Thermal performance and optimization of hyperbolic annular fins under dehumidifying operating conditions – analytical and numerical solutions

The thermal performance of hyperbolic profile annular fins subjected to dehumidifying operating conditions is studied. An analytical solution for completely wet fin is derived using an approximate linear temperature–humidity relationship. A numerical solution using actual psychrometric relationship for completely and partially wet operating conditions is then obtained to account for the actual temperature–humidity ratio psychrometric relationship under both partially and fully wet operating conditions. An excellent agreement is observed between analytical and numerical solutions for completely wet fin. The fin optimization is presented based on the analytical solution of completely wet fin. Finally, a finite element formulation is used for studying the two-dimensional effects of orthotropic thermal conductivity on the thermal performance of fin under partially and fully wet operating conditions.     

带亲水层波纹翅片管换热器空气侧特性的参数影响分析

为了确定翅片间距、管排数和入口空气相对湿度等参数对析湿工况下带亲水层波纹翅片空气侧特性的影响，对7个带亲水层的波纹翅片管换热器进行了试验研究，并分别以Colbum换热因子和Fanning摩擦因子来反映空气侧换热和压降特性。结果表明，换热和摩擦因子都随着翅片间距的减小而增大。换热因子随着管排数的增加而减小，而摩擦因子受管排数的影响不显著。当入口相对湿度增大时，换热因子增大，而摩擦因子则几乎不变。入口水温越低，则入口空气相对湿度对换热因子的影响越显著。     

翅片管换热器在析湿工况下的积灰特性及对空气侧压降的影响

空调器室内机多数采用翅片管换热器,会因制冷运行过程中表面析湿而粘附灰尘,导致空气流动阻力增大。本文选用空调器中常用的平直翅片、波纹翅片和开窗翅片作为测试样件,翅片间距范围为1.5～2.2 mm,研究了翅片管换热器在析湿工况下的积灰特性及积灰对空气侧压降的影响。结果表明:翅片表面的析湿量决定积灰程度,析湿液滴分布越密集、液桥数量越多,翅片迎风面的堵塞程度越严重且空气侧压降越大。在相同析湿工况下,具有复杂结构的开窗翅片和小翅片间距更容易积灰并增大空气侧压降,因此降低翅片结构复杂程度并适当增大翅片间距有利于空调器的防尘。在积灰过程中,随着换热器表面粉尘沉积量增加,空气侧压降先增大后保持稳定。     

Optimum configurations of vertical fins under condensation of saturated vapor

In the present study, an optimum fin shape envelope was determined via a theoretical procedure that minimized the fin volume subject to constrained heat transfer rate. A unified analysis is presented for both longitudinal and pin fins with vertical orientation of the fin surface. The analysis was carried out on the assumption of a power law fin temperature distribution. Under certain simplified conditions, this optimization model has been validated. Results obtained from the model are also compared with previously published results for the specific set of designed conditions. From optimization study, practical fin profiles are found under the condensation of quiescent vapor atmosphere.     

An analytical method for determination of the performance of a fin assembly under dehumidifying conditions: A comparative study

The present paper establishes an analytical method for determining the performance of a fully wet fin assembly under dehumidifying conditions. A cubic relationship between the humidity ratio of the saturated air and its temperature is taken for calculating driving force for the mass transfer. With this relationship, the governing equation of a fin assembly becomes nonlinear. The Adomian decomposition method is suggested for the solution. The performance parameters, namely, surface efficiency and augmentation factor, are furnished as a function of different design variables. To establish the merit of the work, present results are compared with those values obtained from the previous model and a reasonable difference in results has been noticed. In this point, it can be highlighted that the error associated with the previous model increases with the relative humidity. Finally, the present model is equally useful to predict the performance of a wet fin assembly with the consideration of any other nonlinear effect.     

A Simple Method for Measuring Si-Fin Sidewall Roughness by AFM

The gate oxide reliability and the electrical behavior of FinFETs are directly related to the surface characteristics of the fin vertical sidewalls. The surface roughness of the fin sidewalls is one of the most important structural parameters to be monitored in order to optimize the fin patterning and postetch treatments. Because of the nanometer-scale dimensions of the fins and the vertical orientation of the sidewall surface, their roughness measurement is a serious challenge. In this paper, we describe a simple and effective method for measuring the sidewall morphology of silicon fins by conventional atomic force microscopy. The present methodology has been employed to analyze fins as etched by reactive ion etching and fins repaired by sacrificial oxidation. The results show that sacrificial oxidation not only reduces the roughness of the sidewalls, but also rounds the top corners of silicon fins. The present method can also be applied to characterize sidewall roughness of other nanostructures and materials such as the polysilicon gate of transistors or nanoelectromechanical beams.     

Optimizing the Design of Space Radiators

A procedure for optimizing the configuration of a heat pipe/fin radiating element in terms of heat rejected per radiating mass has been developed. The optimization was carried out analytically by expressing the heat radiated per radiating mass in terms of a function involving a dimensionless heat transfer coefficient and the dimensionless thermal gradient at the root of the fin where it joins the heat pipe. The dimensionless Stefan–Boltzmann radiation equation was solved numerically to determine the value that maximizes the function that determines the heat transfer per radiating mass. Once this value is obtained, the optimum width and thickness of the fins as well as the heat radiated per mass can be specified in terms of the operating temperature, emissivity, diameter, and mass/length of the heat pipe, and the density and thermal conductivity of the fin material. The resulting analytical expression can then be used to determine the maximum heat radiated per radiating mass over a wide range of operating conditions, to optimize the design of a specific heat pipe/fin combination, and to conduct analyses of the influence of design and materials properties on the performance of the system. The optimization procedure was carried out for the case of uniformly tapered fins as well as for flat fins.     

新型电动汽车热泵系统除湿再热性能实验研究

本文设计了一种具备两种除湿再热模式的电动汽车热泵系统,在不同实验工况下研究了两种除湿再热模式的除湿性能与再热性能。结果表明:热泵系统的功耗低于2.0 kW,COP大于2.0;除湿再热模式A的除湿率为0.41～0.83 kg/h,制热量为1.7～3.0 kW;除湿再热模式B的除湿率为0.25～0.55 kg/h,制热量为2.0～3.4 kW。因此除湿再热模式A具备良好的除湿性能,除湿模式B具备良好的再热性能;根据两种除湿再热模式的特点,提出了一种既能满足乘员舱除湿供暖要求,又相对节能的运行策略。     

铜翅片换热器开发应用的分析Ⅰ--铜、铝翅片换热器性能对比

从翅片效率、单个换热单元的传热系数和整个换热器的换热量三个方面对不同翅片结构、不同管子结构和不同工况下的翅片管换热器由铝翅片换为铜翅片前后的换热特性和成本进行了分析比较：详细给出了各个结构和工况参数单独变化对换铜前后的翅片效率、单位制冷剂侧换热面积上的总传热系数和换热器换热量的影响规律。分析结果发现，翅片越薄、越高，管外径越小，风速越大时，换铜后的翅片管的换热能力增强越大，成本增加越小。在所选择的结构和工况范围内，铜管铜片换热器比铜管铝片换热器的翅片效率约提高0．938％～29．86％、总传热系数约提高9.88％～23．276％、总换热量约提高0．112％～22．3％；对于典型的1.1kW空调器的蒸发器，材料成本约增加8～42元，体积可最多缩小18％。     

湿工况下翅片表面冷凝水滴运动的数值模型

了解析湿过程中冷凝水对换热器翅片侧换热和压降的影响机制,需要首先建立湿工况下翅片表面冷凝水滴的运动模型。通过对翅片表面上冷凝水滴进行受力分析,得出了水滴运动的判断条件;建立了水滴接触角预测模型,并结合VOF界面追踪方法来描述气液相界面、计算表面张力,从而建立了预测冷凝水滴在竖直翅片表面运动过程的数值模型。通过水滴运动实验对模型的可靠性进行了验证：水滴与翅片表面接触角的模拟值与实验值的平均误差为2.11%,最大误差为2.51%;水滴运动速度的模拟值与实验值的平均误差为6.5%,最大误差为10%。结果表明：水滴运动模型能够准确的预测水滴在翅片表面的运动规律。     

Conjugate heat transfer in solar collector panels with internal longitudinal corrugated fins—Part I: Overall results

A computational study is conducted to examine the fully developed laminar flow and heat transfer characteristics in solar collector panels with internal, longitudinal, corrugated fins. The fins are integrally attached to the upper and lower panel walls. The objective of the study is to determine the effects of varying the fin pitch (or fin angle), the fin thickness, the ratio of the thermal conductivity of the panel walls and the fin to that of the fluid, and the thermal boundary condition on the panel heat transfer and pressure drop. The solutions of the momentum and energy equations are obtained by using a control-volume-based finite difference algorithm. The results of the study are also applicable to the design of internally-finned channels in compact heat exchangers. The overall panel heat transfer increases when the fin pitch (or the fin angle) is decreased, when the fin thickness is increased, and when the thermal conductivity ratio is increased. The streamwise pressure drop increases with decreasing fin pitch (or fin angle) and increasing fin thickness. For a fixed fin thickness, the selection of a small fin pitch (or fin angle) over the range studied results in a higher heat transfer enhancement per unit pumping power.     

Optimum plate-fin heat sinks by using a multi-objective evolutionary algorithm

This article demonstrates the practical applications of a multi-objective evolutionary algorithm (MOEA) namely population-based incremental learning (PBIL) for an automated shape optimization of plate-fin heat sinks. The computational procedure of multi-objective PBIL is detailed. The design problem is posed to find heat sink shapes which minimize the junction temperature and fan pumping power while meeting predefined constraints. Three sets of shape design variables used in this study are defined as: vertical straight fins with fin height variation, oblique straight fins with steady fin heights, and oblique straight fins with fin height variation. The optimum results obtained from using the various sets of design variables are illustrated and compared. It can be said that, with this sophisticated design system, efficient and effective design of plate-fin heat sinks is achievable and the best design variables set is the oblique straight fins with fin height variation.     

Fouling and pressure drop analysis of milk powder deposition on the front of parallel fins

One method to reduce the energy consumption of industrial milk spray dryers is to recover waste heat from the exhaust dryer air. A significant challenge associated with this opportunity is the air contains a small amount of powder that may deposit on the face and surfaces of a recuperator. This paper introduces a novel lab based test that simulates powder deposition on a bank of parallel plate fins at exhaust dryer air conditions. The fin bank acts like the face of a typical finned tube row in a recuperator. The aim of this study is to look at how deposition on the front of fins is affected by the air conditions. Results show similar characteristics to other milk powder deposition studies that exhibit a dramatic increase in deposition once critical stickiness levels are reached. As powder deposits on the face of the fins, the pressure drop across the bank increases until eventually an asymptote occurs, at which point the rates of deposition and removal are similar. For very sticky conditions, deposition on the face of the fins can cause a rise in the pressure drop by as much as 65%. The pressure drop has also been successfully related to the percentage of open frontal area of the fins with and without deposition. Deposition inside and at the rear of the fin bank was found to be minimal.     

An approximate analytical prediction about thermal performance and optimum design of pin fins subject to condensation of saturated steam flowing under forced convection

An approximate analytical method has been suggested for solving the governing equation for horizontal pin fins subject to condensation while saturated steam flowing over its under laminar forced convection. Adomian decomposition method is used for determination of the temperature distribution, performance and optimum dimensions of pin fins with temperature dependent thermal conductivity under the condensation of steam on the fin surface. From the results, a significant effect on the temperature distribution in the fin and its performances are noticed with the variation in fin-geometric parameters and thermo-physical properties of saturated vapor. Next, a generalized scheme for optimization has been demonstrated in such a way that either heat-transfer duty or fin volume can be taken as a constraint. Finally, the curves for the optimum design have been generated for the variation of different thermo-physical and geometric parameters, which may be helpful to a designer for selecting an appropriate design condition.     

Energy-efficient flat-tube heat exchangers for indirectly cooled display cabinets

Different designs of flat-tube heat exchangers with plain fins have been evaluated theoretically in a parameter study in order to evaluate their performance potential in indirectly cooled display cabinets. Two different types of flat-tube heat exchangers were considered; one with serpentine fins and one with continuous plate fins. Both flat-tube heat exchanger types were adapted to the laminar flow regime on the liquid as well as on the air side. The performance of the two heat exchanger types had previously been verified experimentally under dehumidifying conditions. The results from this parameter study show that considerable savings in the required electric drive power to compressors, pumps and fans can be obtained in comparison with the traditional cooling coil. The savings may be up to 15%. In addition, the required temperature difference for the flat-tube heat exchangers is so small that frost-free operation is possible, which would result in even larger savings.     

Approximate analytical method for prediction of performance and optimum dimensions of pin fins subject to condensation of quiescent vapor

An approximate analytic method is proposed to solve the governing equation of horizontal pin fins subject to the condensation of saturated vapor under laminar free convection. The temperature distribution and performance parameters are determined by using Adomian decomposition method. A numerical scheme followed by the finite difference method has been used to validate the present analytical result. From the results, a significant effect on the temperature distribution and performances with the variation of fin dimensions and thermophysical parameters of saturated vapor is noticed. Next, a scheme for fin optimization has been carried out in such a way that either heat transfer duty or fin volume can be taken as a constraint selected according to the requirement of a design. Finally, dependency of design variables on an optimum condition has been established which may help the designer to adopt physical conditions in a practical application.     

Application of an orthotropy rescaling method to edge cracks and kinked cracks in orthotropic two-dimensional solids

Oblique edge cracks and kinked cracks in orthotropic materials with inclined principal material directions under inplane loadings are investigated. The Stroh formalism is modified by introducing new complex functions, which recovers a classical solution for a degenerate orthotropic material with multiple characteristic roots. An orthotropy rescaling technique is presented based on the modified Stroh formalism. Stress intensity factors for edge cracks as well as kinked cracks are obtained in terms of solutions for a material with cubic symmetry by applying the orthotropy rescaling method. Explicit expressions of the stress intensity factors for a degenerate orthotropic material are obtained in terms of solutions for an isotropic material. The effects of orthotropic parameter, material orientation, and crack angle on the stress intensity factors for the degenerate orthotropic material are discussed. The stress intensity factors for cubic symmetry materials are calculated from finite element analyses, which can be used to evaluate the stress intensity factors for orthotropic materials. The energy release rate for the kinked crack in an orthotropic material is also obtained.     

Experimental Study of Heat Transfer Enhancement in Solar Tower Receiver Using Internal Fins

The receiver is an important element in solar energy plants. The principal receiver’s tubes in power plants are devised to work under extremely severe conditions, including excessive heat fluxes. Half of the tube’s circumference is heated whilst the other half is insulated. This study aims to improve the heat transfer process and reinforce the tubes’ structure by designing a new receiver; by including longitudinal fins of triangular, circular and square shapes. The research is conducted experimentally using Reynolds numbers ranging from 28,000 to 78,000. Triangular fins have demonstrated the best improvement for heat transfer. For Reynolds number value near 43,000 Nusselt number (Nu) is higher by 3.5% and 7.5%, sequentially, compared to circular and square tube fins, but varies up to 6.5% near Re = 61000. The lowest friction factor is seen in a triangular fin receiver; where it deviates from circular fins by 4.6%, and square fin tubes by 3.2%. Adding fins makes the temperature decrease gradually, and in the case of no fins, the temperature gradient between the hot tube and water drops sharply in the planed tube by 7%.     

Estimation of Natural-Convection Heat-Transfer Characteristics from Vertical Fins Mounted on a Vertical Plate

The inverse scheme of the finite difference method in conjunction with the least-squares scheme and experimental measured temperatures is proposed to solve a two-dimensional steady-state inverse heat conduction problem in order to estimate the natural-convection heat transfer coefficient under the isothermal situation [`h] iso from three vertical fins mounted on a vertical plate and fin efficiency hf for various values of the fin spacing and fin height. The measured fin temperatures and ambient air temperature are measured from the present experimental apparatus conducted in a small wind tunnel. The heat transfer coefficient on the middle fin of three vertical fins is non-uniform for the present problem and its functional form can be difficult to be obtained. Thus the whole fin is divided into several sub-fin regions before performing the inverse calculation. In order to validate the reliability of the present estimates, the present estimates of [`h] iso compare with those obtained from the correlations recommended by current textbooks and other previous results. The present estimates of [`h] iso can be applied to obtain a modified correlation of the Nusselt number and Raleigh number.     

Performance and optimum design analysis of convective fin arrays attached to flat and curved primary surfaces

A model has been developed analytically to carry out the performance and optimum design analysis of four fin arrays, namely, longitudinal rectangular fin array (LRFA), annular rectangular fin array (ARFA), longitudinal trapezoidal fin array (LTRA) and annular trapezoidal fin array (ATFA) under convective cooling conditions. The performance parameters such as fin efficiency, fin effectiveness and augmentation factor are evaluated for a wide range of design variables. It has been observed that the conduction through the supporting structure and the convection from the interfin spacing have a pronounced effect on the performance of a fin array. The optimum fin dimensions in a fin assembly have been determined by consideration of the constant total height of the fin assembly and interfin spacing. From the results, it can be highlighted that the optimum fin dimensions in fin arrays differ from that of the individual fins.