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.     

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.     

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.     

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.     

Dimensionless correlations of frost properties on a cold plate

This study proposes dimensionless correlations for predicting the properties of frost formed on a cold plate. Frosting experiments are carried out to obtain the correlations with various environmental parameters including the air temperature, air velocity, absolute humidity, and cooling plate temperature. The thickness, density, surface temperature, effective thermal conductivity, average heat and mass transfer coefficients of the frost layer are correlated as functions of the Reynolds number, Fourier number, absolute humidity, and dimensionless temperature by using a dimensional analysis. The correlations proposed in this study agree well with the experimental data within a maximum error of 10%, and can be used to predict the average frost properties in the following ranges: the air temperature of 5–15 °C, air velocity of 1.0–2.5 m s⁻¹, absolute humidity of 0.00322–0.00847 kg kg_a⁻¹, and cooling plate temperature of −35–−15 °C.     

薄板在周期热流作用下的热响应(Ⅰ):温度响应

基于具有热流延迟相的双曲型热传导方程,研究了薄板在周期热流作用下的温度响应。首先采用分离变量法,求解了以热流矢量为基本未知量的热传导方程,得到了板内热流场分布,然后再利用能量守恒方程,获得了板内温度响应的解析表达式。通过计算,分析了板内温度响应随不同热流矢量延迟相以及边界热流频率的变化趋势,并与经典的Fourier热传导方程所得到的结果进行了比较。结果表明,在高频热流加热下,双曲型热传导模型所给出的温度响应与经典的Fourier热传导模型具有显著的差别。     

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.     

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.     

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.     

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.     

Analysis of Transient Heat Conduction in a Hollow Cylinder Using Duhamel Theorem

The objective of this paper is to derive the mathematical model of two-dimensional heat conduction at the inner and outer surfaces of a hollow cylinder which are subjected to a time-dependent periodic boundary condition. The substance is assumed to be homogenous and isotropic with time-independent thermal properties. Duhamel’s theorem is used to solve the problem for the periodic boundary condition which is decomposed by Fourier series. In this paper, the effects of the temperature oscillation frequency on the boundaries, the variation of the hollow cylinder thickness, the length of the cylinder, the thermophysical properties at ambient conditions, and the cylinder involved in some dimensionless numbers are studied. The obtained temperature distribution has two main characteristics: the dimensionless amplitude ( $A$ ) and the dimensionless phase difference ( $\varphi $ ). These results are shown with respect to Biot and Fourier and some other important dimensionless numbers.     

Picosecond thermal pulses in thin gold films

In this paper it has been shown that, with the advent of lasers with a very short pulse duration, the effect of thermal wave propagation becomes important. To consider this effect, hyperbolic heat conduction in thin gold films was studied. It was shown that for heat fluxes of the order 10⁸ W·cm^–2, a thermal wave is generated in thin gold films. The consideration of the hyperbolicity of heat transfer enables one to describe the temperature profile with one value of fluence.     

Dielectric relaxation and electrical conduction at low field of mineral-filled epoxy

Dielectric properties and conduction of the epoxy and its composites were measured over the temperature range — 20 to 70°C and the frequency range 10^–4-10^–1 Hz. Dielectric properties were obtained by performing Fouriertransforms on the charging and discharging curves. The resulting isothermal frequency spectra of dielectric constants and dielectric loss factors were analysed using the Cole-Cole law to obtain the activation energy for each material. The activation energies were also obtained for isothermal d.c. current. Current density-electric field-temperature characteristics are obtained for field levels up to 60 kV cm^–1, with step excitation of the applied field and currents recorded after a delay time of 10 min. Current density and electric field were computed and plotted for constant temperature. The linear (ohmic) curves were obtained for fields up to about 60 kV cm^–1 for temperatures up to about 20 °C. The non-linearity at the higher fields and temperatures did not imply the occurrence of non-ionic conduction. It has been demonstrated that both electric conduction and relaxation behaviour were ionic and could be fit by the Nakajima model for the unfilled epoxy and the Taylor model for the composites.     

Analytical study for the estimation of thermal properties of processed meat based on hyperbolic heat conduction model

This study proposes an analytical method in conjunction with existing experimental temperature to estimate the unknown relaxation time and thermal diffusivity of processed meat based on the hyperbolic heat conduction model. This analytical method is a combination of the Laplace transform and least squares methods. The thermal contact resistance at the interface between adjacent samples at different temperatures is assumed to be negligible. The relaxation time is estimated from the temperature jump at a specific measurement location. The thermal diffusivity is determined from the definition of the dimensionless spatial coordinate and the resulting relaxation time. The results show that the relaxation time and thermal diffusivity obtained are in good agreement with the existing results. The obtained dimensionless temperature history at a specific measurement location is close to the experimental temperature data. This means that the Cattaneo–Vernottee (CV) model can be suitable for this study. The proposed analytical inverse method can be applied to determine a more accurate estimate of such problems. A comparison of the estimate obtained from CV and dual phase lag models is made.     

Electrical properties of thin metal zinc films

Thin metal zinc films 40 to 200 nm thick are deposited by thermal evaporation at room temperature onto glass substrates with a deposition rate of 0.2 to 0.7 nm sec^–1. The electrical resistivity is measured as a function of film thickness, deposition rate and annealing temperature. The experimental results show that electrical resistivity decreases as the film thickness, deposition rate and annealing temperature increase, while the temperature coefficient of resistivity increases with the increase in the film thickness. The calculated values of the activation energy for the conduction electrons increases as the film thickness and deposition rate increase. The well known Fuchs-Sondheimer model is applied for zinc films. The theoretically calculated values for the electrical resistivity and the temperature coefficient of resistivity are in good agreement with the experimental results.     

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.     

On the analysis of the thermal diffusivity measurement method with modulated heat input

The present paper proposes a simplified way to analyze thermal diffusivity experiments in which the phase shift is measured between the modulations of the temperatures on either face of a disk-shaped sample. The direct application of complex numbers mathematics avoids the use of the cumbersome formulae which hitherto have hampered a wider confirmation of the method and which restricted the range of the phase lag to an angle of 180°. The algorithm exposed makes it more practical to refine the analysis, which may lead to a higher accuracy and a wider use of the method. The origins of some possible errors in the calculated results are briefly reviewed.Nomenclature a Thermal diffusivity, m² · s^–1 - c Index denoting a constant part, dimensionless - c _l, c ₀ Inverse extrapolation length, m^–1 - C _p Specific heat, J · kg^–1 · K^–1 - f Modulation frequency, Hz - l Thickness of disk-shaped sample, m - Q _c Equilibrium energy per unit surface deposited on surface x=l, W · m^–2 - Q _m(t) Energy of modulation per unit surface deposited on surface x=l, W · m^–2 - Q(t) Total energy per unit surface deposited on surface x=l, W · m^–2 - q Complex energy modulation amplitude, W · m^–2 - T _l Equilibrium temperature of heated surface, K - t ₀ Equilibrium temperature of nonheated surface, K - T(x, t) Total temperature of any plane at distance x and at time t, K - T _m(x, t) Modulation temperature at any distance x and at time t, K - t Time, s - x Distance perpendicular to the specimen's surface and with the nonheated surface as the reference, m - Thermal linear expansion coefficient, dimensionless - Intermediary parameter, m^–2 - Phase difference between heated and nonheated specimen face, radian - ₀ Phase difference between energy modulation and nonheated face, radian - _l Phase difference between energy modulation and heated face, radian - Total emissivity, dimensionless - _s Spectral emissivity, dimensionless - Temperature, amplitude of modulated part argument, K - Thermal conductivity, W · m^–1 · K^–1 - Density, kg · m^–3 - Stefan-Boltzmann constant, 5.66961×10^–8W · m^–2 · K^–4 - Angular frequency=2f, s^–1     

Thermal conductivity and electrical resistivity of cadmium arsenide (Cd3As2) in the temperature range 4.2–40 K

Results on electrical resistivity and thermal conductivity measured in the temperature range 4.2–40 K are presented for single-crystal and polycrystalline samples of Cd₃As₂. Hall effect has been studied at temperatures of 4.2, 77, and 300 K. The calculated value of the conduction electron concentration was in the range 1.87–1.95 10²⁴m^–3. Electrical resistivity of all investigated samples was independent of temperature up to about 10K and increased slowsly at higher temperatures. The thermal conductivity shows a maximum in the region in which the lattice component of thermal conductivity dominates. The strong anisotropy of the lattice component determines the anisotropy of the total thermal conductivity. The electronic component of thermal conductivity does not exhibit any anisotropy and shows a maximum at a temperature of about 300 K.Paper submitted to the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Thermoelastic stress analysis with standard thermographic equipment by means of statistical noise rejection

A statistical method of signal processing allows for the quantification of small periodic temperature changes, using a standard IR camera and short image sequences without the necessity of any synchronization device. The attenuation of the signal in a high emissivity coating such as a black paint has been quantified by means of a 1D thermal model. This same model is used to analyze the heat conduction effects on thermoelastic stress measurements. By analogy with the resolution power of optical systems, a thermal spatial resolution power is calculated. The spatial resolution appears to be limited by the heat conduction at low frequencies and by the performance of the radiometer at high frequencies.

Nomenclature

Roman letters a Thermal diffusivity (m².s^–1) - c_p Specific heat at constant pressure (J.kg^–1.K^–1) - f Frequency (Hz) - h Surface exchange coefficient (W.m^–2.K^–1) - k Thermal conductivity (W.m^–1.K^–1) - q Heat source (W.m^–3) - t Time (s) - T Instantaneous temperature (K) - T₀ Initial specimen temperature (K) Greek letters Coefficient of thermal expansion (K^–1) - = 2f - Phase difference (rd) - Density (kg.m^–3) - _kl Components of Cauchy's stress tensor (MPa)