In many cases, electric fields interact with heat transfer, either directly or indirectly. Traditional models, such as theconduction-convection and radiation exchange models, can be used to model heat transfers in the absence of electric fields. However, when electric fields are present, they can play an important role in the heat transfer process. As a result, itis important to incorporate electric fields into heat transfer simulations.The STAR-CCM+ modeling and simulation environment provides a powerful tool for simulating electric fields and heat transfer in combined systems. STAR-CCM+ uses a coupled electric field and solid heat transfer physical model to simulate the electric fields and heat transfer in a solid structure. This model is based on the principles of electromagnetism, which are applied to heat transfer. In this model, the electric field is solved using a simple vector potential formulation, and the heat transfer is solved using the finite element method.The coupled electric field and solid heat transfer physical model is especially useful for microscale simulations of heat transfer, as it can accurately model the electric fields and how they can influence the heat transfer process. Additionally, it can be used to model thermal management systems, such as cooling systems, in which electric fields interact with heat transfer.The following section presents a simple example of a heat transfer simulation, with electric fields included, using the STAR-CCM+ coupled electric field and solid heat transfer physical model.Example:The example presented here is a simple heat transfer simulation of a solid structure, with the electric field included. The model is built in STAR-CCM+, and the physical properties of the material are assumed to be homogeneous across the entire domain.The first step is to define the geometry of the solid structure. In this example, the geometry consists of two cuboids which are connected to each other with a small gap between them. The size of the gaps can be varied, if desired. The next step is to define the electric field. In this case, a constant electric field is used, with a strength of 10V/m. The direction of the electric field can be changed as necessary. The third step is to set the boundary conditions. For the walls of the cuboid, the temperature is set to 300K, and the electric field is set to zero at these boundaries. For the gap between the two cuboids, the electric field is set to 10V/m, and the temperature is set to 280K.The last step is to define the thermal properties of the material. In this example, the thermal conductivity of the material is set to 0.5 W/mK, and the material is assumed to be homogenous across the entire domain.After all of the parameters are set, the model can be run and the results can be visualized. The following figure shows the temperature distribution in the model, with the electric field included. The electric field can be seen to have an influence on the temperature distribution in the solid structure.Conclusion:This paper introduced the coupled electric field and solid heat transfer physical model in STAR-CCM+. This model can be used to include the effect of electric fields on heat transfer simulations of solid structures. A simple example was presented to illustrate the use of this model. The results showed that the electric field can have a significant effect on the temperature distribution in a solid structure, and this effect can be accurately modeled using this model.。
项目名称：微纳尺度相界面作用机理及调控方法提名者：中华人民共和国教育部提名意见：我单位认真审阅了该项目推荐书及其附件材料，确认全部材料真实有效，相关材料均符合国家科学技术奖励办公室的填写要求。
微能源系统挑战性难题是界面效应和通道尺寸效应的耦合机理，本项目围绕该关键科学问题开展了原创研究，在微能源相界面理论、测量及调控方面取得了重要进展，发现了边界条件绝对性和相对性，建立了热边界层再发展强化传热并减小阻力新原理；发现微通道沸腾传热角部核化、气泡爆炸、三区传热，提出沸腾数表征界面效应和通道尺寸效应影响沸腾传热的相对重要性；创造种子气泡传热原理和方法。
已获教育部自然科学一等奖。
8篇代表性论文他引796次，其中SCI他引480次，来自40个国家和地区的他引作者（含诺贝尔奖获得者1人、国内外院士15人等）正面评价项目成果，并被40余本国内外专著正面引用。
徐进良连续四年入选Elsevier中国高被引科学家，担任Energies等国际期刊编委；担任第四届微纳流动会议（英国，2014）、国际传热与热力学循环会议(英国，2016)大会主席之一，是唯一来自中国的学者，主持了CO2动力循环国际会议(北京，2018)、国际传热研讨会（北京，2014）及微能源国际研讨会（三亚，2005），在国内外会议上作特邀报告30次，提升了我国学者在微能源方面的影响力。
成果已应用于指导工程设计，部分成果用于小卫星微推力系统的研究，推动了多相流与微尺度热物理学科的发展，培养了活跃在国际学术前沿的研究队伍。
对照国家自然科学奖授奖条件，推荐该项目申报2019年国家自然科学二等奖。
项目简介本项目属多相流动学及微尺度热物理学领域。
航空航天及电子信息等高新技术快速发展，催生微能源系统新型学科。
微能源系统指能量转换及传递发生在微小空间，实现电能生产、动力供给等功能的系统。
相变型（沸腾、冷凝）微系统中固液、气液界面效应和通道尺寸效应耦合强烈，界面厚度为亚微米或纳米，通道尺寸为亚毫米、微米或纳米。
微纳尺度芯片散热技术探究：解决设备散热难题的新途径Microscale Heat Dissipation in ChipsWith the continuous advancement in chip technology, the miniaturization of electronic devices has become a prominent trend. However, as the size of chips decreases, the issue of heat dissipation becomes increasingly challenging. Efficient heat dissipation is crucial for maintaining the performance and reliability of electronic devices.At the microscale, several techniques are employed to enhance heat dissipation in chips. One common approach is the integration of heat sinks or heat spreaders directly onto the chip surface. These structures provide additional surface area for heat transfer and help dissipate heat more effectively.Another technique is the incorporation of microchannels or microfluidic cooling systems within the chip. These channels allow a flow of coolant, such as liquid or gas, to extract heat from the chip. This method enables localized cooling and can effectively remove heat from hotspots within the chip.Furthermore, the use of advanced materials with high thermal conductivity, such as graphene or carbon nanotubes, has shown promise in improving heat dissipation in chips. These materials can efficiently conduct heat away from the chip, preventing heat buildup and potential damage.In conclusion, microscale heat dissipation in chips is a crucial aspect to consider in the design and development of electronic devices. By implementing techniques like heat sinks, microchannels, and advanced materials, we can effectively manage and dissipate heat, ensuring optimal performance and reliability.中文回答：芯片微纳尺度散热随着芯片技术的不断进步，电子设备的微型化已成为一个突出的趋势。
碳纳米管热导碳纳米管是一种具有优异热导性能的纳米材料，由碳原子通过特定的方法排列而成。
它的热导性能在许多领域具有重要的应用价值。
本文将介绍碳纳米管的热导特性及其在科学和工程领域的应用。
碳纳米管的热导性能主要受到其结构和尺寸的影响。
碳纳米管具有纳米尺度的直径和长长度，这使得它们能够在热传导过程中保持高效的热导率。
此外，碳纳米管的晶格结构也对其热导性能起着重要作用。
研究表明，碳纳米管的热导率可以达到数千瓦特/米·开尔文，远远高于其他材料，如铜和铝。
碳纳米管的高热导性能使其在许多领域具有广泛的应用。
首先，碳纳米管被广泛应用于热界面材料中。
热界面材料是用于提高热能传递效率的材料，常用于电子设备和光电器件等领域。
碳纳米管的高热导率使其成为理想的热界面材料之一，可以有效地降低热阻，提高设备的散热性能。
碳纳米管在热电转换器件中也有重要的应用。
热电转换是一种将热能直接转化为电能的过程，可以用于能源收集和节能领域。
碳纳米管具有高热导率和良好的电子输运性能，可以作为热电转换器件的优良材料。
通过将碳纳米管与其他材料结合，可以制备出高效的热电材料，提高热电转换效率。
碳纳米管还可以应用于热传感器和热成像技术中。
由于碳纳米管具有高灵敏度和高空间分辨率，可以用于检测微小的温度变化和热量分布。
这些特性使碳纳米管成为制备高性能热传感器和热成像器件的理想材料。
除了上述应用之外，碳纳米管的热导性能还在热管理、热界面涂层、热导复合材料等领域得到广泛应用。
通过合理设计和调控碳纳米管的结构和性质，可以进一步提高其热导率和应用性能。
碳纳米管具有优异的热导性能，在科学和工程领域有广泛的应用价值。
通过充分利用碳纳米管的热导性能，可以改善热传导效率，提高能源利用效率，推动科技和工程的发展。
未来，随着对碳纳米管热导性能的深入研究，相信会有更多的应用领域被开发出来，为人类的生活和工作带来更多的便利和创新。
Microscale heat transfer enhancement using thermal boundarylayer redeveloping conceptJ.L.Xua,*,Y.H.Gana,b,D.C.Zhang c ,X.H.LicaGuangzhou Institute of Energy Conversion,Chinese Academy of Sciences,Nengyuan Road,Wushan,Guangzhou 510640,PR ChinabDepartment of Thermal and Energy Engineering,University of Science and Technology of China,Hefei 230027,Anhui Province,PR ChinacInstitute of Microelectronics,Peking University,Beijing,100871,PR ChinaReceived 18May 2004;received in revised form 6December 2004AbstractWe demonstrated a new silicon microchannel heat sink,composing of parallel longitudinal microchannels and sev-eral transverse microchannels,which separate the whole flow length into several independent zones,in which the ther-mal boundary layer is in developing.The redeveloping flow is repeated for all of the independent zones thus the overall heat transfer is greatly enhanced.Meanwhile,the pressure drops are decreased compared with the conventional micro-channel heat sink.Both benefits of enhanced heat transfer and decreased pressure drop ensure the possibility to use ‘‘larger’’hydraulic diameter of the microchannels so that less pumping power is needed,which are attractive for high heat flux chip cooling.The above idea fulfilled in microscale is verified by a set of experiments.The local chip temper-ature and Nusselt numbers are obtained using a high resolution Infrared Radiator Imaging system.Preliminary expla-nation is given on the decreased pressure drop while enhancing heat transfer.The dimensionless control parameter that guides the new heat sink design and the prospective of the new heat sink are discussed.Ó2005Elsevier Ltd.All rights reserved.1.IntroductionIn macroscale heat transfer can be enhanced by inter-rupting the boundary layer formation and providing more surface area.Louvered fins are examples to fulfill such heat transfer enhancement in the compact heat exchanger designs,which are widely used in several industry applications [1,2].The available experimental/numerical studies show that the new boundary layer for-mation along the fin surface can have higher heat trans-fer coefficients [1].In this paper we use the thermal boundary layer redeveloping concept in microscale and propose a new design of the silicon-based microchannel array with transversal channels.As an example shown in Fig.1,the new microchan-nel heat sink consists of ten parallel longitudinal trian-gular microchannels and five transverse trapezoid microchannels,which separate the whole flow length into six independent zones.Once liquid enters the ten microchannels of each separated zone,the thermal boundary layer is in developing due to the short flow length,ensuring higher heat transfer coefficient.Such0017-9310/$-see front matter Ó2005Elsevier Ltd.All rights reserved.doi:10.1016/j.ijheatmasstransfer.2004.12.008*Corresponding author.Tel./fax:+862087057656.E-mail address:xujl@ (J.L.Xu).International Journal of Heat and Mass Transfer 48(2005)1662–1674/locate/ijhmtthermal boundary layer redeveloping process repeats for all of the six independent zones,thus the overall heat transfer is enhanced.A comparative conventional microchannel heat sink has all of the same sizes except that there are no transverse microchannels.2.Literature survey on microchannelflow and heat transferThe objective of this paper focuses on demonstration of the thermal boundary layer redeveloping mechanism that can be incorporated in the microchannel heat sink design.The detailed literature survey of theflow and heat transfer in microchannels is beyond the scope of the present paper,but can be found in some review papers such as[3–5]etc.The literature is becoming rich in microchannel studies.However,as shown,the results are often conflicting,especially considering their perfor-mance as compared to classicalflow and heat transfer relations.The conflicting results are generally coming from the microchannel fabrication and the measurement methods that are key to determine theflow and heat transfer characteristics[6].The benchmark data is scarce.Microscale effects are quite different for gas and liquidflow in microchannels.Rare gas effect occurs if the channel size is down to the same order of themean J.L.Xu et al./International Journal of Heat and Mass Transfer48(2005)1662–16741663free path of the gas.The pressure drop may have a non-linear distribution along theflow direction due to the compressible effect[7].Liquids have the densities that may be one thousand times of gas.Liquid molecules are closely packed with each other.Small size down to nano or micron scale may induce the slip boundary con-dition due to the intermolecular force between solid and liquid particles[8].In additional to these,any clean li-quid may contain metal particles that may induce the electrical-double-layer(EDL)near the solid wall.Pres-sure-driven liquidflow in microchannels may include the electrical viscous effect[9].For the microchannel size typically applied in MEMS device between1l m and 1.0mm,the above microscale effects may partially,com-bined,or not influence theflow and heat transfer be-cause the channel size has so wide range.Up to now it is still difficult to identify the‘‘true’’microscale effect from the experiment due to the difficulties in instrumentation.Very high heatflux chip cooling requires smaller hydraulic diameter and largerflow rate,leading to very high pressure drop.Careful attention should be given to balance theflow and heat transfer for the microchannel heat sink.Fully developedflow and heat transfer assumption is valid for very small channel size.How-ever,when the hydraulic diameter of the microchannels are relative large,such as larger than100l m,they have longer‘‘thermal entrance length’’to reach the thermal1664J.L.Xu et al./International Journal of Heat and Mass Transfer48(2005)1662–1674developedflow.Generally a high heatflux chip may have the length that is several times of the thermal devel-oping length.If we can separate the wholeflow length into several independent zones that ensure the thermal developingflow in each independent zone,the overall heat transfer can be enhanced,which can partially com-pensate the hydraulic diameter effect(generally larger channel size will deteriorate the heat transfer perfor-mance).Thus it is possible to use‘‘larger’’microchannel size,while the pressure drop is sharply decreased.As noted,most of the available studies were performed for the developedflow of the microchannel heat sinks, very little was conducted on the thermal developingflow in microscale[6].Moreover,much attention was paid on the improved chip temperature measurements using a high resolution Infrared Radiator Imaging System in this paper.3.Test section and experimental apparatus3.1.Description of the microchannel heat sinkTwo silicon microchannel heat sinks were fabricated in clean room environment.One is the heat sink incor-porating the thermal boundary layer redeveloping con-cept(Fig.1)and the other is the conventional one with the same size but without the transverse microchannels.Both silicon wafers are30mm in length,7mm in width,525l m in thickness.The pyrex glass plate that is bounded with the silicon wafer has the thickness of 410l m.The whole length of the parallel microchannels in longitudinal direction is21.45mm,and the total width coving the ten triangular microchannels is 4.35mm.The triangular microchannel has the hydraulic diameter of155l m A thin platinumfilm was deposited at the backside of the silicon wafer by‘‘chemical vapor deposition’’technique to provide a uniform heatflux. The thinfilm has the same length of the longitudinal microchannels,but has the total width of 4.20mm, which is narrower by half triangular microchannel width,to ensure the safe operation of the silicon wafer at extremely high heatflux.The silicon wafer has the effective heating length of16.0mm,symmetrical located about the wafer.The heater was connected to a precision ACpower supply unit and heat generated in the heater was transferred to the liquidflow from microchannels.In Fig.1five transverse trapezoid microchannels were uniformly arranged in theflow direction,forming six independent zones.The centerline distance between each transverse microchannel is 3.694mm.Such dis-tance is close to the thermal developing length for the velocity of1m/sflowing in triangular microchannels. This configuration design ensures the thermal develop-ingflow in each independent zone thus higher heat transfer performance is obtained covering all of the pres-ent experimental data range.3.2.Experimental setup and procedureFig.2shows the experimental setup and the corre-sponding apparatus.Water is pressed by the nitrogen gas andflows successively through a liquid valve,a 2l mfilter,the silicon wafer test section,a heat exchan-ger,andfinally returns to a collection container.The pressure of the water tank is well controlled by adjusting the high precision pressure regulator valve located be-tween the nitrogen gas tank and the water tank.The liquid temperature in the water tank is controlled by a constant temperature control unit(PID control unit) with the uncertainty of±0.5°C.In order to decrease the heat loss to the environment and keep the inlet tem-perature of the test section as the predetermined value, the high quality heat insulation material was wrapped on the outer surface of the connection tube between the outlet of the water tank and the inlet of the test sec-tion.The steady water massflow rate was determined by weighing the mass increment over a longer given period of time using a high precision electronic balance,which has the accuracy of0.02g.The inlet and outlet temper-atures were measured by the high precision jacket thermocouples with the diameter of1.0mm.These ther-mocouples have the measurement errors within±0.3°C. The inletfluid pressure was measured by a Setra pres-sure transducer(Model206),which was calibrated against a known standard and the uncertainty in the pressure measurements was less than1%.All of the pres-sure and temperature signals were collected by a HP data acquisition system.At the top of the silicon wafer, a microscope(Leica series,Germany)was installed to monitor theflow status through the microchannels.This is important to keep the single-phase liquidflow in microchannels at high heatfluxes.Boiling is never initiated.J.L.Xu et al./International Journal of Heat and Mass Transfer48(2005)1662–167416653.3.Chip temperature measurementDistinct with other studies,the wafer temperatures of the backside thinfilm were measured by a high resolu-tion,high accuracy Infrared Radiator Imaging System (FLIR ThermaCAM SC3000IR).This system has a thermal sensitivity of0.02°Cat30°C,a spatial resolu-tion of1.1mrad,a typical resolution of320·240over the focused area,and an image frequency of50Hz, allowing precise determination of the temperature gradi-ents across the chip surface.Throughout all of the tests,the IR camera was situ-ated so that the heating area of the silicon wafer (16.0·4.2mm2)is in thefield of ing this tech-nique,the temperature gradient,the maximum tempera-ture and the transient response could be detected.The IR Imaging System was connected to a PC.For each run case,the PCstores the imagefile and the corre-sponding datafile which contains6080data points re-lated to the focused thinfilm heating area.The measurement of temperature by means of the radiation power emitted from a surface requires a care-ful calibration of the emissivity,which depends strongly on the surface topography and the wavelengths that are interrogated[10].The spatial resolution is limited to the working wavelength of the IR camera that is can-tered in one of the atmospheric windows8–9l m.The ThermaCAM SC3000has a GsAs,Quantum Well Infrared Photon FPA detector working in the spectral range of8–9l m.This is the physical limitation.We use an addition microlens over the IR camera,forming the real spatial resolution of17.5l m.A very thin ‘‘black lacquer’’was uniformly coated on the thinfilm surface of the silicon wafer.An emissivity of approxi-mately0.94resulted in good measurement accuracies. The temperature dependence of emissivity within the considered range can be neglected.Such procedure is similar to that of Hapke et al.[11].Using this technique, the IR Imaging System was calibrated against a set of known standard temperatures with the accuracy of 0.3°C.It is noted that the measured surface temperature is strongly depended on the emissivity.Other factors,such as the ambient temperature,the air humidity and the distance between the camera lens and the silicon wafer that are put into the software have little influences.Be-cause the black paint is only focused on the effecting heating area,there is a stiffemissivity change at the heat-ing element boundaries.The IR camera sees more area larger than that of the heating element thus poor read-ings are obtained with the area beyond the effective heat-ing surface due to that the‘‘bright’’thin Ptfilm with lower emissivity is directly exposed in the camera view. However,these poor readings are not used for the data process.We are only interested in the temperature read-ings within the painted heating area.The experiment covers the following ranges:inlet pressures of1–2bar,pressure drops of10–100kPa, inlet temperatures of30–70°C,massfluxes of534.79–4132.85kg/m2s,and the project heatfluxes of10–100W/cm2,which is defined as the total heating power that is received by the liquid divided by the effective heating area.Deionized water is used as the working fluid.4.Data reduction4.1.Dimensionless pressure dropThe data reduction procedure is similar to Wu and Chen[12].It is convenient to use the dimensionless pres-sure drop in this paper instead of the friction factor, while the later is usually defined for the fully developed and uninterruptedflow.They have the same form ex-pressed asf¼D pÁD hLÁ12q uð1Þwhere D p is the pressure drop measured by the pressure drop transducer across the microchannel heat sink,q is the liquid density in terms of the mean value of the inlet and outlet temperatures,D h and L are the hydraulic diameter and the whole length of the longitudinal micro-channels,and u is the average velocity of water.Using the measured massflow rate of water,M,the dimensionless pressure drop is rewritten asf¼D pDhq N2A2c2LMð2Þwhere A c is the cross-sectional area of each triangular microchannel,N is the number of the longitudinal microchannels.4.2.Overall heat transfer coefficientThe overall heat transfer coefficient for the deionized waterflowing through the longitudinal microchannels is defined ash¼QNA w D T mð3Þwhere A w is the total area of the side walls of longitudi-nal microchannels.The pyrex glass is assumed to have an adiabatic condition.Q is the heating power that is received by water,which is calculated by the energy conservation equation from the inlet to outlet liquid ing the powermeter readings as the power input results in uncertainties which maybe differ-ent from case to case.The heat extracting efficiency g is1666J.L.Xu et al./International Journal of Heat and Mass Transfer48(2005)1662–1674defined as Q divided by the total heating power.Cover-ing the present data range g is in the range of90%to 96%.It acquires the lower range for the lower heating power and higher end for the higher heating power,con-sidering the total heat loss to the environment.The mean temperature difference D T m between the channel wall and the water is calculated byD T m¼T wÀ1ðT inþT outÞ¼P152i¼1P40j¼1T ij6080À12ðT inþT outÞð4Þwhere T w is the average wall temperature,T ij is the chip local temperature measured by the IR Imaging System at each point in the heating area(black painted area). The heating area totally forms6080data points,i is the longitudinal grid and j is the transverse grid.Totally there are152grids for i direction and40grids for j direc-tion.For simplicity,the temperature differences between the thinfilm and the side wall of the microchannels is ne-glected due to the very large thermal conductivity of the silicon wafer.T in and T out are the inlet and outlet bulk temperatures of water.The average Nusselt number in terms of various mea-surements is written asNu¼MC p D hðT outÀT inÞNkA w D T mð5Þwhere C p and k are the specific heat and the thermal con-ductivity of water.The mean temperature of water (T in+T out)/2was used to characterize the physical prop-erties of water,including q,m,k,and C p,which are assumed to be independent of pressure.In order to per-form the comparative analysis between the wafer heat sinks with and without the transverse microchannels, the data reduction follows the same procedures for the two heat sinks.4.3.Local heat transfer coefficientThe local heat transfer coefficients and Nusselt num-bers are obtained in terms of local temperatures in x–y coordinateshðx;yÞ¼QNA wðT wðx;yÞÀT fðxÞÞð6ÞNuðx;yÞ¼hðx;yÞD hkð7ÞIn Eq.(6),the local liquid temperature T f is assumed to have a linear distribution along theflow direction. The local Nusselt number in terms of various measure-mentsfinally yields:Nuðx;yÞ¼MC p D hðT outÀT inÞNA w kðT wðx;yÞÀT fðxÞÞð8Þ4.4.Error analysisIn terms of Eqs.(2),(5)and(8),the errors accountingfor f,Nu,and Nu(x,y)come from the measurementerrors of a set of parameters,that are listed in Table1.Performing the standard error analysis[13],the maxi-mum uncertainties in determining these parameters aregiven in Table1.It is seen that the maximum errorsdue to the measurements are less than3.33%,2.93%,2.93%for f,Nu and Nu(x,y)respectively.Even thoughall the temperatures measured by the thermocouplesand the IR camera are carefully calibrated,the maxi-mum errors of0.5°Care used for the error analysis.Normalizing such error with respect to the minimum in-let liquid temperature such as30°Cyields the maximumpossible error of1.67%for the temperatures.5.Experimental results and discussion5.1.Chip temperature and Nusselt number distributionfor the conventional heat sinkA typical run case for the project heatflux high up to104W/cm2is shown in Fig.4,in which Fig.4a–c are forTable1Measurement errorsParameters Maximum errors Parameters Maximum errorsD h 1.29%D p0.1%L0.01%T0.5°C(1.67%)L h0.01%D T m 1.67%A c 1.15%Re 2.96%A w0.77%f 3.33%M 1.02%Nu 2.93%J.L.Xu et al./International Journal of Heat and Mass Transfer48(2005)1662–16741667the chip temperature distributions,Fig.4d for the Nus-selt number distributions.The fully developed hydraulic flow is maintained due to the Prandtl number much greater than unity.However,the thermaldevelopingFig.4.Chip temperatures and local Nusselt numbers for the conventional heat sink (T in =30.9°C,Q =69.7W,G =3705.8kg/m 2s,D p =99.8kPa,Re =871,q =104W/cm 2;(a)IR color image for the temperatures;(b)three-dimensional temperatures;(c)chip temperatures versus flow length and (d)Nusselt numbers versus flow length).1668J.L.Xu et al./International Journal of Heat and Mass Transfer 48(2005)1662–1674flow is maintained because Lþh ¼0:0275which is onlyhalf of the transition value of Lþh ¼0:05at which thethermal developedflow is approached[14].The color IR image(Fig.4a)intuitionisticly illustrates the chip temperature and its gradient in x–y plane of the focused heating area.The temperatures in a three-dimen-sional form shown in Fig.4b behave the‘‘horseback’’shape with apparent positive gradient in x-direction but slight gradient in y-direction.It is seen that the chip tem-perature along theflow direction is not linear.The tem-perature difference between the chip and the liquid is increased with increasing x but reaches the maximum va-lue at x=14mm,close to the end of the heating area at x=16mm.A slight negative gradient is observed from x=14mm to x=16mm,attributed to the thermal con-duction in solid silicon near the end of the heating area in x-direction.The chip temperatures are slightly higher at the chip center region(little differences were identified between y/W=0.256and y/W=0.513).But they are slightly lower at y=0(the margin of the heating loca-tion),also attributed to the thermal conduction in solid silicon in y-direction.The temperature difference be-tween y/W=0and y/W=0.513is about4–5°C.As observed in Fig.4d the following phenomena could be identified:(1)The Nusselt numbers are much higher at the‘‘entrance region’’.The thermal developing region is longer than half of the total heating length.(2) The Nusselt numbers are higher at the margin of the heating area at y/W=0and y/W=1,corresponding to the lower temperatures at these locations due to the ther-mal conduction in solid silicon.(3)A very slight positive gradients of the Nusselt numbers occur at the end of the heating area(x/L h=1),also due to the thermal conduc-tion in the solid silicon.(4)The Nusselt Numbers approach uniform in the center of the heating sera in y-direction.For instance,they tend to collapse to a sin-gle curve at y/W=0.256and y/W=0.513.When x+>0.013,the local Nusselt numbers at the chip center region can match the theoretical solution for the circular tube at the constant heatflux condition in macroscale predicted by[14].It is noted that for theflow and heat transfer analysis at high heatflux conditions,careful attentions should be given on the liquid property variations.Under such con-ditions if the liquid temperatures increase20°C,the liquid Prandtl number decreases by35%from30°Cto 50°C,which affects the development of the thermal boundary layer.In terms of the present experimental observations,the future numerical modelings should in-clude the whole silicon wafer as the calculation domain, and account for the liquid physical property variations. Flow and heat transfer in all of the microchannels shall be coupled with the whole silicon wafer.For all of the case tested,the measured parameters are exactly symmetry about the centerline of y/W=0.5 This is also true for the new microchannel heat sink.5.2.Chip temperature and Nusselt number distribution for the heat sink with transverse microchannelsVerifying Figs.4and5a–d,the chip temperatures and Nusselt numbers have the following similar behaviors for both heat sinks with and without the transverse microchannels:(1)Non-linear distribution along the flow length.(2)Parameter gradients occur at the mar-gins of y/W=0,y/W=1,x/L h=0,and x/L h=1,due to the thermal conduction in solid silicon at the junction between the heated and the un-heated area.However, the chip temperatures and Nusselt numbers for the heat sink with the transverse microchannels display the cycle behavior along theflow length(see Fig.5a–d),support-ing the periodic thermal boundary layer redeveloping concept.Note in Fig.3b that there are four independent zones in the focused heating area.Thus four cycles of the chip temperatures and Nusselt numbers along theflow length occur.At the four transverse trapezoid micro-channel regions,four thin horizontal‘‘brighter line’’can be identified(see Fig.5a),resulted from the smaller flow velocity in the transverse microchannels.Narrow the width of the transverse trapezoid microchannel and increase the thickness of the silicon wafer can definitely reduce or release such local temperature gradient and the corresponding thermal stress.In Fig.5d,it is shown that thefirst zone has larger Nusselt numbers.The second,third and fourth zones repeat the very similar distributions.Each cycle of the Nusselt number corresponds to each independent zone. The smallerflow velocity in the trapezoid microchannel induces smaller Nusselt number.But they have a step in-crease once liquid reenters the parallel longitudinal microchannels,followed by a slow decrease until the liquid enters the next transverse microchannel.The relative short length of the thermal boundary layer Lþh;s for each independent zone provides higher Nusselt numbers.parisons between the two microchannel heat sinks5.3.1.Heat transfer enhancement of the new microchannel heat sinkIn order to further identify the benefits that we can obtain from the new microchannel heat sink,a pair of comparative run cases are given in Fig.6a–d,which are based on the similarflow conditions for both heat sinks,with same inlet liquid temperature of30°C,effec-tive heating power of70W and meanflow velocity of 3.2m/s.The color IR images(see Fig.6a–b)intuitionis-ticly illustrate that the new heat sink lowers the chip temperatures.The chip temperatures and the Nusselt Numbers show smaller differences between the two wafers in thefirst zone.However,the new heat sink can decrease the temperatures by14°Cmaximally inJ.L.Xu et al./International Journal of Heat and Mass Transfer48(2005)1662–16741669other regions.The Nusselt numbers,which are higher for the new heat sink,display the cycle behavior for the four independent zones.In each independent zone,the Nusselt numbers are lower in the transverse micro-channel regions,but will have a sharp increase followed by a slow decrease.The overall Nusselt number fortheFig. 5.Chip temperatures and local Nusselt numbers for the new heat sink (T in =29.8°C,Q =69.1W,G =1469.3kg/m 2s,D p =20.2kPa,Re =345,q =103W/cm 2;(a)IR color image for the temperatures;(b)three-dimensional temperatures;(c)chip temperatures versus flow length and (d)Nusselt numbers versus flow length).1670J.L.Xu et al./International Journal of Heat and Mass Transfer 48(2005)1662–1674new heat sink is 7.954,which is increased by 26.4%com-pared with the conventional one.For all of the run cases tested,even though the chip temperatures are higher relative to the neighboring region in thetransverseFig. parisons between two heat sinks:(a)for conventional heat sink T in =29.5°C,Q =69.8W,G =3216.9kg/m 2s,D p =82.2kPa;(b)for new heat sink,T in =29.8°C,Q =69.8W,G =3238.9kg/m 2s,D p s =60.3kPa;(c)chip temperatures along the flow length for the two heat sinks;and (d)Nusselt numbers along the flow length for the two heat sinks.J.L.Xu et al./International Journal of Heat and Mass Transfer 48(2005)1662–16741671microchannel regions,but they are still quite lower than those in the corresponding regions for the conventional heat sink.For a given geometry design of the new heat sink,the heat transfer enhancement is controlled by the dimen-sionless parameter,Lþh;s ¼L h;s=ðD h Re PrÞ,for each inde-pendent zone.Neglecting the total widths of the transverse microchannels,we haveLþh;s ¼Lþh=ðN sþ1Þð9ÞTheoretically the heat transfer enhancement ratio/ is defined as the overall Nusselt number for the new heat sink divided by that for the conventional one without the transverse microchannels:/¼Nu sNu¼ðN sþ1ÞR Lþh;sNu d xþRðN sþ1ÞLþh;s Nu d xþð10ÞFig.7demonstrates the higher overall Nusselt num-bers for the new heat sink than for the conventional one.The conventional triangular microchannels can match the theoretical solution of the circular tube in macroscale[14].Note that Fig.7is obtained using the non-dimen-sional parameters of Nusselt numbers and effective heating length.The curve for the conventional micro-channels can be extended to other microchannel arrays, providing that the hydraulic diameter of the microchan-nel is larger enough such as more than100l m thus the possible microscale effects can be neglected.The varied physical properties are considered because the curve is experimental determined.However,the curve of the Nusselt numbers versus the non-dimensional effective heating length is only for the new microchannel arrays with the heating length crossingfive transverse channels over four independent zones in which the thermal boundary layer is developing.Future numerical/experi-mental studies will be focused on the heat transfer per-formance for the microchannel arrays with different transverse channels.The experimental decided heat transfer enhancement ratio in terms of data illustrated in Fig.7is in the range of1.31–1.12within the non-dimensional heating length Lþhof0.02–1.10.It is noted that the net heat transfer enhancement ratio consists of two mechanisms,one is the thermal boundary layer redeveloping effect and the other is the wet heat transfer area increase effect.For the present microchannel array with transverse channels, the heat transfer area is increased by10.8%from the conventional microchannel heat sink of83.2mm2to the new microchannel heat sink of92.2mm2within the effective heating length of16.0mm.Therefore,the net heat transfer enhancement ratio for the new microchan-nel heat sink due to the thermal boundary layer redevel-oping effect is from1.202to1.01.At the lower end of the heat transfer enhancement ratio,the new heat sink is approaching the developed thermal boundary layer.5.3.2.Pressure drop reduction of the new microchannel heat sinkFor the comparative run cases shown in Fig.6,the new microchannel heat sink decreases the pressure drop by27%.The very smallflow velocity in the transverse microchannels leads to the neglected pressure drops across the width of the transverse trapezoid microchan-nels.Assuming the linear distribution of the pressure drop versus theflow length for the hydraulically devel-opedflow,the total pressure drops for the two heat sinks have the following relationshipD ps¼ðLÀN sÁwÞD p=Lð11ÞHere L is the wholeflow length of the longitudinal microchannel,N s and w are the number and the width of the transverse trapezoid microchannels,D p s and D p are the pressure drops for the new heat sink and the con-ventional one,respectively.In Eq.(11)LÀN sÆw is the ‘‘effectiveflow length’’for the new microchannel heat sink.In terms of the geometry parameters,the pressure drop for the new heat sink should be decreased by26% compared with the conventional one based on Eq.(11). Such simple estimation of the pressure drops related to the two microchannel heat sinks conforms the measured values well.Fig.8illustrates the decreased dimensionless pressure drops for the new heat sink than for the conventional one,as expected.At lower Reynolds numbers such as less than300,the dimensionless pressure drops for the conventional triangular microchannels are very close to those for the circular tube.However,at higher Reynolds numbers,the dimensionless pressure drops are larger than those of the circular tubes.Such differ-1672J.L.Xu et al./International Journal of Heat and Mass Transfer48(2005)1662–1674。
