Coupled thermal and hydrodynamic models of flat micro heat pipes for the cooling of multiple electronic components

An analytical solution for both the liquid and vapour flows inside a flat micro heat pipe (MHP) coupled to an analytical solution for the temperature inside the MHP wall is presented. The maximum heat transfer capability of a flat MHP, on which several heat sources and heat sinks are located, is calculated. The capillary structure inside the MHP is modeled by considering a porous medium, which allows to take into account capillary structures such as meshes or sintered powder wicks. The thermal model is able to calculate the part of heat flux transferred only by heat conduction in the MHP wall from the heat transferred by change of phase.     

Effect of variations in thermophysical properties and design parameters on the performance of a V-shaped micro grooved heat pipe

The paper presents a detailed simulation of a V-shaped micro heat pipe. The effect of the substrate temperature on the model has been considered. A new method for calculating dry-out length has been proposed. The sensitivity of the model to variations in thermophysical properties and design parameters has been studied. The variations in the contact angle for the substrate-coolant liquid system, surface tension and viscosity of the coolant liquid, inclination, groove angle, length of adiabatic section and radius of ungrooved substrate have been considered. The effect of design and operating parameters on the performance of the heat pipe has been studied. The variations in contact angle have been found to significantly affect the performance of a micro heat pipe. The performance of a micro heat pipe is susceptible to ungrooved area of a V-shaped micro heat pipe. If the groove is not sharp enough i.e., the radius of ungrooved substrate is more; the micro heat pipe may cease to work even before it reaches its other operating limits. The various sensitivity studies made in this work gives better understanding of variations in thermophysical properties and design parameters of a micro heat pipe.     

Experimental investigation of micro heat pipes of different cross-sections having same hydraulic diameter

Effects of micro heat pipe （MHP） cross-sections and orientations on its thermal performance are experimentally investigated in this study. Tests are conducted using five different cross-sections （circular, semicircular, elliptical, semi-elliptical and rectangular） of micro heat pipes having same hydraulic diameter of 3 rnm placed at three different inclination angles （0°, 45°, 90°）, where water is used as the working fluid. Evaporator section of the MHP is heated by an electric heater and the condenser section is cooled by circulation of water in an annular space between condenser section and the water jacket. Temperatures at different locations of the MHP are measured using five calibrated K type thermocouples. Heat supply is varied using a voltage regulator which is measured by a precision ammeter and a voltmeter. It is found that thermal performance tends to deteriorate as the MHP is flattened. Thus among all cross-sections of MHP, circular one exhibits the best thermal performance in terms of heat flux dissipation followed by semi-elliptical, semi-circular, elliptical and rectangular cross-sections. Moreover, its heat transfer capability also decreases with decreasing of its inclination angle. Finally, a correlation is developed which covers all the experimental data within ＋7%.     

Thermal analysis of optimally designed inclined micro heat pipes with axial solid wall conduction

The effect of gravity on the thermal performance of inclined micro heat pipes with axial conduction in the solid wall is reported. A one-dimensional, steady-state model is developed from first principles in which the continuity, momentum, and energy equations of the liquid and vapour phases, together with the Young–Laplace equation, are solved numerically to yield the heat and fluid flow characteristics of an inclined micro heat pipe which is operated optimally at a certain operating temperature. The analysis covers both the favourable and adverse effects of gravity on the performance of a micro heat pipe. The effects of gravity, through the angle of inclination, on the heat transport capacity, the optimal charge level of the working fluid, the liquid volume fraction distribution, the circulation strength of working fluid and the solid wall temperature distribution are analysed, to provide a better insight for the design of inclined micro heat pipes.     

Ladder shape micro channels employed high performance micro cooling system for ULSI

The success of an IC cooling system or heat sink for ULSI depends on the ability to achieve effective heat transfer rate to the flowing liquid and superior flow performance of the micro channels. The effective heat transfer requires large wall area that is in contact with the flowing liquid and availability of large mass of fluid to carry away the heat. Conventionally a collection of parallel rectangular micro channels have been used to achieve this. However, there is a practical maximum limit on the number of channels that can be imbedded in the back surface of the substrate by bulk etching. In this paper, the authors propose a collection of ladder shape micro channels with rectangular cross section that effectively increases the wall area thus decreasing the thermal resistance and increases heat transfer coefficient. Two parallel rectangular channels are connected by one or more link channels to form a ladder shape micro channel. The flow performance of these ladder shape micro channels have also been studied using COMSOL multi physics and the comparison of the flow performance indicating parameters of the collection of conventional rectangular channels with the proposed collection of ladder shape micro channels show that the high performance heat sinking can be achieved using the proposed ladder shape micro channels. Further the thermal responses of these micro systems have also been studied extensively and these studies show that the thermal resistance decreases with the introduction of ladder shape micro channels considerably. Finally the substrate strength has also been estimated using IntelliSuite Software and it shows that the rigidity of the substrate is slightly lower in ladder shape micro channel carved substrates but the degradation is highly insignificant.     

Fabrication and test of radial grooved micro heat pipes

This paper describes the development of radial grooved micro heat pipes (MHPs) with a three-layer structure. The MHPs were designed to allow separation of the liquid and vapor flow to reduce the viscous shear force. The 5×5 cm² MHP array was fabricated by using bulk micromachining and eutectic bonding techniques on 4-in. (1 0 0) silicon wafers. Experiments were undertaken to evaluate the performance of wafers with three different wafer fill rates at different input powers. We glued a heater below the evaporator section, pumped cold water through a square copper heat exchanger above the heat pipe, and pasted 15 K-type thermocouples on both sides of MHP structure to record the variations of surface temperature. After the evaluation, the MHP with 70% fill rate showed the best performance as compared to samples with smaller fill rates.     

Evaporation heat transfer characteristics of a grooved heat pipe with micro-trapezoidal grooves

A detailed mathematical model predicting the effect of contact angle on the meniscus radius, thin film profile and heat flux distribution occurring in the micro-trapezoidal grooves of a heat pipe has been presented. The model can be used to determine the maximum evaporating heat transfer rate in the evaporator including the effects of disjoining pressure and surface tension. The equation of meniscus radii calculation in the evaporator at given heat load based on the liquid wicks configuration has been put forward. The numerical results show that while the capillary limitation governs the maximum heat transport capability in a grooved heat pipe, the thin film evaporation determines the effective thermal conductivity in a grooved heat pipe. The ratio of the heat transfer through the thin film region to the total heat transfer through the wall to the vapor phase decreases when the contact angle increases. The superheat effects on the heat flux distribution in the thin film region also have been conducted and the results show that the disjoining pressure plays an important role in this region. The current investigation will result in a better understanding of thin film evaporation and its effect on the effective thermal conductivity in a grooved heat pipe.     

Experimental investigation of the transient thermal performance of a bent heat pipe with grooved surface

A bent copper–water heat pipe with grooved inner surface has been investigated experimentally. A comparison between the bent and the straight heat pipes was performed at different inclination angle. Experimental results show that there is a small temperature difference between the condenser of the straight and that of the bent at the vertical orientation. The temperature difference increases as an inclination angle increases. Furthermore, the response time increases as the inclination angle increases. The thermal response of the straight to a sudden heat load is slightly faster than that of the bent. However, as the inclination angle increases to after the horizontal, the heat flux at the condensers decreases nonlinearly and the response time increases nonlinearly. A two-phase flow map has been proposed to explain the nonlinear performance of the thermal response and the heat flux, based on force balance among gravity, capillary, friction and buoyancy force acting on the working fluids. The nonlinear performance of the thermal response and the heat flux results from the capillary blocking due to formation of liquid bridge of two-phase flow. It was also found that the bent heat pipe is more sensitive to the change of the inclination angle than the straight in terms of the thermal response time and the heat flux of the condenser. The heat flux of the bent decreases faster than that of the straight after the horizontal orientation.     

高低热导率相间表面强化饱和池沸腾的格子玻尔兹曼模拟

采用格子玻尔兹曼方法模拟高低热导率相间表面的饱和池沸腾过程,研究不同表面高低热导率区域热导率比值、低热导率区域宽度和深度对沸腾换热性能的影响。对比均匀热导率表面与高低热导率相间表面的沸腾曲线发现：高低热导率相间表面的沸腾过程可被分为5个阶段,并且其临界热流密度最高可达均匀表面的12倍;高低热导率相间可促使表面维持一定的温度差异,从而保持明显的气液流动;随着低热导率区域宽度增大,气液分离更加明显,低热导率区域宽度存在一个最优值,其与毛细长度的量级接近;随着低热导率区域的深度增大,表面过热度的差异更加明显。     

Modulated wick heat pipe

In heat pipes, modulation of evaporator wick thickness provides extra cross-sectional area for enhanced axial capillary liquid flow and extra evaporation surface area, with only a moderate increase in wick superheat (conduction resistance). This modulated wick (periodic stacks and grooves over a thin, uniform wick) is analyzed and optimized with a prescribed, empirical wick superheat limit. A thermal-hydraulic heat pipe figure of merit is developed and scaled with the uniform wick figure of merit to evaluate and optimize its enhancement. The optimal modulated wick for the circular and flat heat pipes is found in closed-form expressions for the viscous-flow regime (low permeability), while similar results are obtained numerically for the viscous-inertial flow regime (high permeability which is also gravity sensitive). The predictions are compared with the experimental result of a prototype (low permeability, titanium/water pipe with the optimal design) heat pipe which gives a scaled figure of merit of 2.2. Good agreement is found between the predicted and measured performance. The maximum enhancement is limited by the pipe inner radius (tapering of the stacks), the wick effective thermal conductivity, and the prescribed wick superheat limit.     

Study on flow and heat transfer characteristics of heat pipe with axial “Ω”-shaped microgrooves

A theoretical model of fluid flow and heat transfer in a heat pipe with axial “Ω”-shaped grooves has been conducted to study the maximum heat transport capability of these types of heat pipes. The influence of variations in the capillary radius, liquid–vapor interfacial shear stress and the contact angle are all considered and analyzed. The effect of vapor core and wick structure on the fluid flow characteristics and the effect of the heat load on the capillary radius at the evaporator end cap, as well as the effect of the wick structure on the heat transfer performance are all analyzed numerically and discussed. The axial distribution of the capillary radius, fluid pressure and mean velocity are obtained. In addition, the calculated maximum heat transport capability of the heat pipe at different working temperatures is compared with that obtained from a traditional capillary pressure balance model, in which the interfacial shear stress is neglected. The accuracy of the present model is verified by experimental data obtained in this paper.     

A mathematical model for analyzing the thermal characteristics of a flat micro heat pipe with a grooved wick

A mathematical model is developed for predicting the thermal performance of a flat micro heat pipe with a rectangular grooved wick structure. The effects of the liquid–vapor interfacial shear stress, the contact angle, and the amount of liquid charge are accounted for in the present model. In particular, the axial variations of the wall temperature and the evaporation and condensation rates are considered by solving the one-dimensional conduction equation for the wall and the augmented Young–Laplace equation, respectively. The results obtained from the proposed model are in close agreement with several existing experimental data in terms of the wall temperatures and the maximum heat transport rate. From the validated model, it is found that the assumptions employed in previous studies may lead to significant errors for predicting the thermal performance of the heat pipe. Finally, the maximum heat transport rate of a micro heat pipe with a grooved wick structure is optimized with respect to the width and the height of the groove by using the proposed model. The maximum heat transport rate for the optimum conditions is enhanced by approximately 20% compared to existing experimental results.     

Effect of interfacial phenomena on evaporative heat transfer in micro heat pipes

A three-dimensional steady-state model for predicting heat transfer in a micro heat pipe array is presented. Three coupled models, solving the microregion equations, the two-dimensional wall heat conduction problem and the longitudinal capillary two-phase flow have been developed. The results, presented for an aluminium/ammonia triangular micro heat pipe array, show that the major part of the total heat input in the evaporator section goes through the microregion. In addition, both the apparent contact angle and the heat transfer rate in the microregion increase with an increasing wall superheat. It is also shown that the inner wall heat flux and temperatures as well as the contact angle decrease all along the evaporator section.     

Effects of surface roughness of capillary wall on the profile of thin liquid film and evaporation heat transfer

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低体积分数水基SiO2纳米流体沸腾换热关键物性参数研究

在不添加任何分散剂和改变pH值的情况下,通过两步法将比表面积为150 m~2/g的气相SiO_2纳米颗粒制备成均匀稳定、透明度高、分散性能好的纳米流体。并对该功能性纳米流体进行了导热系数、黏度、表面张力和壁面接触角的测量。低体积分数下,功能性纳米流体较基液的导热系数几乎没有变化,但黏度却有较大改变。传统固液两相混合物黏度模型不再适用功能性纳米流体的计算,其主要原因是传统公式低估了分子间作用力对纳米流体黏度的影响。因此,建立了功能性纳米流体的黏度经验公式。由于纳米颗粒的存在提高了沸腾表面的粗糙度,从而使纳米流体的壁面湿润性能大大提高。实验结果表明,纳米流体的黏性和壁面接触角是沸腾换热发生骤变的关键。     

The experimental and numerical investigation of a grooved vapor chamber

An effective thermal spreader can achieve more uniform heat flux distribution and thus enhance heat dissipation of heat sinks. Vapor chamber is one of highly effective thermal spreaders. In this paper, a novel grooved vapor chamber was designed. The grooved structure of the vapor chamber can improve its axial and radial heat transfer and also can form the capillary loop between condensation and evaporation surfaces. The effect of heat flux, filling amount and gravity to the performance of this vapor chamber is studied by experiment. From experiment, we also obtained the best filling amount of this grooved vapor chamber. By comparing the thermal resistance of a solid copper plate with that of the vapor chamber, it is suggested that the critical heat flux condition should be maintained to use vapor chamber as efficient thermal spreaders for electronics cooling. A two-dimensional heat and mass transfer model for the grooved vapor chamber is developed. The numerical simulation results show the thickness distribution of liquid film in the grooves is not uniform. The temperature and velocity field in vapor chamber are obtained. The thickness of the liquid film in groove is mainly influenced by pressure of vapor and liquid beside liquid–vapor interface. The thin liquid film in heat source region can enhance the performance of vapor chamber, but if the starting point of liquid film is backward beyond the heat source region, the vapor chamber will dry out easily. The optimal filling ratio should maintain steady thin liquid film in heat source region of vapor chamber. The vapor condenses on whole condensation surface, so that the condensation surface achieves great uniform temperature distribution. By comparing the experimental results with numerical simulation results, the reliability of the numerical model can be verified.     

Study on high performance evaporator with micro‐grooves (Measurement of capillary force in a single groove and modeling of heat and mass transfer)

A micro‐grooved evaporator is composed of µm‐wide grooves on a heat transfer plate in which the inter‐line regions at the liquid–vapor meniscus of coolant become identifiable. The high‐heat performance of the evaporator is realized by this inter‐line region (ILR) where the liquid thin film reduces the thermal resistance on the heat transfer surface. In this report, we propose a numerical simulation model of heat and mass transfer in a single groove to predict its capillary force and heat flux. The capillary force performance (capillary‐rise length in a groove) of a single groove was measured for samples of varying width, superheat, and inclination. The performance was found to be a maximum at a specific groove width of 200–400 µm, which is in good agreement with the predicted results calculated by the proposed model. For a better prediction of capillary‐rise length, the effective capillary force and the effective flow resistance were considered. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20257     

Heat Transfer Performance of Microgroove Back Plate Heat Pipes with Working Fluid and Heating Power

Micro heat pipes(MHP) cooling is one of the most efficient solutions to radiate heat for high heat flux electronic components in data centers. It is necessary to improve heat transfer performance of microgroove back plate heat pipes. This paper discusses about influence on thermal resistance through experiments and numerical simulation with different working fluids, filling ratio and heat power. Thermal resistance of the CO_2 filled heat pipe is 14.8% lower than the acetone filled heat pipe. In the meantime, at the best filling ratio of 40%, the CO_2 filled heat pipe has the optimal heat transfer behavior with the smallest thermal resistance of 0.123 K/W. The thermal resistance continues to decline but the magnitude of decreases is going to be minor. In addition, this paper illustrates methods about how to enhance heat pipe performance from working fluids, filling ratio and heat power, which provides a theoretical basis for practical applications.     

Analytical study of the heat transfer limits of a novel loop heat pipe system

A novel loop heat pipe system was designed for use in solar hot water heating and an analytical model was developed to investigate its thermal performance and determine six major limits to system operation, i.e. capillary limit, entrainment limit, viscous limit, boiling limit, sonic limit, and filled liquid mass limit. Relations among the limits and several associated parameters, i.e. the heat pipe operating temperature, wicks type, heat pipe diameter, and height difference between the absorbing pipes array and condenser (heat exchanger), were established through a comprehensive analyses. It was found that the levels of capillary, entrainment, viscous, sonic, and filled liquid mass limits increased with the increasing temperature; however, the boiling limit was in the adverse trend. It was also found that the mesh screen wicks were able to obtain a higher capillary limit than sintered powder wicks, whilst other limits remained same. Larger pipe diameters would lead to higher operating limits. The height difference between the condenser (heat exchanger) and absorbing pipes (absorber) was the most important factor impacting on heat transfer capacities of the system, and largely affected the capillary limit of the system. It was noted when the pipe (inner) diameter increased to 5.6 mm or above, the governing limit of the system switched from entrainment to capillary. Relationship between the system governing limit, i.e. capillary limit, and the above addressed parameters were analysed. Adequate system configuration and operating conditions were suggested, which were summarized as follows: 6 mm of pipe inner diameter with mesh screen wicks, 58°C of heat pipe operating temperature, and 1.3 m height difference between absorber and condenser (heat exchanger). Copyright © 2010 John Wiley & Sons, Ltd.     

An investigation of the thermal performance of cylindrical heat pipes using nanofluids

In this work, a two-dimensional analysis is used to study the thermal performance of a cylindrical heat pipe utilizing nanofluids. Three of the most common nanoparticles, namely Al₂O₃, CuO, and TiO₂ are considered as the working fluid. A substantial change in the heat pipe thermal resistance, temperature distribution, and maximum capillary heat transfer of the heat pipe is observed when using a nanofluid. The nanoparticles within the liquid enhance the thermal performance of the heat pipe by reducing the thermal resistance while enhancing the maximum heat load it can carry. The existence of an optimum mass concentration for nanoparticles in maximizing the heat transfer limit is established. The effect of particle size on the thermal performance of the heat pipe is also investigated. It is found that smaller particles have a more pronounced effect on the temperature gradient along the heat pipe.