Superconductor Thermal Stability Under the Effect of a Two-Dimensional Dual-Phase-Lag Heat Conduction Model

The thermal stability of superconducting thick wire has been numerically investigated under the effect of a two-dimensional 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.     

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.     

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.     

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.     

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.     

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。     

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.     

Quenching of technical superconductors by heat and magnetic field pulses

The transition of a superconductor into the normal conducting state can be caused by external or internal disturbances. The initiation of normal conduction by external disturbances was investigated for technical superconductors by means of thermal and magnetic pulses applied locally to the superconductor. The dependence on transport current and matrix material respectively of the minimum energy and the minimum magnetic field to initiate normal conduction were determined. The conclusion was that the heat conducting along the superconductor has the most effective influence in stabilizing against thermal disturbances. The transition to normal conduction by magnetic field pulses could be explained by eddy current heating in the matrix. A 50 μm single core conductor was insensitive to the highest applied magnetic field pulses up to 0.3 T amplitude and a field rise of 75 Ts^?1 and consequently did behave according to the adiabatic stability criteria.     

An axisymmetric heat conduction model for a multi-material cylindrical system with application to analysis of carbon nanotube based composites

A model for axisymmetric steady-state heat conduction in a multi-material cylindrical system containing a thermal superconductor is presented. An analytical solution in terms of series involving Bessel functions is derived for the temperature distribution in the multi-material system. The model may be applied to analyze the thermal behaviors of carbon nanotube based composites. Some results are obtained for specific cases of the multi-material system.     

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.     

Evaluation of thermal gradients and thermosiphon in dual channel cable-in-conduit conductors

In an effort to optimize superconductor cryogenics of large coils, dual channel cable-in-conduit conductors (CICC) have been designed. The qualitative and economic rationale of the conductor central channel is here justified but brings high complexity to the conductor cooling characteristics. Temperature gradients in the cable must be quantified to guarantee conductor temperature margin during coil operation under heat disturbance and set adequate inlet temperature. A simple one-dimensional thermal model, with neither fluid nor strand or jacket conduction, allows to better understand and quantify the steady state behavior of CICC central and annular channels. This thermohydraulic model with homogeneous central and annular temperatures and no jacket conduction is summarized with explicit thermal coupling equations. Local convection coefficients chosen proportional to friction factors lead to a model of global interchannel heat exchange coefficient serving the bithermal model. A first stationary experimental evaluation of the internal heat transfer coefficient using the interchannel heat exchange space constant at various heat loads and mass flow rates is illustrated on two full size samples tested at cryogenic temperatures. Annular heaters experiments with low distributed power achieve pertinent model correlation. Discrepancy between model and experimental data may be linked to the simplistic homogeneous annular temperature hypothesis, to the estimate of CICC mass flow distribution among channels, and to gravitational effects at high heat loads. Perturbation due to the thermosiphon generated between the two channels is considered since neither the experiments nor the expected applications are free of gravity.     

Effect of axial conduction and metal-helium heat transfer on the local stability of superconducting composite media

The growth or collapse of a local normal zone in a superconducting winding structure saturated with single phase liquid helium (composite superconductor) is studied analytically. The history of a given temperature disturbance is derived from the solution to the transient heat conduction equation in a one-dimensional infinite solid with temperature dependent rate of internal heat generation, communicating laterally with a channel filled with stagnant helium. The combined diffusion by axial heat conduction and lateral heat transfer to the helium channel and its effect on the collapse or growth behaviour of a local disturbance is presented analytically. The paper develops a theoretical criterion for local stability (recovery) expressed in terms of dimensionless groups accounting for heat generation in the normal zone, metal axial conduction cooling, lateral cooling provided by the helium channel and, most importantly, the amount and spatial extent of the sudden release of energy responsible for the local disturbance.     

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.     

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.     

Take-off and recovery current behaviour of copper stabilized NbTi

For stability studies of NbTi/CU superconductor specimens a simple measuring technique was applied to the determination of take-off and recovery currents. The studies were performed on various conductor geometries and with varied copper stabilizing fractions as a function of the magnetic field (B ≤ 7.5 T) under helium bath and forced cooling conditions. The electrical matrix resistance and the maximum heat transfer current density in helium nucleate boiling determine the take-off current, while the recovery current is not only dependent on the matrix resistance, but also on the minimum heat transfer at film boiling and on heat conduction conditions.     

A lumped-parameter thermal model for scroll compressors including the solution for the temperature distribution along the scroll wraps

A lumped-parameter thermal model is presented to predict the temperature in different chambers and components inside scroll compressors with particular attention to gas superheating in the suction process. Thermal resistances between the components are based on global heat transfer conductances, whereas conduction heat transfer through the scroll wraps is solved via a one-dimensional finite volume method. The thermal model was coupled to a thermodynamic model of the compression cycle and then applied to simulate the compressor performance under different conditions of speed and pressure ratio. The model was able to correctly predict the compressor temperature for operating conditions within the range of those adopted for its calibration. The results showed a strong coupling between the compressor thermal profile and the temperatures of the motor and lubricating oil. It has also been found that heat conduction through the scroll wraps reduces slightly the discharge temperature.     

Propagation of normal zone in superconducting tapes due to heating in near-electrode area

Local disturbances of thermal stability in the superconducting materials may initiate the formation of the normal zones. One of the reasons for these disturbances is thermal processes in metal leads connected to the superconductor. Here, superconducting tapes with metal leads are analyzed thermally and from the point of view of current distribution. The results show that the Joule's heat, generated in the vicinity of the metal-superconductor junction may initiate propagation of a normal zone in the superconductor and may cause its thermal runaway.     

Investigation of 2D Transient Heat Transfer under the Effect of Dual-Phase-Lag Model in a Nanoscale Geometry

Analytical and numerical solutions of the 2D transient dual-phase-lag (DPL) heat conduction equation are presented in this article. The geometry is that of a simplified metal oxide semiconductor field effect transistor with a heater placed on it. A temperature jump boundary condition is used on all boundaries in order to consider boundary phonon scattering at the micro- and nanoscale. A combination of a Laplace transformation technique and separation of variables is used to solve governing equations analytically, and a three-level finite difference scheme is employed to generate numerical results. The results are illustrated for three Knudsen numbers of 0.1, 1, and 10 at different instants of time. It is seen that the wave characteristic of the DPL model is strengthened by increasing the Knudsen number. It is found that the combination of the DPL model with the proposed mixed-type temperature boundary condition has the potential to accurately predict a 2D temperature distribution not only within the transistor itself but also in the near-boundary region.     

Stability of compound superconductors under localized heat pulses

Superconducting state stability of commercial Nb-Ti superconductors under heat pulses, generated at different lengths of superconductor, was investigated. The case of a one-dimensional superconductor without heat transfer to liquid helium was examined. It was found that due to dissipation of heat along the superconductor, the energy of irreversible quench may exceed considerably the energy needed for its adiabatic heating to critical temperature T_c (at given magnetic field and current). Such overheating, as it follows from the simplified analytical model and from experiments, depends on current density, magnetic field, the length of the heat generation and on the properties of matrix, but it is in broad limits independent of the form and duration of the pulse. Possible reasons of quantitative disagreement between calculations and experimental results are discussed.