A Correction Factor-Based General Thermal Resistance Formula for Heat Exchanger Design and Performance Analysis

Methods for the analysis of heat exchangers with various flow arrangements modeling, design, and performance are essential for heat transfer system modeling and its integration with other energy system models. This paper proposes the use of the linear-transfer law for the heat exchanger design and performance analysis as a function of the thermal resistance related to the ratio of a linear temperature difference to the total heat transfer rate. Additionally, we derived a correction factor that represents the influence of the flow arrangement on the heat transfer performance by the effective thermal conductance, as a function of correction factor, heat transfer coefficient, and surface area. Based on the effective thermal conductance, we propose the hot-end NTU and cold-end NTU for deriving a standardized and general thermal resistance formula for different types of heat exchangers by the combination of the correction factor with linear-transfer law. Moreover, for parallel-flow, cross-flow, and 1-2 Tubular Exchanger Manufacturers Association(TEMA) E shell-and-tube heat exchangers, we derived and obtained alternative correction factor expressions without introducing any temperatures. Two cases about heat exchanger design and performance analysis show that the calculation processes using the correction factor-based general thermal resistance are straightforward without any iteration and the calculation results are accurate. Finally, the experimental validation shows that the general thermal resistance formula is appropriate for analyzing the heat transfer performance. That is, the correction factor-based general thermal resistance formula provides a standardized model for heat exchanger analysis and heat transfer/integrated energy system modeling using the heat current method.     

Thermal Stress Analysis in Magneto-Electro-Thermo-Elasticity with a Penny-Shaped Crack Under Uniform Heat Flow

ABSTRACT

The magnetoelectroelastic material possesses the dual feature that the application of magnetic field induces electric polarization and electric field induces magnetization. Piezoelectric-piezomagnetic materials exhibit magneto-electric effect. When magneto-electro-elastic materials are subjected to thermal flow, they can fracture prematurely due to their brittle behavior. Hence, it should be important to know the fracture behavior of magneto-electro- elastic materials. The penny-shaped crack problem in a medium possessing coupled electro-magneto-thermo-elastic is considered in this paper. It is assumed that the crack is isothermal. The analysis is an exact treatment of penny-shaped crack in a magneto-electroelastic solid subjected to uniform heat flow far away from the crack region. The governing equations of temperature, elastic displacements and electric potential as well as magnetic potential for an anisotropic magneto-electro-elastic medium are partial differential equations of second order, which are solved by means of the Hankel transform technique. Expressions for elastic displacements, thermal stresses, electric displacements and magnetic inductions are determined from the dual integral equation method. Exact thermal stress intensity factor of the problem is obtained, and the near crack tip solutions are provided.     

Thermal modeling of vacuum web coating

The paper presents an analytical model for the prediction of the substrate temperature in vacuum web coaters. The model is based on the theory of heat transfer between a continuously moving workpiece and a stationary source, or sink, of energy. The investigation concerns the Physical Vapor Deposition (PVD) of a metal layer on a polymer film by means of thermal evaporation, but many aspects apply equally well to sputtering and electron beam evaporation. The contributions to the specific heat load on the web are quantified, and the influence of the heat exchange between the film and the cooling drum is discussed in detail. After satisfactorily comparing the predictions with available literature results, the model is used as a guideline for a series of experimental tests aimed at determining the influence of the operating conditions on the final quality of the products obtained from vacuum deposition of thick metal layers on thin polymer substrates. The experimental results demonstrate the influence of the mechanical traction of the web on the thermal conductance between the film and the cooling drum.     

A Multiple-Relaxation-Time Lattice Boltzmann Model for Natural Convection in a Hydrodynamically and Thermally Anisotropic Porous Medium under Local Thermal Non-Equilibrium Conditions

To investigate the natural convective process in a hydrodynamically and thermally anisotropic porous medium at the representative elementary volume(REV)scale,the present work presented a multiplerelaxation-time lattice Boltzmann method(MRT-LBM)based on the assumption of local thermal non-equilibrium conditions(LTNE).Three sets of distribution function were used to solve the coupled momentum and heat transfer equations.One set was used to compute the flow field based on the generalized non-Darcy model;the other two sets were used to solve the temperature fields of fluid and solid under the LTNE.To describe the anisotropy of flow field of the porous media,a permeability tensor and a Forchheimer coefficient tensor were introduced into the model.Additionally,a heat conductivity tensor and a special relaxation matrix with some off-diagonal elements were selected for the thermal anisotropy.Furthermore,by selecting an appropriate equilibrium moments and discrete source terms accounting for the local thermal non-equilibrium effect,as well as choosing an off-diagonal relaxation matrix with some specific elements,the presented model can recover the exact governing equations for natural convection under LTNE with anisotropic permeability and thermal conductivity with no deviation terms through the Chapman-Enskog procedure.Finally,the proposed model was adopted to simulate several benchmark problems.Good agreements with results in the available literatures can be achieved,which indicate the wide practicability and the good accuracy of the present model.     

Thermal Management of Electronic Packages for Space Applications

This paper describes the state of the art for thermal mathematical modeling of electronic packages during transient operation. The methods for calculating thermal contact conductance, view factors, and heat transfer coefficients are reviewed, and an algorithm for computer software is provided. Monte Carlo treatment of the data uncertainties is explained. The computer algorithm uniquely incorporates the subroutines for calculating the thermal contact conductance, absorption factor, and statistical representation of the thermal parameters for Monte Carlo analysis.     

Electrocaloric Refrigeration using Multi-Layers of Electrocaloric Material Films and Thermal Switches

The electrocaloric effect in thin films of electrocaloric material has the potential to be used for efficient cooling systems. We numerically calculated the effect of the parameters in electrocaloric refrigeration with multi-layers of electrocaloric material films and thermal switches by changing the contact thermal conductance to improve thermal performance. It was found that the average heat transfer efficiency was 10% and the average heat flux transferred to the cold side of the system was 2.4 × 10⁴ W/m² for the standard conditions of a frequency of 100 Hz and a temperature difference between the hot side and the cold side of the system of 20 K. The average heat flux transferred to the cold side of the system was maximum when the thickness of the electrocaloric material was 70 µm and thickness of the heat storage material 100 µm. The average heat transfer efficiency was maximum at the two layers of the electrocaloric material.     

热循环载荷下BGA封装体热应力特性

构建了热循环条件下球栅阵列(ball grid array,BGA)封装体传热和应力耦合的非稳态理论模型,通过器件自身发热功率随时间变化来实现循环热载荷,研究工作过程中流场、温度场、应力场的动态变化,并采用有限元方法进行数值求解,分析了热循环载荷对器件所处物理场的影响。研究结果表明:热循环过程中,器件整体温度与方腔内自然对流强度在高温保温时间开始时刻出现峰值,在低温保温时间结束时刻出现谷值;BGA封装体最高温点均位于作为热源的芯片上,承受应力最大点位于阵列最外拐点与上下侧材料的连接部位;随着循环次数的增加,每个热循环周期中关键焊点上端点处的最大等效应力不断增加。     

A three-dimensional analysis of the effect of anisotropic gas diffusion layer(GDL) thermal conductivity on the heat transfer and two-phase behavior in a proton exchange membrane fuel cell(PEMFC)

A three-dimensional and two-phase model was employed to investigate the effect of the anisotropic GDL thermal conductivity on the heat transfer and liquid water removal in the PEMFCs with serpentine flow field and semi-counter flow operation. The GDL with different anisotropic thermal conductivity in the three directions (x, y, z) was simulated for four cases. As a result, the water saturation, temperature, species, current, potential distribution and proton conductivity were obtained. According to the comparison between the results of each case, some new conclusions are obtained and listed as below: (1) The anisotropic GDL produces the high temperature difference than that of isotropic case, and the in-plane thermal conductivity perpendicular to the gas channels is more important than that of along channels, which may produce the larger temperature difference. (2) Water saturation decreases due to the large temperature difference in the anisotropic case, but some water vapor may condense in the area neighbor to the channel ribs due to the cool function of the current collector and the great temperature difference. (3) The anisotropic thermal conductivity in the through-plane direction and the in-plane direction perpendicular to the gas channels can lead to the decrease of the membrane conductivity. (4) The isotropic GDL is better than that of anisotropic one for the uniform current density. Also, in-plane thermal conductivity perpendicular to the channels has more negative effect on the current density distribution in the membrane than that of the along channels one.     

Thermal radiation and the second law

The purpose of this paper is to collect and interrelate the fundamental concepts about second law analysis of thermal radiation. This heat transfer mode plays a leading role in solar energy utilization and in high-temperature devices, representing a significant contribution to irreversibility that is frequently omitted in engineering analysis. Entropy and exergy of thermal radiation are reviewed first. Radiative transfer processes are reviewed next, including exchange between surfaces, the presence of a participative medium, and the analysis of combined heat transfer modes. Emphasis is put on grey body radiation when treating with non-black body radiation, due to its relevance in engineering applications. The mathematical formulation of second law analysis of thermal radiation is complex, which limits its use in conventional heat transfer analysis. For this reason, numerical approaches reported to date deal with quite simple cases, leaving an open promising field of research.     

An Experimental Study on the Air-Side Heat Transfer Coefficient and the Thermal Contact Conductance in Finned Tubes

The objective of this experimental study is to evaluate the heat transfer coefficient outside a tube with annular transverse fins, derived from strips of copper mechanically bound and coupled outside. Water is used as the heating medium, in turbulent conditions and flowing at different temperatures inside the tube. Petukhov's correlation has been selected to calculate the water heat transfer coefficient in the tube. The experimental data obtained are compared with a correlation from literature, and a similar trend is observed. A fitting of the data provides a correlation for the three tubes of different external diameter (30 mm, 22 mm, and 15.6 mm) that agrees very well with the experimental values. The thermal contact conductance is identified as the main reason for the difference between data and the original Briggs and Young correlation. An estimation of the contact conductance between fins and tubes provides values between 3500 and 11000 W/m²-K, slightly increasing with the air Reynolds number (based on the external diameter of the tube), whose range is 2000 to 8000. The thermal contact resistance is estimated and its importance is confirmed, contributing 30 to 50% to the total air-side thermal resistance in the tubes used in the experiments.     

Thermal conductance of a rough elastic contact

From an existing theory of the elastic contact of an isotropically rough Gaussian surface in terms of moments of its power spectrum, limiting expressions for the number and average size of contact spots are derived and hence an upper-bound expression for the solid thermal contact conductance is obtained in terms of the separation of the contacting surfaces. It is shown that over a realistic range of loads, conductance and number of contacts are approximately proportional to the load and contact size is almost independent of load. Equivalent moments are defined such that the geometry of anisotropic surfaces can be represented by equivalent isotropic equations in good agreement with experiment.

The problems of quantifying the moments are discussed and it is shown how equivalent moments may be obtained from simple measurements on two profiles at right angles.     

The Impact of Thermal Contact Conductance on the Spreading and Solidification of a Droplet on a Substrate

The interfacial thermal contact conductance between an impinging molten droplet and a cold substrate plays an important role in the droplet spreading and solidification. In this paper, a simple correlation for the thermal contact conductance during a rapid contact solidification process was obtained. By introducing this correlation into the numerical model, a non-constant thermal contact conductance that varies with time and position was adopted for the first time to simulate the spreading and solidification of a molten droplet on a substrate. It was found that the droplet spreading and final bump shape are sensitive to the thermal contact conductance. Experiments were also performed to observe the final bump shape of the droplet. Qualitative agreement between the numerical and the experimental results justified the present method. Because the thermal contact conductance is not required to be prescribed, the present method is applicable to different operation conditions.     

Thermal Fracture of an Interpenetrating Phase Composite: Effects of Local Thermal Nonequilibrium

When subjected to thermal shocks, an interpenetrating phase composite may undergo significant, long range temperature difference between the constituent phases due to the interconnected microstructural networks, which facilitate faster heat transfer in the phase of higher thermal diffusivity. This temperature differential may alter the macroscopic temperature field thereby inducing additional thermal stresses in the composite. This work presents a local thermal nonequilibrium (LTNE) thermoelasticity theory for interpenetrating phase composites. In the LTNE thermoelasticity theory, the temperatures of the constituent phases are governed by the LTNE heat conduction equations based on the continuum theory of mixtures. A weighted average of temperatures for the constituents is employed in the thermoelastic constitutive equations of the homogenized composite. The model is subsequently applied to an infinite composite strip with an edge crack subjected to a thermal shock. Asymptotic solutions of temperature, thermal stress, and thermal stress intensity factor are obtained using the Laplace transform technique. The numerical results for an interpenetrating Al₂O₃/Al composite show that the temperature and thermal stress fields of the LTNE theory deviate from those of the classical theory. More importantly, the thermal stress intensity factor is reduced by considering the LTNE effect, which indicates that interpenetrating networks enhance the thermal fracture resistance of ceramic-metal composites.     

Parallel-Flow Heat Exchangers with Ambient Thermal Interaction

A mathematical model is developed to study the performance of a parallel-flow heat exchanger in which both fluid streams are interacting thermally with the surroundings. The fluid temperatures are found to be dependent on the magnitude of the ambient temperature relative to fluid inlet temperatures, the ratios of conductances between the fluids and the ambient and the interfluid conductance, the ratio of minimum to maximum fluid capacities, and the number of transfer units, NTU, for the heat exchanger. Two heat exchanger effectiveness criteria, one each for the hot and cold fluids, are used to study performance. The effectiveness is found to be adversely affected by increasing conductance ratios, increasing NTU, and increasing temperature difference between the ambient and the fluid of interest. For very high values of the conductance ratios, the heat exchanger will not perform as expected and both fluid temperatures will approach that of the ambient. The parallel-flow arrangement is compared to counterflow and is found to be less effective under the external heat transfer condition.     

Homotopy Perturbation Method for Thermal Stresses in an Annular Fin with Variable Thermal Conductivity

An approximate analytical solution method for thermal stresses in an annular fin with variable thermal conductivity is presented. Homotopy perturbation method (HPM) is employed to estimate the non-dimensional temperature field by solving nonlinear heat conduction equation. The closed-form solutions for the thermal stresses are formulated using the classical thermoelasticity theory coupled with HPM solution for temperature field. The plane state of stress conditions are considered in this study. The effects of thermal parameters such as variable thermal conductivity parameter (β), thermogeometric parameter (K), and the non-dimensional coefficient of thermal expansion (χ) on the temperature field and stress field are studied. The results for temperature field and stress field obtained from HPM-based solution are found to be in very close agreement with the results available in literature. Furthermore, the HPM solution is found to be very efficient and handles nonlinear heat transfer equation with greater convenience.     

Homogenized thermal conduction model for particulate foods

This paper deals with the definition of an equivalent thermal conductivity for particulate foods. An homogenized thermal model is used to asses the effect of particulate spatial distribution and differences in thermal conductivities. We prove that the spatial average of the conductivity can be used in an homogenized heat transfer model if the conductivity differences among the food components are not very large, usually the highest conductivity ratio between the foods components is lower than 5. In the general case we propose to use a standard spatial homogenisation procedure. Although the heterogeneity give rise to an anisotropic heat transfer behaviour, this effect is negligible when the food particles are randomly distributed. When we use pre-mixed particulate foods a statistical average can be defined from a small number of possible particle arrangements.     

Effects of Thermal Radiation for Electronic Cooling on Modified PCB Geometry under Natural Convection

In this study, the discrete ordinates method (DOM) model is employed to estimate the effect of thermal radiation from multiple heat sources in a natural-convection flow field. It is found that the flow field around the chips can be altered by natural convection as induced by radiative heat transfer. The influence of thermal radiation is higher than 65% when the chipboard is in a vertical orientation. Furthermore, even if the chip surface temperature is only 317 K, the influence of radiative heat transfer is still up to 18%. Therefore, radiative heat transfer cannot be ignored for electronic component computational fluid dynamics simulation under natural convection.     

A study on the thermal contact conductance in fin–tube heat exchangers with 7 mm tube

The thermal contact resistance has been frequently neglected in the process of design of heat exchangers because of the difficulty of measurement and the lack of accurate data. However, the thermal contact resistance is one of principal parameters in heat transfer mechanism of fin–tube heat exchangers. The objective of the present study is to investigate new factors such as fin types and manufacturing types of the tube affecting the thermal contact conductance and to find a correlation between the thermal contact conductance and the effective factors in fin–tube heat exchangers with 7 mm tube. The thermal contact conductances in the 22 heat exchangers with 7 mm tube have been investigated through the experimental–numerical method. A numerical scheme has been employed to calculate the thermal contact conductance and the portion of thermal resistances using the experimental data. As a result, the thermal contact conductance has been evaluated quantitatively, and a new correlation including the influence of new factors such as fin types and manufacturing types of the tube has been developed in the fin–tube heat exchanger with 7 mm tube. Also, the portion of each thermal resistance has been evaluated in each case.     

Effect of electroplating on the thermal conductance of fin–tube interface

This paper presents the experimental results of thermal contact conductance, heat transfer and interfacial temperature drop of finned tube heat exchanger test specimens. The results were based on the measured temperatures at several locations on the test specimen so that the thermal contact conductance could be directly determined. Each test specimen was assembled by mechanically expanding seven tubes into a single fin. The geometry of the specimens was based on a commonly used model of heat exchangers. The specimens included one bare tube (non-coated) specimen and four electroplated tube specimens. The plating metals were zinc, tin, silver and gold. The thickness of the plating in each case was 5 μm.Experiments have been conducted in both vacuum and nitrogen. Maximum enhancement was obtained when the tube was coated with tin. This indicates that, although the thermal conductivity is important, the softness of the plating material also plays an important role in enhancing the thermal conductance of the interface. The presence of an interstitial gas such as nitrogen is beneficial for the heat transfer and the thermal contact conductance. It is also noted that the interfacial temperature drop alone does not fully reflect the efficiency of the heat exchanger.     

多层打孔隔热材料热分析计算模型研究

基于能量守恒定律,构建可应用于空间机构热防护的多层打孔隔热材料热性能分析计算模型,该模型考虑相邻两层反射屏间辐射换热、反射屏与间隔物接触导热、间隔物本身导热以及残余气体导热,能够准确预测多层打孔隔热材料内部传热特性。并在此基础上,进行了隔热材料热真空实验研究,以验证所建热分析计算模型的准确度。