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.     

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.     

Numerical analysis of two-dimensional lagging thermal behavior under short-pulse-laser heating on surface

In this work, the dual-phase-lag (DPL) model of heat conduction is introduced in treating the transient heat conduction problems in finite rigid mediums under short-pulse-laser heating. Two-dimensional numerical solutions in a rectangular and an axially symmetric system are given by finite difference method. Calculations are performed to exhibit various two-dimensional lagging thermal behavior of conduction heat transfer, such as wavy, wavelike, and diffusive behavior.     

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.     

The dimensionless analysis of the stability of composite superconductors with respect to thermal disturbances

The stability of superconductors with respect to thermal disturbances is determined by many factors: external conditions, properties of the composite, and nature of the heat exchange with the environment. To simulate the thermal processes mathematically, it was necessary to consider non-linear heat conduction equations which take into account the temperature dependences of the specified thermophysical parameters. The results obtained in this way depend on many parameters, which hinder establishing any general regularities. The solution of the corresponding equations in a dimensionless form reduces the number of variables and hence a generalized analysis of the phenomena can be performed     

On dual-phase-lag thermoelasticity theory with memory-dependent derivative

A new mathematical model of generalized thermoelasticity with memory-dependent derivatives for the dual-phase-lag heat conduction law is constructed. The governing equations of the new model are applied to a half-space subjected to ramp-type heating. Laplace transforms technique is used. The solution is obtained for different types of functions representing the thermal shock and for different values of the parameter of the time fraction derivative of the model. The effects of time-delay and arbitrary kernel function on elastic material are studied and represented graphically. The predictions of the theory are discussed and compared with dynamic classical coupled theory.     

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.     

Thermoelastic analysis of a partially insulated crack in a strip under thermal impact loading using the hyperbolic heat conduction theory

In this paper, the transient temperature and thermal stresses around a partially insulated crack in a thermoelastic strip under a temperature impact are obtained using the hyperbolic heat conduction theory. Fourier and Laplace transforms are applied and the thermal and mechanical problems are reduced to solving singular integral equations. Numerical results show that the hyperbolic heat conduction parameters, the thermal conductivity of crack faces, and the geometric size of the strip have significant influence on the dynamic temperature and stress field. The results based on hyperbolic heat conduction show much higher temperature and much more dynamic thermal stress concentrations in the very early stage of impact loading comparing to the Fourier heat conduction model. It is suggested that to design materials and structures against fracture under transient thermal loading, the hyperbolic model is more appropriate than the Fourier heat conduction model.     

Heat Transport Analysis of Femtosecond Laser Ablation with Full Lagrangian Modified Molecular Dynamics

The purpose of this study is to analyze the heat transport mechanism of femtosecond laser ablation. Under the condition that laser pulse duration is on the order of femtoseconds, a thermal nonequilibrium state between an electron and atom exists and must be taken into account. In order to describe physical phenomena such as heat transport under a nonequilibrium state, a new method, modified molecular dynamics in which molecular dynamics (MD) couples with the two-temperature model (TTM) in a particle-based method, is proposed. In this method, MD simulates the motion of an atom and TTM simulates both electron heat conduction and energy exchange through electron-atom interactions. This approach yields the use of laser intensity as a parameter. For nonequilibrium heat transport, electron heat conduction transports most of the absorbed laser energy and becomes the dominant heat transport mechanism. At thermal equilibrium, above the ablation threshold fluence, electron heat conduction and thermal waves are dominant, while below the ablation threshold fluence, only electron heat conduction is dominant.     

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.     

Numerical analysis of propagation of thermal disturbances in brass-stabilized REBCO tapes

An extensive characterization of commercially available High-Temperature Superconducting (HTS) REBCO tapes has been recently performed at KIT. The main thermo-physical properties of the tapes have been measured, and heat slug and quench propagation have been investigated in vacuum at LN₂ temperature, using a resistive heater as driver and recording the voltage and temperature evolution after the pulse at several locations along the tapes.In this paper, we present a study of thermal disturbance propagation in a HTS tape with brass stabilizer. The experimental data are analyzed first, to identify the phenomena that influence heat propagation in the tape, and namely the heat loss to the sample holder and the non-ideal efficiency of the resistive heater. A numerical tool is then developed, which solves the 1D transient heat conduction equation in each layer of the tape and accounts for the thermal coupling between layers. The heat loss to the sample holder and the non-ideal efficiency of the resistive heater are taken into account in the model.A first validation of the thermal part of the model against an extended database of heat slug propagation tests is then performed: the comparison between simulation and experiment confirms the very good capability of the model to reproduce the measured temperature evolution. Finally, the results of the simulations of quench propagation are compared with experimental data, showing the capability of the model to reproduce the experiment, within the uncertainty in the input parameters.     

导热相复合陶瓷微波烧结传热模式数值分析

根据微波加热的特点,采用二维稳态导热数值分析法,建立了导热相复合陶瓷微波烧结的传热模式. 研究了导热相的浓度、导热相弥散分布状况、基质类型以及保温方式对复合陶瓷内部二维稳态温度场分布的影响,并设计了导热相SiC晶须复合TZP陶瓷的微波烧结致密化实验,对建立的复合陶瓷的微波烧结传热模式进行了验证. 结果表明：导热相复合陶瓷设计时宜选取具有高导热系数的基体,保持导热相有较高的浓度,使导热相均匀分布于基体中,且微波烧结传热宜采用合适的保温设施.     

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.     

An iterative regularization method in estimating the unknown energy source by laser pulses with a dual-phase-lag model

In the present study an inverse problem for hyperbolic heat conduction with a dual-phase-lag model is solved by the conjugate gradient method (CGM) in estimating the unknown heat generation, due to the ultra-short duration laser heating, based on the interior temperature measurements. Results obtained in this inverse problem will be justified based on the numerical experiments where two different heat source distributions are to be estimated. Results show that the inverse solutions can always be obtained when choosing the initial guesses of the heat sources equal to zero. Finally, it is concluded that accurate heat sources can be estimated in this study. Copyright © 2008 John Wiley & Sons, Ltd.     

热传导波动效应对各向异性高Tc超导薄膜内禀热稳定性的影响

所提出的高Ｔｃ超导薄膜内禀热稳定性准则不同于经典的超导磁体低温热稳定性准则,也不同于其它的忽略导热波动效应的超导薄膜内禀热稳定性准则。高Ｔｃ超导薄膜内产生的热扰动在向外传输到冷却介质的过程中,即使受热传导波动效应的影响,超导薄膜也能传输正常工作电流而不至于发生失超现象,这种新的热稳定性准则更符合高Ｔｃ超导薄膜的实际工作情况。     

非保守力和热载荷作用下FGM梁的稳定性

研究了在热载荷和切向均布随从力作用下FGM梁的稳定性问题。假设材料常数(即弹性模量和密度)随温度及沿截面高度连续变化,且材料常数按各材料的体积分数以幂率变化,温度分布满足一维热传导方程,计算了不同梯度指标和不同温度下FGM梁的弹性模量随截面高度变化情况。基于Euler-Bernoulli梁理论,建立梁的控制微分方程,用小波微分求积法(WDQ法)求解,分析了梯度指标、温度、随从力等参数对简支FGM梁振动特性与稳定性的影响。     

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.     

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.     

A finite element method for non-Fourier heat conduction in strong thermal shock environments

Non-Fourier effect is important in heat conduction in strong thermal environments. Currently, generally-purposed commercial finite element code for non-Fourier heat conduction is not available. In this paper, we develop a finite element code based on a hyperbolic heat conduction equation, which includes the non-Fourier effect in heat conduction. The finite element space discretization is used to obtain a system of differential equations for the time. The transient responses are obtained by solving the system of differential equations, based on the finite difference, mode superposition, or exact time integral. The code is validated by comparing the numerical results with exact solutions for some special cases. The stability analysis is conducted and it shows that the finite difference scheme is an ideal method for the transient solution of the temperature field. It is found that with mesh refining (decreasing mesh size) and/or high-order elements, the oscillation in the vicinity of sharp change vanishes, and can be essentially suppressed by the finite difference scheme. A relationship between the time step and the space length of the element was identified to ensure that numerical oscillation vanishes.