Optimum dimensions of longitudinal rectangular fins and cylindrical pin fins with variable heat transfer coefficient

Considering a temperature dependent heat transfer coefficient, the optimum dimensions of longitudinal rectangular fins and cylindrical pin fins have been investigated analytically. Employing the parameters of fin thickness or fin diameter and tip temperatures, the optimum dimensions, heat dissipation, and efficiency of fins are obtained by Lagrange's multiplier method. It is shown that the fin efficiency of an optimum cylindrical pin fin is higher than that of an optimum rectangular fin. To facilitate the thermal design of the heat transfer components, very simple mathematical expressions for the optimum dimensions of fins are presented in this study.     

求解相变传热问题的等效热容法

采用等效热容法求解伴有相变过程的瞬态热传导问题.在整个区域建立统一的能量方程,将分区域求解问题化为整个区域的非线性问题处理.给出了解决相变温度为单一温度或者相变温度区间很小时产生的数值奇异问题的方法.用热焓判据判断单元是否发生相变,并考虑了固液两相材料物性参数的变化,相变界面位置按线性插值计算.算例表明,等效热容法求解相变传热问题,程序简单,计算效率高,相变界面位置计算准确.     

二种开缝翅片特性的试验及数值模拟比较研究

为了强化空冷器的换热性能,利用红外热像仪和Fluent软件等对增压空冷器空气侧的X型及圆环扇面型2种4排开缝翅片的传热和阻力性能进行了试验和数值模拟研究,在试验的Re数范围内得出了传热和阻力的特性曲线,并通过模拟得出了气流在2片翅片间的温度场、流场以及阻力和换热特性曲线在试验Re数范围内的对比。结果表明,数值模拟与试验值基本吻合,X型开缝翅片的传热性能不仅高于圆环扇面型开缝翅片,同时X型的压力损失还小于圆环扇面型开缝翅片。     

方翅圆管翅片效率的理论分析及数值计算

针对方翅圆管翅片效率进行了理论分析,采用有限差分方法建立了计算模型,计算了方翅圆管的翅片效率,绘制了方翅圆管翅片效率的计算用图.通过与通常采用的近似计算方法进行比较,说明了近似计算方法的误差大小及应用条件.     

肋片和多孔介质强化梯级相变储热系统性能的对比研究

针对于相变材料（PCM）导热性能差引起的梯级相变储热系统传热速率低的问题,利用三维数值仿真研究肋片和多孔介质对梯级相变储能系统放热性能的强化作用,在此基础上提出了梯度孔隙率进一步提升系统的放热性能,从PCM的放热速率和放热效率两个方面对梯级相变储能系统的不同强化方法进行了分析对比。结果表明肋片在显热放热阶段强化传热作用更显著,而多孔介质在潜热放热阶段强化传热更显著。整个放热过程只加入多孔介质比只加入肋片表现出更好的放热性能。同时添加肋片和多孔介质时,梯级相变系统放热性能最优,PCM完全凝固时间减少了40%。三种孔隙率梯度工况下,系统的放热效率无明显差异,但在负梯度孔隙率情况下,放热速率更高且更均匀。相比于正梯度孔隙率的情况,负梯度孔隙率具有更优的热性能。     

肋片和多孔介质强化梯级相变储热系统性能的对比研究

针对于相变材料（PCM）导热性能差引起的梯级相变储热系统传热速率低的问题,利用三维数值仿真研究肋片和多孔介质对梯级相变储能系统放热性能的强化作用,在此基础上提出了梯度孔隙率进一步提升系统的放热性能,从PCM的放热速率和放热效率两个方面对梯级相变储能系统的不同强化方法进行了分析对比。结果表明肋片在显热放热阶段强化传热作用更显著,而多孔介质在潜热放热阶段强化传热更显著。整个放热过程只加入多孔介质比只加入肋片表现出更好的放热性能。同时添加肋片和多孔介质时,梯级相变系统放热性能最优,PCM完全凝固时间减少了40%。三种孔隙率梯度工况下,系统的放热效率无明显差异,但在负梯度孔隙率情况下,放热速率更高且更均匀。相比于正梯度孔隙率的情况,负梯度孔隙率具有更优的热性能。     

水平放置离散矩形直翅片的自然对流传热性能研究

本文实验研究了自然对流时,温差为９０－２００Ｋ范围内,水平放置离散矩形直翅片组的稳态传热性能,着重探讨了翅片列间距对翅片组散热的影响。从单位传热基面面积的传热量的翅片材料的使用量综合考虑。在本文所用的翅片范围内,翅片列间距为１２～１８ｍｍ的直线排列离散翅片组和翅生列间距一翅片长度相等匆匆韭我离散翅片组效果为优。通过因次分析的方法建立离散翅间空气自然对流的传热准数关系式。     

计算多孔催化剂有效系数的新方法——等效反应温度法

本文第一次提出了等效反应温度T_a的概念,即把一个等温n级反应或非等温一级反应等效为一个在T_a温度下进行的等温一级反应,从而大大简化了多孔催化剂有效系数的计算过程,并得到了等温和非等温催化剂有效系数的近似解析表达式.利用这些表达式来计算催化剂的有效系数,不仅简单易行,而且计算结果与用数值方法得出的结果相比,也较现有的近似计算方法更精确.     

Tip Deflection and Blocking Force of Soft PZT-Based Cantilever RAINBOW Actuators

A piezoelectric/electrostrictive RAINBOW actuator is a monolithic bending device consisting of an electromechanically active layer and a reduced passive layer formed in a high-temperature reduction treatment. When the piezoelectric or electrostrictive layer is driven under an electric field or when the environmental temperature changes, bending deflection is produced because of the constraint of the reduced inactive layer or because of the thermal expansion coefficient difference of the two layers. In this study, general analytical expressions relating tip deflection, blocking force, and equivalent moment with an applied electric field and temperature change are derived for a cantilevered RAINBOW actuator. It is shown that optimal actuator performance can be achieved in the RAINBOW actuator by choosing a suitable thickness ratio of the reduced layer to the PZT layer. A series of RAINBOW cantilever actuators have been experimentally prepared from high-density, soft, lead zirconate titanate (PZT) ceramics. Different reduction layer thickness is obtained by adjusting the processing parameters, such as reduction temperature and time. The measured results on tip deflection and blocking force agree well with theoretical prediction under a weak electric field. However, when a high driving electric field is used, deviation is observed, which can be attributed to a nonlinear piezoelectric response and a nonlinear elastic behavior associated with soft PZT materials under high driving electric fields.     

Numerical Study on Plate‐Fin Heat Exchangers with Plain Fins and Serrated Fins at Low Reynolds Number

A simpler numerical model for plate‐fin heat exchangers with plain fins and serrated fins is presented, which incorporates the characteristics of fluid flow and heat transfer. The numerical simulations for heat exchangers with two fins at low Reynolds numbers are carried out by employing the simplified model and using the CFD code FLUENT. The results of heat transfer rate and pressure drop in numerical simulations are compared with the experimental results from the literature. It is shown that the results are in good agreement and the numerical model is reasonable and appropriate. The characteristics of fluid flow and heat transfer are analyzed and compared based on the numerical results. It is concluded that by applying the average heat transfer coefficient in practice, the heat transfer rate of the primary surface is overestimated, and the heat transfer rate and efficiency of the secondary surface are underestimated. The numerical modeling and conclusions provide the method and theoretical basis for the selection, optimization and analysis of plate‐fin heat exchangers.     

Role of bond thickness on adhesive failure

An analytical, numerical and experimental program is described which establishes the basic fracture mechanics properties of an adhesive joint. A finite element analysis of a homogeneous finite tapered double cantilever beam is first presented and the results compared with elasticity and strength of materials solutions. Using analytical results developed in another paper, a finite bond line thickness correction factor is introduced to determine the crack tip stress intensity factor as a function of crack length. An experimental program is described wherein the crack tip stress intensity factor for the cantilever beam adhesive joint is measured by the compliance method and the results compared with those obtained by analytical and numerical methods. Finally, the critical value of the adhesive crack tip stress intensity factor is determined using the analytical and experimental techniques presented.     

三种小波函数处理含噪声重叠峰的比较

运用连续小波变换用于处理分析化学信号可得到信号的近似导数。通过Haar小波函数、三次样条函数的导函数、二阶样条小波为小波母函数的连续小波变换法对模拟含噪声重叠信号的处理结果表明：二阶样条小波的连续小波变换法所得结果的信噪比明显高于前两种方法。该方法为分析信号,特别是信噪比较低的重叠信号的处理提供了一种有效工具。     

Comparative measurement of interfacial tension by transient dynamic methods

An experimental comparison between different techniques for the interfacial tension measurement is presented for polyamide‐6 and polystyrene pair. The techniques are transient dynamic methods, which include the breaking thread (BT) method, the imbedded fiber retraction (IFR) method, the deformed drop retraction (DDR) method, and two modified DDR methods. The modified DDR methods combine the analytical power of the DDR method with experimental simplicity of the BT and IFR methods, respectively. Interfacial tension values obtained by the modified DDR method that combines the BT method is much lower than those by the other methods. Among all techniques, the modified DDR that combines the IFR method is found to be most convenient and accurate method. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99:1910–1918, 2006     

Effectiveness of catalytic archipelagos—II: Random arrays of random islands

Voronoi polygons are used to simulate a random distribution of irregularly shaped catalytic islands. Finite element mathematics is used to determine the catalytic effectiveness of the islands when adsorbed reactants diffuse and disappear by a first order reaction at their boundaries. It is found that the catalytic effectiveness of the islands at any fractional coverage can be estimated reasonably accurately either from asymptotic formulae, valid for certain values of diffusion, adsorption, and reaction constants, or from the equivalent annulus approximation found earlier to be accurate for certain regular arrays of regular islands. The equivalent annulus approximation allows analytic prediction of the catalytic effectiveness for any set of parameter conditions given only the fraction area ratio Γ/Ω. Both of these quantities of which can be determined directly from a photomicrog of a representative sample.     

Optimum designs of longitudinal fins

Employing fin parameter and tip temperature, a new concept with Lagrange's multiplier method is proposed to obtain the optimum width, height, heat dissipation, and efficiency of longitudinal fins for boiling heat transfer. A power-law type heat transfer coefficient is assumed in this analysis. Longitudinal fins of rectangular, convex parabolic, triangular, and concave parabolic profiles are first investigated. It is found that the optimum dimensions of a fin depends upon fin profile area, heat transfer coefficient at the fin base, and the thermal conductivity of the fin. Then, the least material fin profile is derived for each single heat transfer mode. To facilitate the thermal design of heat transfer components, simple mathematical expressions for the optimum dimensions of fins are presented in this study.     

Dissolution of a Polydisperse Ensemble of Particles in a Flow Apparatus

A mathematical model of continuous dissolution of salts in a liquid solution based on the crystal size distribution density function is considered. It is assumed that crystals have a spherical shape and the particle dissolution rate is a power-law function of the particle radius. A stationary solution is obtained, and its stability is analyzed. Features of the solution are noted for a particular case—batch process. For a nonstationary solution, the evolution equation for the undersaturation of the liquid solution is derived. An approximate analytical method for solving this equation is proposed; the solution found by this algorithm is quite close to that obtained by numerical methods. The concept of dissolution efficiency coefficient in continuous dissolution is introduced; analytical expressions for this coefficient are derived.     

Two Analytical Approaches for Solution of Population Balance Equations: Particle Breakage Process

Various particulate systems were modeled by the population balance equation (PBE). However, only few cases of analytical solutions for the breakage process do exist, with most solutions being valid for the batch stirred vessel. The analytical solutions of the PBE for particulate processes under the influence of particle breakage in batch and continuous processes were investigated. Such solutions are obtained from the integro‐differential PBE governing the particle size distribution density function by two analytical approaches: the Adomian decomposition method (ADM) and the homotopy perturbation method (HPM). ADM generates an infinite series which converges uniformly to the exact solution of the problem, while HPM transforms a difficult problem into a simple one which can be easily handled. The results indicate that the two methods can avoid numerical stability problems which often characterize general numerical techniques in this area.     

Dynamic optimization of dissipative PDE systems using nonlinear order reduction

This article presents computationally efficient methods for the solution of dynamic constraint optimization problems arising in the context of spatially distributed processes governed by highly dissipative nonlinear partial differential equations (PDEs). The methods are based on spatial discretization using the method of weighted residuals with spatially global basis functions (i.e., functions that cover the entire domain of definition of the process and satisfy the boundary conditions). More specifically, we perform spatial discretization of the optimization problems using the method of weighted residuals with analytical or empirical (obtained via Karhunen-Loève expansion) eigenfunctions as basis functions, and combination of the method of weighted residuals with approximate inertial manifolds. The proposed methods account for the fact that the dominant dynamics of highly dissipative PDE systems are low dimensional in nature and lead to approximate optimization problems that are of significantly lower order compared to the ones obtained from spatial discretization using finite-difference and finite-element techniques, and thus, they can be solved with significantly smaller computational demand. The resulting dynamic nonlinear programs include equality constraints that constitute a low-order system of coupled ordinary differential equations and algebraic equations, which can then be solved with combination of standard temporal discretization and nonlinear programming techniques. We employ backward finite differences (implicit Euler) to perform temporal discretization and solve the nonlinear programs resulting from temporal and spatial discretization using reduced gradient techniques (MINOS). We use two representative examples of dissipative PDEs, a diffusion-reaction process with constant and spatially varying coefficients, and the Kuramoto-Sivashinsky equation, a model that describes incipient instabilities in a variety of physical and chemical systems, to demonstrate the implementation and evaluate the effectiveness of the proposed optimization algorithms.     

Dispersed plug flow model for steady-state laminar flow in a tube with a first order sink at the wall

Steady state, laminar flow transport in a tube with a first order sink at the wall involves two dimensions—radial and axial. In this paper, a novel iterative technique has been proposed for reducing such a two-dimensional model to an equivalent one-dimensional dispersed plug flow model. The latter yields an analytical expression for the equivalent axial dispersion and a simple, closed form, but approximate, analytical solution of the original two-dimensional problem. The operating range in which this analytical solution is useful has been investigated for a system with mass transfer at the wall.     

波纹内翅片管的管内对流换热特性研究

通过实验研究了波纹形内翅片换热管的对流换热和阻力特性,拟合了所测Re范围内对流换热和阻力实验关联式,并运用相同质量流量、相同泵功率、相同阻力降这三种准则比较了该翅片管与普通光管之间的传热效果。结果表明,这种波纹形内翅片管有较强的换热效果,特别是在低Re条件下,强化效果更加明显。