Superconductor Thermal Stability under the Effect of the Dual-Phase-Lag Conduction Model

The superconductor thermal stability is investigated under the effect of the dual-phase-lag heat conduction model. Two types of superconductors are considered, Types I and II. It is found that the dual-phase-lag model predicts a wider stable region as compared to the predictions of the parabolic and the hyperbolic heat conduction models. Also, the superconductor thermal stability under the effect of different design, geometrical and operating conditions is studied.     

Thermal Behavior of a Multi-layered Thin Slab Carrying Periodic Signals Under the Effect of the Dual-Phase-Lag Heat Conduction Model

The thermal behavior of a two–layered thin slab carrying periodic signals under the effect of the dual-phase-lag heat conduction model is investigated. Two types of periodic signals are considered, a periodic heating source and a periodic imposed temperature at the boundary. The deviations among the predictions of the classical diffusion model, the wave mode, and the dual-phase-lag model are investigated. Analytical closed-form solutions are obtained for the temperature distribution within the slab. The effect of the angular frequency, thickness of the plate, dimensionless thermal relaxation time, dimensionless phase-lag in temperature gradient, thermal conductivity, and thermal diffusivity on the temperature distribution of the slab was studied. It is found that the deviations among the three models increase as the frequency of the signals increases and as the thickness of the plate decreases. It is found that the use of the dual-phase-lag heat conduction model is necessary when the metal film thickness is of order 10^–6 m and the angular frequency of the signals is of order 10¹²rad · s^–1.     

The Dual-Phase-Lag Heat Conduction Model in Thin Slabs Under a Fluctuating Volumetric Thermal Disturbance

In the present work, the thermal behavior of a thin slab, under the effect of a fluctuating volumetric thermal disturbance described by the dual-phase-lag heat conduction model is investigated. It is found that the use of the dual-phase-lag heat conduction model is essential at large frequencies of the volumetric disturbance. It is found that the hyperbolic wave model deviates from the diffusion model when and the dual-phase-lag model deviates from the diffusion model when . where is the angular velocity of the fluctuating wall temperature, is the phase-lag in the heat flux vector and is the phase-lag in the temperature gradient vector.     

Thermal Behavior of a Stagnant Gas Confined in a Horizontal Microchannel as Described by the Dual-Phase-Lag Heat Conduction Model

The transient thermal behavior of a stagnant gas confined in a horizontal microchannel is investigated analytically under the effect of the dual-phase-lag heat conduction model. The microchannel is formed from two infinite horizontal parallel plates where the upper plate is heated isothermally and the lower one is kept adiabatic. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in this study. The effects of the Knudsen number Kn, the thermal relaxation time _q, and the thermal retardation time _T on the microchannel thermal behavior are investigated using three heat conduction models. It is found that the deviations between the predictions of the parabolic and the hyperbolic models are insignificant. On the other hand, the deviations between the parabolic and dual-phase-lag models are significant under the same operating conditions.     

Transient Thermal Response of a Homogeneous Composite Thin Layer Exposed to a Fluctuating Heating Source under the Effect of the Dual-Phase-Lag Heat-Conduction Model

The transient thermal behavior of a homogeneous composite domain described by three macroscopic heat-conduction models, under the effect of a fluctuating heating source, was investigated analytically. The composite domain consists of a matrix (domain 1) and inserts (domain 2), each made of different material. The matrix has a high concentration or volume fraction (>0.5) while the insert has a low concentration or volume fraction (< 0.5). The range of parameters within which the use of the hyperbolic or the dual-phase-lag heat-conduction models is a necessity was traced. The role that the frequency and amplitude of the fluctuating thermal disturbance plays in using the appropriate macroscopic heat-conduction model was studied.     

Thermal Behavior of Perfect and Imperfect Contact Composite Slabs Under the Effect of the Hyperbolic Heat Conduction Model

This work studies the heat transfer mechanisms during rapid heating of two-layer composite thin slabs from a macroscopic point of view using the hyperbolic heat conduction model. The composite slabs consist of two thin metal layers which may be in perfect or imperfect thermal contact. The effects of parameters such as the two films' thickness ratio, thermal conductivity ratio, heat capacity ratio, thermal relaxation time, and interfacial heat transfer coefficient on the thermal behavior of the composite slabs are investigated.     

Unsteady Natural Convection Fluid Flow in a Vertical Microchannel under the Effect of the Dual-Phase-Lag Heat-Conduction Model

The unsteady hydrodynamics and thermal behavior of fluid flow in an open-ended vertical parallel-plate microchannel are investigated semi-analytically under the effect of the dual-phase-lag heat conduction model. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in the study. The effects of the Knudsen number Kn, the thermal relaxation time τ _q , and the thermal retardation time τ _T on the microchannel hydrodynamics and thermal behavior are investigated using the dual-phase-lag and hyperbolic-heat-conduction models. It is found that as Kn increases the slip in the hydrodynamic and thermal boundary condition increases. Also, the slip in the hydrodynamic behavior increases as τ _T and τ _q decrease, but the effect of τ _T and τ _q on the slip of the thermal behavior is insignificant.     

The Validity of Using the Microscopic Hyperbolic Heat Conduction Model Under a Harmonic Fluctuating Boundary Heating Source

The validity of using the microscopic hyperbolic heat conduction model under a harmonic fluctuating boundary heating source is investigated. It is found that using the microscopic hyperbolic heat conduction model is essential when . The phase shift between the electron-gas and solid-lattice temperatures is found to be . This phase shift reaches a fixed value of 1.5708 rad at very large values of . It is found that the use of the microscopic hyperbolic heat conduction model is essential when ¯>1×10⁹ rads^–1 for most metallic layers independent of their thickness.     

Transient Behavior of a Thermoelectric Device Under the Hyperbolic Heat Conduction Model

The major objective of this work is to describe the dynamic thermal behavior of thermoelectric generators and refrigerators under the effect of the hyperbolic heat conduction model. In practical situations, these devices work under transient operating conditions due to the time change in the imposed current, voltage, and hot or cold temperatures. Results for transient temperature distributions were obtained for different parameters. The coefficient of performance was obtained as a function of time for increasing current flow.     

The Validity of Using the Microscopic Parabolic Heat Conduction Model in Place of the Macroscopic Parabolic Model Under the Effect of a Moving Heating Source

The validity of the use of the microscopic parabolic heat conduction model under the effect of a moving heating source is investigated. Two configurations are considered which are the finite and the semi-infinite domains. For each configuration, two types of thermal boundary conditions are considered which are the isothermal and the insulated types. Four dimensionless parameters are found to control the thermal behavior of the considered problem which are the dimensionless heating source speed U, heat capacity ratio C _R, dimensionless amplitude of the heating source S ₀, and dimensionless plate thickness ₀ for the finite domain configuration. It is found that the use of the microscopic parabolic heat conduction model instead of the parabolic macroscopic model is essential when the dimensionless speed of the source U > 0.1 The heat capacity ratio C _R is found to have insignificant effect on the domain thermal behavior. However, the deviation between the microscopic and macroscopic models increases as ₀ decreases. The deviation between the two models is significant within the very early stages of time.     

Overshooting Phenomenon in the Hyperbolic Microscopic Heat Conduction Model

The overshooting phenomenon under the effect of the microscopic hyperbolic heat conduction model is investigated. A map tracing the region within which the overshooting phenomenon occurs is presented. The two most important parameters which control the overshooting phenomenon are found to be the first and second time-derivatives of the temperature at t=0. However, in order for the overshooting to appear, a higher initial value of the second time-derivative of the temperature change is required than the initial value of the first time-derivative of the temperature. Overshooting is more likely to appear in the parabolic, rather than in the hyperbolic, microscopic heat conduction model.     

各向异性介质二维稳态热传导问题的分析解

本文利用双变量函数及其偏导数在闭区间上完整的双重付里叶级数表达式求得矩形区域中各向异性介质稳态热传导问题的分析解。文中例子给出各向异性介质内的温度场和热流密度的数字结果,并讨论介质的各向异性效应。     

Analytical Prediction of Quench Energies of Cooled Superconductors Based on the Hyperbolic Heat Conduction Model

The critical energy characteristics of cooled composite superconductors is analytically predicted based on the one-dimensional hyperbolic heat conduction model. The temperature dependence of the Ohmic heat generation, the finite speed of heat transfer, and the finite duration and finite length of the thermal disturbances are taken into account in the present model. The critical energies are calculated using a model based on the analytical solution of the hyperbolic heat conduction equation by the Laplace transformation method. The computational model results show that the critical energy depends on the relaxation time and disturbance duration. It is found that the hyperbolic conduction model predicts a lower-critical energy as compared to the predictions of the parabolic heat conduction model.     

Transient Free Convection Fluid Flow in a Vertical Microchannel as Described by the Hyperbolic Heat Conduction Model

The transient hydrodynamics and thermal behaviors of fluid flow in an open-ended vertical parallel-plate microchannel are investigated analytically under the effect of the hyperbolic heat conduction model. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in this study. The effects of Knudsen number Kn and thermal relaxation time τ on the microchannel hydrodynamics and thermal behaviors are investigated using the hyperbolic and the parabolic heat conduction models. It is found that as Kn increases, the slip in the hydrodynamic and thermal boundary condition increases. Also, this slip increases as τ decreases.     

An Inverse Analysis to Estimate Relaxation Parameters and Thermal Diffusivity with a Universal Heat Conduction Equation1

This paper presents an inverse analysis for simultaneous estimation of relaxation parameters and thermal diffusivity with a universal heat conduction model by using temperature responses measured at the surface of a finite medium subjected to pulse heat fluxes. In the direct analysis, the temperature responses in a finite medium subjected to a pulse heat flux are derived by solving the universal heat conduction equation. The inverse analysis is performed by a nonlinear least-squares method for determining the two relaxation parameters and thermal diffusivity. Here, the nonlinear system of algebraic equations resulting from the sensitivity matrix is solved by the Levenberg–Marquardt iterative algorithm. The inverse analysis is utilized to estimate the relaxation parameters and the thermal diffusivity from the simulated experimental non-Fourier temperature response obtained by direct calculation.     

Specific Heat Measurements by a Thermal Relaxation Method: Influence of Convection and Conduction

This paper involves the well-known thermal relaxation method for measurement of the specific heat (c) of thin solid samples. Although this method was applied successfully in recent years for the characterization of different materials, in this work some aspects that must be taken into account in order to avoid problems based on satisfying the required experimental conditions of heat flux imposed by the physical model used for data analysis and processing will be discussed. For this purpose, for a given experimental geometry, the heat diffusion equation will be solved in order to obtain the sample’s requirements for reliable measurements of c, regarding its thickness and thermal conductivity. An experimental device is described that can be used for the study of the influence of heat dissipation by convection on the method. A computer simulation was performed for comparing the simple model with one that takes to in account the gradient of temperature inside the sample. The results of measurements are presented.Paper presented at the Seventeenth European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.Part of this work was performed when the author was at Universidad de La Habana, Facultad de Física, San Lázaro y L, Vedado 10400, La Habana, Cuba.     

脂肪族聚酯的热稳定性研究

用热失重(TG)和F lynn方法(等转化率方法)研究了聚丁二酸乙二醇酯(PESu),聚丁二酸丁二醇酯(PBSu),聚丁二酸已二醇酯(PHSu),聚癸二酸己二醇酯(PHSe)的热稳定性。结果表明,这些聚酯的热分解温度和分解活化能均随酯基浓度的降低而升高。该研究可对脂肪族聚酯的分子设计、合成和加工工艺提供参考。     

Analysis of Two-Dimensional Effect in the Measurement of Thermal Diffusivity of Thin Films with an AC Calorimetric Method1

An ac calorimetric method for measuring the thermal diffusivity of thin-film materials has been widely applied. In the application of this method, the systematic errors caused by the heat loss effect, the edge reflection effect, etc., have been analyzed and corresponding correction methods have been developed. But when measuring films with low thermal diffusivity or with thickness comparable to the thermal diffusion length, a two-dimensional effect which will also result in a systematic error of the measurement is present. In this paper, the mechanism of two-dimensional heat conduction within a thin sample which is supplied a periodic heat flux by a chopped light beam is analyzed. A numerical analysis method is developed to study the effect of the two-dimensional heat conduction on the measured thermal diffusivity values. The relations between the measured thermal diffusivity and independent parameters such as frequency, thickness of sample, width of light spot, etc., are demonstrated to indicate the two-dimensional effect. The experimental precondition for minimizing the systematic error caused by the two-dimensional effect is determined. In addition, the analysis method presented in this paper should be useful for more difficult problems such as error estimation of the thermal diffusivity measurement of coatings or composite films.