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.     

基于恒截面流道矩形单元体的积耗散率最小传质构形优化

以质量积耗散率最小为优化目标,对恒截面高渗透率通道的矩形单元体传质构形问题进行了分析和优化,得到结构体内平均传质效果最好的结构外形。结果表明:对于单元体和各级构造体,其平均传质压差均为最大传质压差的2/3。因为高渗透率材料中质流率密度符合线性分布,所以基于积耗散率最小与最大压差最小的最优构形完全一致。所得最优构形同时使得传质能力和传质安全性最好。     

Improvement of constructal tree-like network for “volume-point” heat conduction with variable cross-section conducting path and without the premise of optimal last-order construct

The constructal “tree-like” network has been proved an effective way for “volume-point” heat conduction. This paper aims to further improve the constructal “tree-like” network with the optimization objectives of minimizations of maximum thermal resistance and entransy dissipation rate respectively. By removing the constraint that the last-order construct must be optimal, and using variable cross-section conducting path, the maximum thermal resistance and entransy dissipation rate can be greatly reduced. It is also found that the optimal construct for minimum peak temperature is similar to the optimal one for minimum entransy dissipation rate. They hold the same shape and configuration, and the main difference of them is the shape of high-conductivity path.     

Heat transfer and flow characteristics of offset fins in the low-Reynolds-number region

The characteristics of heat exchangers with offset-type plate fins for space stations are studied for Reynolds numbers less than 300 based on the hydraulic diameter. A three-dimensional analysis is carried out to study the effects of the following parameters on the heat transfer and the flow characteristics: (a) the thermal boundary layer developing on the bottom plate and on the fins on the plate, (b) the aspect ratio (height/pitch) of the cross section of the flow passage, the fin thickness, the fin length in the direction of the flow, the thermal conductivity of the fluid and the fins, and the Prandtl number of the fluid. The results obtained are as follows. (1) The heat-transfer coefficient on the fin surface is characterized by the thermal-conductivity ratio of fluid to fin material. When the thermal conductivity of the fin material approaches that of the fluid, the heat-transfer coefficient on the fin surface becomes low. (2) The optimum condition of the aspect ratio depends on the value of the thermal-conductivity ratio between the fluid and the fins. (3) When the aspect ratio becomes large or small, the friction factor of offset fins approaches that of fully developed duct flow with the same aspect ratio as the Reynolds number decreases. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(4): 249–261, 1997     

球突翅片的传热流动特性及等效热阻数值分析

为了提高翅片管换热器的传热系数和减小压降,提出了一种球突型翅片,通过数值模拟研究其传热与流动性能,同时应用(火积)耗散理论对其传热的不可逆性进行分析。计算结果表明:与平片相比,其传热能提高26.21%～39.53%,而阻力系数仅提高16.62%～27.04%,同时综合性能增加16.54%～32.56%;这说明该翅片具有高传热系数低压降的特点,是一种性能优良的翅片。通过(火积)耗散分析可以看出:球突翅片的等效热阻减小,其传热的不可逆性减弱。     

Performance and optimization analysis of SRC profile fins subject to simultaneous heat and mass transfer

Fin material near the tip of a uniform cross sectional (UC) fin does not participate actively in transferring heat. This effect may seem to have progressed much with the increase in fin length. A uniform cross sectional fin with a step reduction in local cross section (SRC) not only increases the effective utilization of fin material near the tip but also it promotes the ease of fabrication. In this study, an effort has been devoted to determine analytically the overall fin performance of both longitudinal and pin fins of SRC profile under fully dry, partially wet and fully wet conditions. The effect of various design and psychometric parameters on the fin performance of SRC fins has been investigated and compared it is with the corresponding UC fin. A scheme for optimizing SRC fins has also been demonstrated in the present work. From the result, it can be highlighted that the optimum values of Biot number and aspect ratio of SRC fins increase with the increase in relative humidity for the same fin volume. In comparison with the UC fin for the identical fin volume, the SRC fin transfers more rate of heat and consequently, this difference in heat transfer rate increases slowly with the relative humidity.     

Numerical analysis of a cool-thermal storage system with a thermal conductivity enhancer operating under a freezing condition

Enhancing the cooling process of water in a cool-thermal storage system is investigated in this paper. The system is utilized to cool air during on-peak power consumption hours to save energy. The system consists of parallel plates filled with water and triangular corrugated fins. A finite element model for the system is used to predict the cooling time of water for different water's initial temperatures, and also to study the effect of fins design on the cooling process. The result indicates that the aspect ratio of the triangular fin has a significant effect the cooling process of water, and cooling rate increases for the aspect ratio greater or less than 0.75. Temperature contours, average water temperature, and Nusselt number are presented for the cooling process.     

Optimization of short micro pin fins in minichannels

Finned minichannels are modeled in order to optimize microstructure geometry and maximize heat transfer dissipation through convection from a heated surface. Six pin fin shapes – circle, square, triangle, ellipse, diamond and hexagon – are used in a staggered array and attached to the bottom heated surface of a rectangular minichannel and analyzed. Also, using square pin fins, different channel clearance over fins are investigated to optimize the fin height of the fins with respect to that of the channel. Fin width and spacing are investigated using a ratio of fin width area to the channel width. Fin material is then varied to investigate the heat dissipation effects. Triangular fins with larger fin height, smaller fin width, and spacing double the fin width maximizes the number of fins in each row and yields better performance. Correlations describing the Nusselt number and the Darcy friction factor are obtained and compared to previous ones from recent studies. These correlations only apply to short fins in the laminar regime. Completely understanding the effects of micro pin fins in a minichannel is essential to maximizing the performance in small scale cooling apparatuses to keep up with future electronic advancements.     

Natural-convection characteristics of a horizontally-based vertical rectangular fin-array in the presence of a shroud

The steady-state natural convective cooling of horizontally-based, vertical rectangular fins, when in close proximity to an adiabatic horizontal shroud, situated adjacent to and above the horizontal fin-tips, was investigated experimentally. The resuls are of significance for the designers of electronic arrays, the components of which should be maintained at temperatures less than 65°C in order to ensure operational reliability. The optimal fin separation, which corresponds with the maximum rate of heat loss from the fin-array, has been deduced for various combinations of fin protrusions and distances of the shroud above the vertical fins, when the fins' base was maintained at a uniform temperature of 40 ± 0·5°C above that of the environment (21·0 ± 0·5°C). For a constant temperature-difference between the fin-base and the environment, lower optimal fin separations and higher steady-state heat-dissipation rates ensued when the shroud clearance to the fin height ratio was increased from zero to unity. Increasing the fin protrusion above the horizontal base also resulted in higher heat-dissipation rates from the fin-array. However, the fin-array with maximum shroud clearance is a much more favourable configuration (e.g. with respect to requiring less material) for achieving heat-transfer enhancement, than the fin array which employs large fin protrusions. For an open-ended duct of approximately the dimensions considered in this project (i.e. of maximum rectangular section 240 mm × 180 mm), the fins should protrude to less than half the internal height of the duct in order that a high convective performance of the fins is achieved. There is an optimal value of the shroud clearance to fin height ratio which exceeds unity for each specific operation, i.e. the exact optimal ratio being dependent upon the geometry and temperatures involved.

Average Nusselt numbers, evaluated from the experimental data, are correlated non-dimensionally with respect to the fin-array geometry and the Grashof number. This correlation indicates that variations of the shroud clearance to fin height ratio produce only marginal variations in the average Nusselt number.     

Thermal Analysis of Orthotropic Pin Fins With Contact Resistance: A Closed-Form Analytical Solution

Light weight composite fins are considered to deal with thermal management problems for many microelectronic components. These composite fins are inherently anisotropic, therefore cannot be handled by a traditional one-dimensional approach; however, these materials can be designed to provide high thermal conductivity values in the desired direction to handle application-specific demands. In this article, we present analytical solutions for temperature distribution and heat transfer rate for orthotropic two-dimensional pin fins subject to convective-tip boundary condition and the contact resistance at the fin base. The generalized results are presented in terms of fin aspect ratio (fin length-to-radius ratio) and three dimensionless fin parameters that relate the internal conductive resistance to three convective resistances discussed in terms of dimensionless variables such as contact, tip, and axial Biot numbers, in addition to the axial-to-radial conductivity ratio. Several special cases including the insulated tip boundary condition are presented. It is demonstrated that the temperature distribution and heat transfer rate from the two-dimensional isotropic annular fin introduced earlier in the literature, can easily be recovered from the benchmark solutions presented in this article. Furthermore, dimensionless heat transfer rates are presented for the pin fins with contact resistance that can help to solve design and optimization problems of many natural-to-forced convection composite fins that are typically encountered in many microelectronic applications.     

Analysis of thermal performance and optimization of concentric circular fins under dehumidifying conditions

The analysis of wet fins was carried out by many investigators with the variation of a linear relationship between specific humidity and the corresponding saturation temperature of air adjacent to the fin surface. For determination of the fin surface temperature under this scheme, fin-tip temperature is essentially known a priori which can be employed to calculate the psychrometric parameters associated with the dehumidification process. On the other hand, the tip temperature is only known after the salving the governing equation and it is also a function of the psychrometric properties of air. Thus for the simplicity, dew point temperature is considered as the tip temperature for calculating only the psychrometric parameters of fully wet fins in a recent publication. Nevertheless, in the actual situation this dew point temperature never satisfies at the tip and therefore psychrometric parameters calculated with the assumption of the dew point temperature at the tip may be incorrect. In the present work, an iterative scheme is demonstrated for determination of the actual tip temperature and local fin surface temperature. With considering this aspect, thermal analysis of a new geometric fin, namely, annular step fin (ASF) is proposed for the more effective utilization of fin material in comparison with the annular disc fin. An optimization study has also been made by using the modified thermal analysis of fully wet fins and the analysis of partially wet fins, separately. A remarkable change in results has been noticed when they are compared with that of the published result. Finally, it is worthy to mention that the maximum heat transfer rate per unit volume for an ASF is always higher than that of the annular disc fin for the identical design condition.     

Effectiveness of Composite Fins Under Maximum Heat Dissipation

This paper is devoted to the determination of the effectiveness and the optimization of two-dimensional (2-D), longitudinal rectangular composite fins under convective conditions through the concept of relative inverse thermal admittance. The influence of composite layer thickness and the composite and fin thermal conductivity ratio on the optimum geometry is determined. Effectiveness is used as the fundamental parameter to prove that the fin is fulfilling the objective of increasing heat dissipation. Once the optimum thickness has been obtained, the Biot number and the effectiveness are easily calculated. The optimization process is carried out through universal graphs in which the range of parameters covers most of the practical cases a designer will find and ensuring fins operate as a real dissipation device.     

Heat exchanger design: Optimal thickness (under natural convective conditions) of vertical rectangular fins protruding upwards from a horizontal rectangular base

Steady-state rates of heat transfer from an array of vertical, rectangular polished duralumin fins under natural convective conditions have been measured. The horizontal base, which was manufactured of the same material, was kept at the uniform temperature of either 20·0 (±0·2)°C or 40·0 (±0·2)°C above the local air temperature of 20 (±0·2)°C.

The optimal thickness of the fins in this array, corresponding to a maximum rate of heat dissipation, was deduced. For a base of width 190 mm and length 500 mm, the optimal thickness for fins of 60 mm protrusion rose from 2·0 mm to 4·5 mm when the fin separation was increased from 20 mm to 60 mm. This optimal fin thickness was almost invariant with respect to the change of the considered base temperature.     

A spreadsheet solution of transient conduction in composite fins

Transient heat transfer through composite fins is investigated by numerical methods. In this regard, governing differential equations of the two‐dimensional fin and one‐dimensional cladding are studied to examine the effect of Biot number and ratio of thermal conductivities of the fin material to the cladding, on the dimensionless temperature profiles. In addition, the use of spreadsheet programs in solving the composite fin problems is investigated in somewhat more detail with regard to the solution as well as presentation of the graphical results. The results show that one‐dimensional analysis, traditionally used in fin analysis, is not applicable for composite fins, particularly when the conductivity ratio of the composite fin materials is very high. Copyright © 2002 John Wiley & Sons, Ltd.     

A new approach to analysis and optimization of evaporative cooling system II: Applications

After introducing the concepts of moisture entransy, moisture entransy dissipation and thermal resistance based on moisture entransy dissipation (TRMED) in part I of this study, we further analyze several direct/indirect evaporative cooling processes based on the above concepts in this part. The nature of moisture entransy, moisture entransy dissipation and TRMED during evaporative cooling processes was reexamined. The results demonstrate that it is the moisture entransy, not the enthalpy, that represents the endothermic ability of a moist air, and reducing the entransy dissipation by both enlarging the thermal conductance of heat and mass transfer, and decreasing the temperature potential of the moist air, i.e. the difference between the dry-bulb temperature of moist air over its dew-point temperature, will result in a smaller system TRMED, and consequently a better evaporative cooling performance. Then, a minimum thermal resistance law for optimizing evaporative cooling systems is developed. For given mass flow rates of both moist air and water, with prescribed moist air and water conditions, minimizing the TRMED will actually lead to the most efficient evaporative cooling performance. Finally, the thermal conductance allocation for an indirect evaporative cooling system is optimized to illustrate the application of the proposed minimum thermal resistance law.     

一种新型永磁磁力耦合器导风散热片的仿真研究

本研究针对一款新型永磁磁力耦合器导风散热装置的导风散热片进行仿真分析。首先设计单因素实验,对其部分几何参数进行研究,利用Fluent软件进行流固耦合模拟,得出几何参数对最高温升及阻力距的影响关系,为正交实验提供合理的参数范围。然后设计正交实验,利用极差分析得出合理的参数组合。最后利用上文参数组合建模,模拟安装不同导风散热片个数的散热效果,寻找合适个数。并与未安装导风散热片的模型进行对比,得出此新型导风散热片设计合理,具有一定的实用价值。     

Analysis of two‐dimensional porous fins with variable thermal conductivity

Analysis of porous fins for their higher heat transfer in comparison with solid fins with identical volumes has attracted significant attention. In this paper, a two‐dimensional thermal analysis of a porous fin having variable thermal conductivity coefficient is performed using finite difference method. Heat transfer through porous media is simulated using passage velocity from Darcy's model. The thermal conductivity of the solid phase is considered as a linear function of temperature. It is found that the temperature profile of the fin is completely two‐dimensional even for high Rayleigh and Darcy numbers (Ra = 10³～10⁴, Da = 0.01), because the temperature changes significantly along the transverse axis especially for lower Rayleigh and Darcy numbers. Also, the effects of important nondimensional parameters such as Rayleigh and Darcy numbers, porosity, Nusselt, thermal conductivity, and aspect ratio on the temperature profile are investigated. The results demonstrate that the temperature distribution is strongly dependent on the Rayleigh and Darcy numbers.     

NATURAL CONVECTION AND ENTROPY GENERATION FROM A CYLINDER WITH HIGH CONDUCTIVITY FINS

The problem of laminar natural convection from a horizontal cylinder with multiple equally spaced high conductivity fins on its outer surface was investigated numerically. The effect of several combinations of number of fins and fin height on the average effective Nusselt number was studied over a wide range of Rayleigh numbers. The results showed that there was an optimal combination of number of fins and fin height for maximum heat transfer from the cylinder for a given value of Rayleigh number. A high number of short fins slightly decreased the heat transfer from the cylinder. The calculated velocity and temperature profiles also were used to study the total entropy generation. The total entropy production was dominated by entropy generation due to thermal effects. The exception was at Ra _D = 10³ and a large cylinder diameter where entropy generation was dominated by entropy generation due to viscous effects. This information can be used to access the changes in the thermodynamic efficiency due to the addition of fins to enhance the natural convection heat transfer from a horizontal cylinder.     

基于火积理论的多级套管式相变蓄热系统优化

本文基于最小火积耗散热阻原理,在考虑相变材料导热热阻以及非稳态传热过程的基础上,对多级套管式相变蓄热系统的融化温度进行了数值优化,获得了最优融化温度分布。在此基础上,研究了相变材料导热系数和传热管长度对最优融化温度、火积耗散热阻和平均蓄热速率的影响。研究结果表明,与现有理论优化方法相比,本文提出的数值优化方法具有更好的适用性;优化后多级套管式相变蓄热系统可有效提高相变蓄热系统的平均蓄热速率,降低火积耗散热阻;随着相变材料导热系数增大和传热管长度增加,多级套管式相变蓄热系统最优融化温度的温差愈加明显,其强化传热性能呈上升趋势。     

A new approach to analysis and optimization of evaporative cooling system I: Theory

Using the analogy between heat and mass transfer processes, the recently developed entransy theory is extended in this paper to tackle the coupled heat and mass transfer processes so as to analyze and optimize the performance of evaporative cooling systems. We first introduce a few new concepts including the moisture entransy, moisture entransy dissipation, and the thermal resistance in terms of the moisture entransy dissipation. Thereinafter, the moisture entransy is employed to describe the endothermic ability of a moist air. The moisture entransy dissipation on the other hand is used to measure the loss of the endothermic ability, i.e. the irreversibility, in the coupled heat and mass transfer processes – this total loss is shown to consist of three parts: (1) the sensible heat entransy dissipation, (2) the latent heat entransy dissipation, and (3) the entransy dissipation induced by a temperature potential. Finally the new thermal resistance, defined as the moisture entransy dissipation rate divided by the squared refrigerating effect output rate, is recommended as an index to effectively reflect the performance of the evaporative cooling system. In the end, two typical evaporative cooling processes are analyzed to illustrate the applications of the proposed concepts.