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.     

Accurate predictions for optimum design of a T-shaped fin under an actual wet load condition

An effort is made to develop an analytical model for predicting the thermal performance and optimum design parameters of a wet T-shaped fin by considering variable thermal conductivity of the fin material and variable convective heat transfer coefficient. The temperature distribution is obtained by solving the highly non-linear governing equations by employing three different analytical techniques, namely Variational Iteration Method, Adomian Decomposition Method and Differential Transform Method, and validated by that obtained from the Finite Difference Scheme. The optimisation analysis is carried out by employing the Lagrange multiplier technique. A complete multivariable geometric optimisation is executed, where all the geometric parameters are varied simultaneously to establish the optimum condition. Furthermore, the analysis is done for both insulated and convective fin tip conditions and a comparative analysis on the temperature distribution, fin performance and optimum design parameters is presented between these two cases.     

小管径椭圆管开缝翅片换热器的数值模拟

对小管径椭圆管开缝翅片换热器空气侧的流动与传热特性进行数值模拟,对影响其换热性能的2个主要参数椭圆管偏心率和开缝翅片开缝错列高度分布进行优化,与传统管翅式换热器换热性能进行比较。模拟结果表明:当椭圆管两轴之比Rx:Ry=2:3(偏心率),开缝高度分布为0.8 mm,0.6 mm和0.4 mm时,换热效果最好。与传统管翅式换热器相比,小管径椭圆管开缝翅片换热器换热系数提高10%~20%,而压降几乎相等,总体换热性能提高。     

Mathematical analysis for the efficiency of a semi-spherical fin with simultaneous heat and mass transfer

In this paper an analytical solution for the efficiency of a semi-spherical fin when subjected to simultaneous heat and mass transfer mechanisms is studied. For the mathematical analysis of a wet fin equation, a relationship between humidity ratio and temperature of the saturation air is needed. The driving forces for the heat and mass transfer are the temperature and humidity ratio differences, respectively. Analytical solutions are obtained for the temperature distribution over the fin surface when the fin is fully wet. It is observed that in humid conditions the fin has high efficiency to be used in industry. The variation effects of these parameters have been considered. Finally linear relation has been proposed for humidity and temperature on the fin surface.     

整体翅片式微通道换热器的数值模拟

采用CFD数值模拟的方法,对整体翅片式微通道换热器空气侧的流动与传热特性进行研究,用场协同的原理分析翅片参数(长度、高度、间距)对换热器性能的影响,并与传统微通道换热器空气侧性能进行对比。结果表明:在考查的翅片尺寸范围内,随着翅片长度的缩短、高度的增加、间距的减小,温度场和速度场的协同性随之改善,有利于换热效果的提高;与传统的微通道换热器相比,整体翅片式微通道换热器空气侧换热性能变差,但是阻力大大降低,总体性能有所改善。     

Application of the decomposition method to thermal stresses in isotropic circular fins with temperature-dependent thermal conductivity

Summary A stress-field of a perfect elastic isotropic circular fin with variable thermal conductivity is obtained. The thermal conductivity is considered temperature dependent. The nonlinear conduction-convection-radiation heat transfer equation of the circular fins subjected to the nonlinear boundary conditions is solved by Adomian's double decomposition method. The thermal stress distribution is obtained by direct integration of the temperature distribution. Fow low temperature difference between the fin base and the ambiance, the effect of thermal conductivity on pure convection and convection-radiation is important and can be negligible in pure radiation.     

Identification of materials in a hyperbolic annular fin for a given temperature requirement

This article deals with the prediction of parameters in an annular hyperbolic fin with temperature-dependent thermal conductivity. Three parameters such as thermal conductivity, variable conductivity coefficient and the surface heat transfer coefficient have been predicted for satisfying a prescribed temperature distribution on the surface of fin. This is achieved by a hybrid differential evolution-nonlinear programming optimization method. The effect of random measurement errors is also considered. It is observed from the present inverse analysis that many feasible materials exist satisfying the given temperature distribution, thereby providing engineering flexibility in selecting any material from the available choices. For a given material, this is possible by regulating the surface heat transfer coefficient.     

Thermal Performance of a Functionally Graded Radial Fin

This paper investigates the steady-state thermal performance of a radial fin of rectangular profile made of a functionally graded material. The thermal conductivity of the fin varies continuously in the radial direction following a power law. The boundary conditions of a constant base temperature and an insulated tip are assumed. Analytical solutions for the temperature distribution, heat transfer rate, fin efficiency, and fin effectiveness are found in terms of Airy wave functions, modified Bessel functions, hyperbolic functions, or power functions depending on the exponent of the power law. Numerical results illustrating the effect of the radial dependence of the thermal conductivity on the performance of the fin are presented and discussed. It is found that the heat transfer rate, the fin efficiency, and the fin effectiveness are highest when the thermal conductivity of the fin varies inversely with the square of the radius. These quantities, however, decrease as the exponent of the power law increases. The results of the exact solutions are compared with a solution derived by using a spatially averaged thermal conductivity. Because large errors can occur in some cases, the use of a spatially averaged thermal-conductivity model is not recommended.     

空气侧结构对多元微通道平行流冷凝器传热流动性能的影响

建立了多元微通道平行流冷凝器的稳态分布参数模型,与实验对比验证了模型的正确性。利用所建立的模型,研究了翅片高度、翅片间距、百叶窗开窗间距、百叶窗开窗角度变化对多元微通道平行流冷凝器传热和流动性能的影响。结果表明,随着翅片高度的增大,换热量逐渐增大,空气侧压降逐渐减小;随着翅片间距或者百叶窗开窗间距的增大,换热量和空气侧压降都是逐渐减小;随着百叶窗开窗角度的增大,换热量和空气侧压降都是逐渐增大。     

Numerical Investigation on the Low Temperature Corrosion Characteristics of Flue Gas Heat Exchanger

Low temperature corrosion characteristics on flue gas heat exchanger surfaces are crucial for reliability of equipment operation. Reasonable fin structure and accurate prediction of sulfuric acid vapor can understand corrosion characteristics and enhance performance. In this paper, a coupling numerical model is adopted to predict the condition of sulfuric acid vapor on heat exchanger surfaces. A rectangular type finned tube is employed to analyze the effect of operating parameters on sulfuric acid condensation and corrosion. The results show that fin regions with higher temperature have higher acid solution concentration. Although the increases of water vapor concentration could result in increase of deposition, the increase of flue gas temperature will reduce corrosion risk. The important is the rectangular fin can avoid high corrosion risk on its leading edge. Therefore, rectangular fin may be considered as an alternative scheme without reducing heat transfer performance and elongating the lifespan of individual fin.     

多孔泡沫材料强化传热特性及场协同分析

实际生产生活中使用到的多孔泡沫材料通常都是非均质的,文章建立了多孔泡沫材料均质与非均质模型,结合场协同理论,从速度与温度梯度矢量的协同关系出发,分析了多孔泡沫材料内部单相流体对流强化换热的物理机制,研究了孔隙率、孔密度以及空气流速对流体顺流方向协同性能的影响。研究表明:场协同原理适用于分析多孔泡沫材料的强化传热机制;多孔泡沫材料孔隙中心与骨架后缘处的协同程度最好,骨架侧缘协同程度最差(协同角接近90°);非均质多孔泡沫材料孔壁附近协同程度较差,相同条件下全场平均场协同角比均质泡沫大;多孔泡沫材料越均匀全场协同情况越好,在相同流速、孔隙率和孔密度下,均质泡沫材料全场平均协同角余弦值可达非均质泡沫的1.2倍。计算结果表明,空气流速为3m/s时,孔隙率为0.8、0.85和0.9的多孔泡沫材料强化传热强度分别是普通平直翅片的3.3倍、1.9倍和1.2倍。该研究对新型散热器设计具有指导意义。     

Boiling heat transfer to liquid helium from multilayered porous structure fins

Heat transfer characteristics of a fin having a novel structure are studied. The fins, manufactured by diffusion welding, have a multilayered porous structure. The experimental results show significant enhancement of heat flux over the entire temperature range. Maximum heat flux is increased up to 10 times compared with that for smooth surfaces. The new structure is effective for high heat flux cooling using boiling heat transfer.     

Efficiency and optimization of an annular fin with combined heat and mass transfer – An analytical solution

An analysis was carried out to study the efficiency of annular fin when subjected to simultaneous heat and mass transfer mechanisms. The temperature and humidity ratio differences are the driving forces for the heat and mass transfer, respectively. Analytical solutions are obtained for the temperature distribution over the fin surface when the fin is fully wet. The effect of the atmospheric pressure on the fin efficiency was also studied, in addition to fin optimum dimensions. It is demonstrated that the closed-form solutions for a dry-fin case presented in many text books are special cases for the solutions presented in this paper.     

Application of Differential Transform Method to Thermoelastic Problem for Annular Disks of Variable Thickness with Temperature-Dependent Parameters

This article analyzes the one-dimensional steady temperature field and related thermal stresses in an annular disk of variable thickness that has a temperature-dependent heat transfer coefficient and is capable of temperature-dependent internal heat generation. The temperature dependencies of the thermal conductivity, Young’s modulus, and the coefficient of linear thermal expansion of the disk are considered, whereas Poisson’s ratio is assumed to be constant. The differential transform method (DTM) is employed to analyze not only the nonlinear heat conduction but also the resulting thermal stresses. Analytical solutions are developed for the temperature and thermal stresses in the form of simple power series. Numerical calculations are performed for an annular cooling/heating fin of variable thickness. Numerical results show that the sufficiently converged analytical solutions are in good agreement with the solutions obtained by the Adomian decomposition method and give the effects of the temperature-dependent parameters on the temperature and thermal stress profiles in the disk. The DTM is useful as a new analytical method for solving thermoelastic problems for a body with temperature-dependent parameters including material properties.     

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.     

Analysis of the heat transfer area distribution in a frosted plain fin-and-tube geometry

The development of frost is a phenomenon that deteriorates thermohydraulic performance on heat exchangers. In this study, several heat-transfer area distributions on a fin-and-tube geometry are proposed and their performances as frost develops are compared using simulation. The frost development at a specific location is determined using a segment analysis. In each segment, a semiempirical model to predict the frost growth based on air temperature, velocity, relative humidity and surface temperature is applied. The analysis considers airflow redistribution among channels, leading to changes in heat transfer and frosting rates with time. Results show that a geometry that allows even flow distribution along the operation time is less sensitive to thermohydraulic deterioration. An area distribution with larger fin spacing and fin length presents an advantage, particularly on the pressure drop, which allows longer operation time between defrost cycles.     

多孔材料辐射-传热耦合性能的统计二阶双尺度计算

对多孔材料辐射-传热耦合计算的数学模型, 即Rosseland方程, 给出了一种统计的二阶双尺度分析方法, 并针对典型问题进行了数值模拟。建立了考虑辐射项的统计二阶双尺度计算公式, 给出了统计意义下热流密度极值的预测算法, 并通过与理论解的比较对算法进行了验证, 利用本文中方法研究了孔洞体分比和空间分布状态对陶瓷多孔材料热传导系数、 辐射传导系数和热流密度极值的影响。结果表明: 孔洞体积分数的增加将导致有效热传导系数下降; 热流密度极值随孔洞体积分数的增加而变大, 并且在高温时辐射的作用明显增大; 数值试验表明, 使用统计二阶双尺度方法及其有限元算法预测孔洞随机分布复合材料结构的热性能是有效的。     

Optimization of a fin-tube type adsorption chiller by design of experiment

This paper presents a numerical analysis of the performance of a fin-tube type adsorption chiller associated with heat and mass transfer mechanisms. A two-dimensional axisymmetric transient model is developed and 10 parameters are used to investigate their effects on the performance of an adsorption chiller and to obtain the optimized conditions of a fin-tube type adsorption chiller. Ten parameters found in many other studies, such as fin pitch, fin thickness, fin height, diffusion coefficient, particle size, cycle time, cycle ratio, temperature of hot water, fluid velocity and porosity, are used in this study. Based on the design of experiment, an orthogonal array of 10 parameters with three levels, L₂₇(3¹³) is used for the analysis of variance (ANOVA) and through this method, each parameter's level of contribution is carefully examined. The result shows that fin thickness and the temperature of hot water are the dominant parameters for COP and SCP, respectively. The optimum conditions having the highest COP of 0.6782 and SCP of 217.68 W kg⁻¹ are found through the result.     

5mm强化管蒸发器中齿高对性能的影响及齿高优化

本文对齿高的变化对5mm内螺纹强化管蒸发器性能的影响进行了研究,结果表明齿高的增加总是增加蒸发器的总换热系数和降低换热器的平均换热温差。利用已有的换热和压降关联式,设计了齿高对系统性能影响的仿真算法,在蒸发器换热性能最优的条件下,定量得出5turn内螺纹强化管齿高设计的推荐值为0．09mm。     

Assessment of condensation heat transfer correlations in the modelling of fin and tube heat exchangers

This is the second paper of a series that assesses the performance of a refrigeration system model by means of cycle parameters. In this case, the condensation temperature is the parameter to study and it is focused on fin and tube condensers. It also studies the influence of the heat transfer models on the estimation of this refrigeration cycle parameter and different correlations for the heat transfer coefficients have been implemented in order to characterise the heat transfer in the heat exchangers. The flow inside the heat exchangers is considered one-dimensional as in previous works. In the cycle definition, other submodels for all the cycle component have been taken into account to complete the system of equations that characterises the behaviour of the refrigeration cycle. This global system is solved by means of a Newton–Raphson algorithm and a known technique called SEWTLE is used to model the heat exchangers. Some experimental results are employed to compare the condensation temperatures provided by the numerical procedure and to evaluate the performance of each heat transfer coefficient. These experimental results correspond to an air-to-water heat pump and are obtained by using R-22 and R-290 as refrigerants.