非傅立叶导热的最新研究进展

对迄今为止有关非傅立叶导热的研究成果进行了全面的综述,其中包括作者在该领域的最新研究进展:空心球体介质双曲线非傅立叶导热模型的分析求解,室温条件下多孔材料内非傅立叶导热的实验结果及数值模拟,非傅立叶导热的“瞬时薄层”模型,非傅立叶导热和非费克质量传递的耦合分析,非傅立叶导热的分子动力学模拟等．文中还对下一步的研究工作进行了展望.      

Axisymmetric non-fourier temperatures in cylindrically bounded domains

Heat conduction solutions are presented for the case where the material obeys a non-Fourier conduction law. In contrast to the Fourier law which predicts an infinite speed of heat propagation, the non-Fourier theory implies that the speed of thermal signals are finite. Axisymmetric problems for regions interior and exterior to a circular cylinder are investigated by using methods of Laplace transformation and asymptotic analysis. Comparisons of the temperature profiles are made with Fourier theory for the case of step function temperature boundary conditions.     

Solution and analysis of hyperbolic heat propagation in hollow spherical objects

The hyperbolic heat conduction process in a hollow sphere with its two boundary surfaces subject to sudden temperature changes is solved analytically by means of integration transformation. An algebraic analytical expression of the temperature profile is obtained. Accordingly, the non-Fourier hyperbolic heat propagation in hollow spherical medium is analyzed and possible hyperbolic anomalies are discussed.     

Unsteady Free Convection along an Infinite Vertical Flat Plate Embedded in a Stably Stratified Fluid-Saturated Porous Medium

The problem of unsteady free convection heat transfer from a one-dimensional (parallel) flow along an infinite vertical flat plate embedded in a thermally stratified fluid-saturated porous medium is considered. Flows are induced by a sudden change in the arbitrary temporal plate temperature. By a formal reduction of the corresponding boundary value problems to well-known Fourier heat conduction problems, analytical solutions of the Darcy and energy equations are obtained. Several special cases are discussed in detail.     

Transient hyperbolic heat conduction in thick-walled FGM cylinders and spheres with exponentially-varying properties

This paper focuses on non-Fourier hyperbolic heat conduction analysis for heterogeneous hollow cylinders and spheres made of functionally graded material (FGM). All the material properties vary exponentially across the thickness, except for the thermal relaxation parameter which is taken to be constant. The cylinder and sphere are considered to be cylindrically and spherically symmetric, respectively, leading to one-dimensional heat conduction problems. The problems are solved analytically in the Laplace domain, and the results obtained are transformed to the real-time space using the modified Durbin’s numerical inversion method. The transient responses of temperature and heat flux are investigated for different inhomogeneity parameters and relative temperature change values. The comparisons of temperature distribution and heat flux between various time and material properties are presented in the form of graphs.     

Non-Fourier heat conduction by axisymmetric thermal waves in an infinite solid medium

The non-stationary heat conduction in an infinite solid medium internally bounded by an infinitely long cylindrical surface is considered. A uniform and time- dependent temperature is prescribed on the boundary surface. An analytical solution of the hyperbolic heat conduction equation is obtained. The solution describes the wave nature of the temperature field in the geometry under consideration. A detailed analysis of the cases in which the temperature imposed on the boundary surface behaves as a square pulse or as an exponentially decaying pulse is provided. The evolution of the temperature field in the case of hyperbolic heat conduction is compared with that obtained by solving Fourier's equation. Received on 28 January 1998     

COLLINEAR LIBRATION POINTS WITH CONTINUOUS LOW THRUST

研究了圆型限制性三体问题的平动点在连续小推力作用下的具体位置和动力学特征的变化. 研究表明,随着小推力方向在空间中的变化,平动点的具体位置也会发生相应的变化,文章详细阐述了这些变化的特征.针对航天任务中应用较多的共线平动点L1和L2,研究了其附近运动的稳定性状态,给出了线性条件稳定解,并在此基础上,构造了条件稳定解的高阶形式,将其结果与数值积分轨道进行了比对,两者符合得很好. 最后,进一步研究了共线平动点附近周期轨道族的演化状态,由于连续小推力引入的非对称性,周期轨道族会发生分岔现象.     

Pulsed laser heating – Fourier and electron kinetic theory approaches

Laser surface pulse heating of engineering metals is in demand in the metal industry and investigation into laser pulse heating becomes fruitful in this regard. Application of Fourier theory to heat conduction due to high power laser irradiation may give closed form solution to the problem. On the other hand, the heat flux through a given plane depends on the electron energy distribution through the material and at the scale of distance required to examine the problem, the material can no longer be considered as being homogeneous continuum, therefore, errors may occur when considering the Fourier theory in laser heating process. The problem requires to be examined in the quantum field. The present study examines the pulse laser heating process when considering both Fourier conduction and electron-kinetic theory approaches. Analytical solution to Fourier conduction equation is obtained for intensity exponential pulses while numerical scheme is introduced to solve the heat transfer equation resulted from kinetic theory approach. It is found that both Fourier and electron kinetic theory approaches result in similar temperature profiles for the pulses having the same energy content. In the case of electron kinetic theory approach the rise time for surface temperature to reach the melting point is shorter than that obtained from the analytical solution. Received on 23 February 1998     

Non-Fourier heat conduction in a finite hollow cylinder with periodic surface heat flux

Analytical solution of the non-Fourier axisymmetric temperature field within a finite hollow cylinder exposed to a periodic boundary heat flux is investigated. The problem studied considering the Cattaneo–Vernotte (CV) constitutive heat flux relation. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used for solving the problem with time-independent boundary conditions, and the Duhamel integral is used for applying the time dependency. The solution is applied for the special cases of harmonic uniform heat flux and an exponentially pulsed heat flux with Gaussian distribution in outer surface for modeling a laser pulse, and their respective non-Fourier thermal behavior is studied.     

非傅里叶热传导研究进展

傅里叶定律能够精确描述大多数的热传导问题,但对于超短脉冲激光加热等热作用的周期时间极短的超急速、超常规热传导等问题,非傅里叶效应将会显得至关重要．对非傅里叶热传导的实质、模型、模型的求解及应用与实验等几个方面的研究进展做了一个较详尽的概括与评述,并指出了今后需要着重研究的方向．      

Heat wave phenomena in solids subjected to time dependent surface heat flux

Hyperbolic heat conduction in a plane slab, infinitely long solid cylinder and solid sphere with a time dependent boundary heat flux is analytically studied. The solution is based on the separation of variables method and Duhamel’s principle. The temperature distribution, the propagation and reflection of the temperature wave and the effect of geometry on the shape of the wave front are studied for the case of a rectangular pulsed boundary heat flux. Comparisons with the solution obtained for Fourier heat conduction are performed by considering the limit of a vanishing thermal relaxation time.     

Influence of laser pulse shape both on temperature profile and hardened layer depth

This paper presents a mathematical modelling and numerical calculations of heat conduction problems where laser generated heat is assumed as a surface heat source. Also the effect of a laser time structure on a hardened layer depth is examined. Temperature profiles for different laser pulse shapes are determined from the solution of a linear one-dimensional heat conduction equation for semi-infinite medium and discussed in terms of the parameters evolution such as dimensionless: temperature, heat flux, hardening depth, laser impulse duration and increasing time of triangular pulse shape.     

结构层热扩散系数对超薄涂层热力性能的影响

将非傅立叶热传导模型(用于超薄热涂层)与傅立叶热传导模型(用于结构层)相结合 求解温度场,运用有限元法求解热涂层热应力和裂纹驱动力,并分析结构层材料热扩散系数 的变化对热涂层的热力学性能(温度场、应力场和断裂性能)的影响. 研究表明,结构层材 料性能变化对温度场的影响主要表现在热冲击后期,对热应力和裂纹尖端驱动力后期的变化 也有一定的影响.     

Wave propagation model of heat conduction and group speed

In view of the finite relaxation model of non-Fourier’s law, the Cattaneo and Vernotte (CV) model and Fourier’s law are presented in this work for comparing wave propagation modes. Independent variable translation is applied to solve the partial differential equation. Results show that the general form of the time spatial distribution of temperature for the three media comprises two solutions: those corresponding to the positive and negative logarithmic heating rates. The former shows that a group of heat waves whose spatial distribution follows the exponential function law propagates at a group speed; the speed of propagation is related to the logarithmic heating rate. The total speed of all the possible heat waves can be combined to form the group speed of the wave propagation. The latter indicates that the spatial distribution of temperature, which follows the exponential function law, decays with time. These features show that propagation accelerates when heated and decelerates when cooled. For the model media that follow Fourier’s law and correspond to the positive heat rate of heat conduction, the propagation mode is also considered the propagation of a group of heat waves because the group speed has no upper bound. For the finite relaxation model with non-Fourier media, the interval of group speed is bounded and the maximum speed can be obtained when the logarithmic heating rate is exactly the reciprocal of relaxation time. And for the CV model with a non-Fourier medium, the interval of group speed is also bounded and the maximum value can be obtained when the logarithmic heating rate is infinite.     

A study on the non-Fourier effects in spherical media due to sudden temperature changes on the surfaces

The non-Fourier effects on the dynamic thermal behavior of spherical media, including solid, hollow and bi-layered composite spheres, due to sudden temperature changes on the surfaces are investigated. The temperature and heat flux histories in the spherical media are predicted by an analytical–numerical technique. The speed of heat propagation is finite, as revealed in the temperature and heat flux calculated by using the hyperbolic heat-conduction equation. Effects of different parameters such as the relaxation time, the imposed temperature ratio on the inner and outer layers of the hollow sphere, the thermal diffusivity ratio, and the relaxation time ratio of the composite sphere are studied and presented.     

Transient heat conduction in non-homogeneous spherical systems

A comprehensive study encompassing a general analytical development and an archival presentation of results is made for transient heat conduction in thermally coupled spherical regions. The system consists of a sphere and its surrounding environment, each region having different thermal properties and different initial temperatures. The general closed form solution, which accommodates an arbitrary inital temperature distribution in the sphere, is specialized to apply to a number of interesting problems. Among these, the situation in which the sphere and the surroundings are initially at different uniform temperatures constitutes a basic problem in the theory of heat conduction. Correspondingly, a comprehensive presentation of transient temperature histories is made for various locations in the sphere and in the surroundings, with relevant thermal property ratios serving as parameters. Characteristics such as the duration of the transient period and the penetration depth of the temperature field into the surroundings are illuminated. Another interesting situation is that in which the thermal conductivity of the sphere is much greater than that of the surroundings, so that the sphere temperature may be regarded as being spatially uniform. In addition to a presentation of temperature histories, the conditions are identified under which the assumed spatial uniformity of the sphere temperature is valid. For the case of a metallic sphere situated in a gaseous environment, it is demonstrated that the transient response can be represented by a single universal curve.     

THERMAL SHOCK OF SEMI-INFINITE BODY WITH MULTI-PULSED INTENSE LASER RADIATION

In order to investigate the thermal shock and the heat conduction property of a target under multi-pulsed laser radiation, analytic expressions of both temperature and thermal stress fields in the target are deduced on the basis of the non-Fourier conduction law and the thermo-elastic theory. Taking a stainless steel target as an example, we can solve the analytic expressions under appropriate boundary conditions by using the finite difference method and MATLAB software, and then reveal the evolution law of both surplus temperaturt, and thermal stress in the target. The results indicate that the temperature curves in the target irradiated by a multi-pulsed laser take on a delayed character in different sections away from the boundary, which is only affected by its relaxation time. The front of the stress wave is very steep in the non-Fourier numerical solutions, which presents an obvious thermal shock, so it is necessary to consider the non-Fourier effect of semi-infinite body under the high energy laser radiation.     

Multiple spatial and temporal scales method for numerical simulation of non-classical heat conduction problems: one dimensional case

A multiple spatial and temporal scales method is studied to simulate numerically the phenomenon of non-Fourier heat conduction in periodic heterogeneous materials. The model developed is based on the higher-order homogenization theory with multiple spatial and temporal scales in one dimensional case. The amplified spatial scale and the reduced temporal scale are introduced respectively to account for the fluctuations of non-Fourier heat conduction due to material heterogeneity and non-local effect of the homogenized solution. By separating the governing equations into various scales, the different orders of homogenized non-Fourier heat conduction equations are obtained. The reduced time dependence is thus eliminated and the fourth-order governing differential equations are derived. To avoid the necessity of C¹ continuous finite element implementation, a C⁰ continuous mixed finite element approximation scheme is put forward. Numerical results are shown to demonstrate the efficiency and validity of the proposed method.     

基于时域间断有限元方法的生物组织非傅立叶热行为数值分析

在热传导分析中,当热流与温度梯度存在时间延迟时,需采用非傅立叶热传导模型进行分析。生物组织具有较强的热松弛时间系数,承受激光、微波及烧烫等作用时,其呈现出较强的非傅立叶行为。本文对脉冲热源作用下生物组织的非傅立叶热传导进行研究,针对强脉冲引起的温度场在空间域的高梯度变化、波阵面的间断行为以及通用传统时域数值方法会带来虚假数值振荡的特点,提出采用所发展的时域间断Galerkin有限元法（DG-FEM ）进行求解计算。对多种脉冲热源作用下的非傅立叶热传导过程进行数值模拟,通过考量强脉冲作用下温度场分布和热致生物组织损伤行为的影响,表明了本文所发展的DGFEM 能够有效、准确地描述温度场空间分布和热传导过程以及非傅立叶行为下的生物热损伤更为明显,在生物组织热行为分析中应该受到重视。