Constructal multi-scale structures for maximal heat transfer density

This paper reviews recent constructal-theory advances: the optimal distribution of discrete heat sources cooled by laminar natural convection. Three scenarios are investigated: (i) many small heat sources mounted on a vertical wall, (i) a few small finite-size heat sources mounted on the side wall of a two-dimensional enclosure, and (iii) one heated area on the wall of a vertical diverging or converging channel with chimney flow. In (i) and (ii), the optimally distributed heat sources are not equidistant. In (iii), the geometry changes by varying the space between the walls, the distribution of heating along the walls, and the angle between the two walls. Numerical simulations in the Rayleigh number range 10⁵≤Ra_H≤10⁷ show that for maximal heat transfer rate density it is better to install heated sections at the channel entrance. The optimal angle between the two walls is approximately zero when Ra_H is large. The robustness of flow architectures with optimized distribution of heat sources is discussed.     

Three-dimensional multi-scale fluid distributor assembly minimizing total viscous dissipation

In this paper, a novel multi-scale transport network geometry has been addressed by means of constructal theory. The channel dimensions are given and justified with an engineering criterion into the design itself. The first stage of this work consists of assembly optimization, which is formulated as follows: find the distribution of channel radii and angle that minimizes total viscous dissipation (or pumping power, pressure drop) under the constraints of fixed total volume of channels and tube material consumed. Analytical resolutions of the problem of optimal channel size distribution for tree-like networks used as flow distributors are obtained. In the subsequent stages, a large number of flow configurations are constructed based on the optimal channel size. The resulting structure is an optimized multi-scale flow distributor. Furthermore, for such configuration, the equality of pressure drops ensuring flow rate uniformity at the outlet ports of the distributor is demonstrated theoretically. Finally, CFD simulations are employed to investigate fully developed smooth turbulent flow on different branch junctions. Numerical results are found to be in good agreement with predicted analytical results and support the relationship between the pressure drop and the liquid flow rate at the inlet port of the constructal liquid distributor.     

Maximum heat transfer density with rotating cylinders aligned in cross-flow

In this paper, we study the thermal behavior of an assembly of rotating cylinders aligned in a cross-flow. The objective is to maximize the heat transfer rate density of the assembly, i.e. the overall heat transfer dissipated per unit of volume, under fixed pressure drop. A numerical model is used to solve the governing equations. Two configurations are studied: i) the cylinders rotate in the same direction, and ii) consecutive cylinders rotate in opposite directions. The spacing between consecutive cylinders is optimized in each case. The second configuration proved to be the more efficient. In that configuration, it is also possible to optimize further the architecture by using a smaller spacing for the flow passage in which the flow is in the direction of the cylinders rotation, and larger spacing for the flow passage in which the cylinders oppose the main stream.     

Constructal multi-scale structures with asymmetric heat sources of finite thickness

This paper details the generation of multi-scale flow structure in a package with heat sources. The model is based on abandoning two common assumptions (1) the assumption that there are many channels (components) in the package, which is traditionally made to exploit simplifications due to symmetry, and (2) the assumption that the heat-generating components have negligible thickness. Numerical simulations document the flow stagnation and separation generated by blunt heat sources, and the effect of these flow phenomena on the optimized internal flow structure. The effect of asymmetric thermal boundary conditions on the optimal spacing between heat-generating plates is significant. If the package has some channels with symmetric boundary conditions, and some with asymmetric boundary conditions, then the optimal structure has multiple spacings. The effect of freedom on design performance is documented by optimizing competing configurations that have different numbers of degrees of freedom.     

T-shaped assembly of fins with constructal entransy dissipation rate minimization

T-shaped assembly of fins is optimized by adopting an analytical method and taking the minimum mean thermal resistance in terms of entransy as optimization objective. The optimal construct of T-shaped assembly is obtained and compared with the optimal construct with maximum temperature difference minimization. The results show that for the two optimization objectives the thicknesses of the optimized fins are almost equal, but the lengths are different obviously: the former length of the elemental fin is almost half the value of the latter length, and the former length of the first-order fin is almost twice as large as the latter length. Compared with the latter optimal construct, the dimensionless mean thermal resistance corresponding to the former optimal construct decreases by 16.4%, and the corresponding dimensionless maximum thermal resistance increases by 9.74%. Both the minimizations of the EDR and the maximum temperature difference (MTD) should be combined to consider the efficiency and the temperature limitation simultaneously for designing the fins.     

An experimental study in determining the local heat transfer coefficients for the plate finned-tube heat exchangers

A three-dimensional inverse problem in determining the local heat transfer coefficients for the plate finned-tube heat exchangers utilizing the steepest descent method (SDM) and a general purpose commercial code CFX4.4 is applied successfully in the present study based on the measured temperature distributions on fin surface by infrared thermography.Two different tube arrangements (i.e. in-line and staggered) with different fin pitch and air velocity are considered and the corresponding local heat transfer coefficients are to be determined. Results show that some interesting phenomena of the local heat transfer coefficients for the finned surface are found in the work and the averaged heat transfer coefficient of the staggered configuration is about 8–13% higher than that of the in-line configuration.     

Maximal heat transfer density: Plates with multiple lengths in forced convection

This paper shows that in a space filled with heat generating parallel plates and laminar forced convection, the heat transfer density can be increased beyond the level known for parallel plates with optimal spacing. The technique consists of inserting in every entrance region new generations of smaller plates, because smaller plates have thin boundary layers that fit in the unused (isothermal) entrance flow. This technique can be repeated several times, and the result is a sequence of multi-scale flow structures that have progressively higher heat transfer densities. The work consists of numerical simulations in a large number of flow configurations, one differing slightly from the next. The complete optimized architecture and performance of structures with one, two and three plate length scales are reported. Diminishing returns are observed as the number of length scales increases. This method can be used to develop multi-scale nonuniform flow structures for heat exchangers and cooled electronic packages.     

Numerical analysis of conjugate heat transfer in a partially open square cavity with a vertical heat source

Conjugate heat transfer in partially open square cavity with a vertical heat source has been numerically studied. The cavity has an opening on the top with several lengths and three different positions. The other walls of cavity were assumed adiabatic. The heat source was located on the bottom wall of cavity and it has got a width such as Printed Circuit Boards (PCB). Steady state heat transfer by laminar natural convection and conduction is studied numerically by solving two dimensional forms of governing equations with finite difference method. The results were reported for various governing parameters such as Rayleigh number (10³ ≤ Ra ≤ 10⁶), conductivity ratio, opening position, opening length, PCB distance and PCB height. The numerical results were discussed with streamlines, isotherms, Nusselt number and velocity profiles on x- and y-directions. It is found that ventilation position has a significant effect on heat transfer.     

Maximum heat transfer density rate enhancement from cylinders rotating in natural convection

In this paper we investigate the thermal behaviour of an assembly of consecutive cylinders in a counter-rotating configuration cooled by natural convection with the objective of maximizing the heat transfer density rate (heat transfer rate per unit volume). A numerical model is used to solve the governing equations that describe the temperature and flow fields. The spacing between the consecutive cylinders is optimised for each flow regime (Rayleigh number) and cylinder rotation speed. It was found that the optimized spacing decreases as the Rayleigh number increases and the heat transfer density rate increases, for the optimized structure, as the cylinder rotation speed is increased. Results further shows that there is an increase in the heat transfer density rate of the rotating cylinders over stationary cylinders.     

Analysis of Heat Transfer Behaviour of the Conduction Cold Plate System

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Heat transfer model with two heat transfer coefficients along a multiperforated plate — Application to combustion chamber wall cooling

Walls‘ cooling of aeronautic propeller combustion chamber is performed with the injection, through the combustion chamber wall, of a part of the air coming from compressors placed upstream. Measurements of the wall thermal fields are made by infrared thermography along the injection wall. This injection wall is pierced by 9 rows of 8 holes (α=90°) in staggered configuration (p/D=s/D=6). We propose a model using two heat transfer coefficients to represent the convective exchanges. The results are non-dimensioned and presented in comparison with the case without holes. The use of this model allows us to define 4 zones. Those 4 zones exist for the 5 blowing rates.     

Numerical investigation on heat transfer rate from the outside environment into the electronic compartment of the measurement-while-drilling tools

With the increase of drilling depth, a large number of high-temperature wells with bottom hole temperatures of more than 150°C appear. However, conventional measurement-while-drilling (MWD) instruments are no longer suitable. Therefore, it is necessary to design a new MWD instrument suitable for high-temperature downhole for a long time. Compared with other active refrigeration methods, a split-Stirling cryocooler is the best choice. In this paper, a new active cooling system is designed, based on the split-Stirling cryocooler. The heat transfer rate entering the instrument cabin of MWD from the external environment is calculated, and the effects of the heat transfer device, insulation material, circuit board, split-Stirling cryocooler, and working condition on heat transfer rate are discussed. The results show that the thermal conductivity of insulation material has a great influence on heat transfer rate. The thermal conductivity of the insulation material filled with the gap in the cabin must be small enough. Meanwhile, the influence of the length of the circuit board is greater than the height and width. If conditions permit, the double-layer circuit can be used. And the thermal power of the circuit board has no effect on the heat transfer rate entering the instrument cabin from outside.     

Distribution of heat sources in vertical open channels with natural convection

In this paper we use the constructal method to determine the optimal distribution and sizes of discrete heat sources in a vertical open channel cooled by natural convection. Two classes of geometries are considered: (i) heat sources with fixed size and fixed heat flux, and (ii) single heat source with variable size and fixed total heat current. In both classes, the objective is the maximization of the global thermal conductance between the discretely heated wall and the cold fluid. This objective is equivalent to minimizing temperature of the hot spot that occurs at a point on the wall. The numerical results show that for low Rayleigh numbers (∼10²), the heat sources select as optimal location the inlet plane of the channel. For configuration (i), the optimal location changes as the Rayleigh number increases, and the last (downstream) heat source tends to migrate toward the exit plane, which results in a non-uniform distribution of heat sources on the wall. For configuration (ii) we also show that at low and moderate Rayleigh numbers (Ra_M ∼ 10² and 10³) the thermal performance is maximized when the heat source does not cover the entire wall. As the flow intensity increases, the optimal heat source size approaches the height of the wall. The importance to free the flow geometry to morph toward the configuration of minimal global resistance (maximal flow access) is also discussed.     

环路型脉动热管的工质流动和传热特性实验研究

建立了部分可视化的环路型铜-乙醇脉动热管试验台,研究了充液率、倾斜角度、环路数目等因素对脉动热管传热性能的影响。结果表明:不能形成脉动效应时工质的流型是间歇振动,形成脉动效应时工质的流型是弹状流或环状流;最佳倾角为70°~90,°最佳充液率在50%左右;热阻随着环路数目的增加而减小。     

An analysis of the heat transfer rate and efficiency of TE (thermoelectric) cooling systems

The heat transfer rate and efficiency of TE (thermoelectric) cooling systems were investigated. The emphasis of the present study is focused on the use of large-scale TE refrigerators for air conditioning applications. A one-dimensional heat transfer analysis was performed to determine the cooling power and electricity consumption of the TE elements. The constant-property results are in good agreement with the variable-property solutions for TE materials and temperatures typical for air conditioning applications. A heat transfer analysis was also carried out for TE refrigerators equipped with a heat exchanger. Both parallel- and counter-flow heat exchangers were considered. Fluid temperature variations of these two flow arrangements were found to be quite different, but the efficiencies and cold fluid exit temperatures differed only slightly when a uniform current was used for all TE elements. If the length of the heat exchanger exceeds an optimal value, the cold fluid temperature begins to rise and the efficiency drops for both parallel- and counter-flow arrangements. The second law of thermodynamics was applied to the optimization of TE refrigerators operating between two constant-temperature reservoirs and between two flowing fluids. It was found that if a TE cooling system incorporates a heat exchanger, a nonuniform current distribution should be used to achieve the maximum efficiency and the lowest cold fluid temperature. The optimization results for TE refrigerators operating between two constant-temperature reservoirs are not applicable to TE cooling systems between two flowing fluids. The most energy-efficient current distribution for the parallel-flow arrangement is the one which increase in the direction of the cold fluid.     

长距离环路热管传热性能实验研究

基于航空航天等领域对环路热管长距离传热的需求,设计制造了一套传热距离8.1m的圆柱型蒸发器环路热管,试验了不同加热功率、不同冷凝温度下该环路热管的启动和变工况运行性能,并对其热阻及最大传热能力进行了分析。研究结果表明：当其他条件一致、初始气液分布相同和不同时,加热功率由100W增大至160W后,本研究中的环路热管启动时间和启动温升均发生一定程度的下降;加热功率100W时,冷凝温度由10℃降低至-10℃使得环路热管启动时间增加,加热功率160W时,冷凝温度由10℃降至-10℃对环路热管的启动时间影响不大。在冷凝温度0℃下,该环路热管在100~500W范围内均能稳定运行,且200W时环路热管传热效率最高,传热温差最小,稳定运行温度最低;另外,由于系统传输距离较长,每个工况达到稳定所需要的时间也较长,分布于1000至3500S内。随着加热功率的增大,环路热管热阻先减小后逐渐增大,该环路热管传热热阻最大不超过0.09℃/W,最小为0.024℃/W;随着传热距离的增大,管路的热损失增加,总压降和热阻也变大。当传热距离基本相同时,蒸发器容积的大小、冷凝器的冷凝能力及气液管线的布置形状均在一定程度上影响环路热管的最大传热能力。     

电机径向通风的空气—空气冷却器传热计算

针对径向通风、管束整体为矩形排列的电机空—空冷却器建立了分区域的传热计算模型,给出了针对不同的内风路温度条件所采取的传热计算方法,采用优选取值法计算方法用于空—空冷却器分区域的传热计算。该计算模型的计算数据通过与实验数据的对比进行了修正。根据该计算模型编制了计算软件进行冷却器设计,目前的冷却器设计软件从换热及与风扇匹配角度来讲均可满足设计要求。     

Forced Convective Heat Transfer in a Porous Plate Channel

INTRODUCTIONHeattransferenllancen1enttechniquesplayaveryimportantroleintllermalcontroltechnologies1lsedwithnlicroelectronicchips,powerfullasermirrors,aerospacecraft,thermalnuclearfusion,etc.Itiswidelyrecognizedthattl1eheattransfercanbein-creasedbyil1creasingthesurfaceareaincontactwiththecoolant.TuckermanandPease[1,2]pointedoutthatforlaminarflowinconfinedchannels,theheattransfercoefficientisinverselyproportionaltothewidthofthechannelsincethelimitingNusseltnum-berisconsta11t.Theybuiltawate…     

板式换热器传热和阻力特性的实验研究

利用搭建的液-液型板式换热器试验平台,根据实验数据运用定性雷诺数法拟合出传热关联式,找出Nu与摩擦因子f之间的通用关系式,为板式换热器的设计计算提供了依据。运用传热量与功率的消耗比来评价板式换热器的性能,找出了影响其性能的主要因素,进一步澄清了单纯依靠提高流速来增加传热性能是不经济的。     

Prediction of friction factors and heat transfer coefficients for turbulent flow in corrugated tubes combined with twisted tape inserts. Part 2: heat transfer coefficients

A simple mathematical model following the suggestion of Smithberg and Landis has been created to predict the heat transfer coefficients for the case of a fully developed turbulent flow in a spirally corrugated tube combined with a twisted tape insert. The heat transfer can be predicted from the combined effects of the axial and the tangential boundary layer flows coupled with an additional “vortex mixing” effect near the wall through the solution of the corresponding momentun and energy transfer equations. The “wall roughness” has an effect simultaneously on the axial velocity, secondary fluid motion and the resulting swirl mixing. The model reflects the influence of the “wall roughness” and the twisted tape on the thermal resistances of the helicoidal core flow, twisting boundary layer flow and the viscous sublayer near the wall. The calculated heat transfer coefficients have been compared to 544 experimental points obtained from 57 tubes tested. Four hundred thirty-eight points (80.5%) have a relative difference of less than ±15% and 106 points (19.5%) have a relative difference between ±(15-20)%.