A steady conjugate heat transfer problem with conduction and free convection

Summary A steady conjugate heat transfer problem dealing with conduction in a heat-generating slab and free convection in the surrounding fluid is studied analytically. Free convection is analyzed by a Görtler-type series solution to the boundary-layer equations for non-uniform surface-temperature variations, while conduction is treated by the standard technique of Fourier transforms. Interfacial temperature and heat flux variations from both solutions in series forms are then formally matched to yield algebraic relations for the coefficients in the series. These coefficients can then be simply evaluated in a given problem in terms of three physical parameters. A numerical example is shown.     

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.     

Non-fourier heat conduction in a plane slab with prescribed boundary heat flux

The non-stationary heat conduction in an infinitely wide plane slab with a prescribed boundary heat flux is studied. An arbitrary time dependent boundary heat flux is considered and a non-vanishing thermal relaxation time is assumed. The temperature and the heat flux density distributions are determined analytically by employing Cattaneo-Vernotte's constitutive equation for the heat flux density. It is proved that the temperature and the heat flux density distributions can be incompatible with the hypothesis of local thermodynamic equilibrium. A comparison with the solution which would be obtained by means of Fourier's law is performed by considering the limit of a vanishing thermal relaxation time.     

AN ANALYSIS OF TRANSIENT HEAT CONDUCTION FOR FUNCTIONALLY GRADED SPHERES BASED ON STATE SPACE THEORY1)

基于状态空间理论研究功能梯度圆球的球对称瞬态热传导问题。根据热传导方程和热流密度的定义,取温度场和热流密度为系统的状态向量,通过将圆球分层和在时域内应用差分格式对控制方程进行离散,建立了系统的状态方程,给出了功能梯度圆球瞬态热传导问题的半解析解。算例分析表明：本文解不但结果正确、计算效率高,而且适用于材料参数沿径向任意梯度变化的圆球瞬态热传导分析。     

Transient heat flow in a composite slab-constant flux, zero flux boundary conditions

Summary The time-dependent, one-dimensional equation of heat conduction is solved for a slab of two layers in perfect thermal contact. At one boundary there is a constant heat flux into the slab, and at the other boundary there is a zero flux. The solution for the temperature distribution is obtained with the aid of the Laplace transformation.This work was supported by the U.S. Naval Weapons Evaluation Facility, Albuquerque, N. M., U.S.A.     

Conduction–radiation interaction in 3D irregular enclosures using the finite volume method

Interaction of conduction and radiation in 3D enclosures is carried out with a gray participating media. Application of block structured grid is shown with the finite volume method (FVM). Radiation modeling is performed with the FVM and is coupled with an ‘in-house’ code to solve the set of transport equations. The detailed numerical results are presented for a cubical and a cylindrical enclosure as these results are not available in the literature. The numerical simulation for the cylindrical enclosure is performed using a block-structured ‘O’ grid. Two additional geometries are considered in order to show the applicability of the present work. Results of temperature, radiative heat flux and total heat flux distributions are presented for different optical thicknesses, scattering albedoes, emissivities and conduction–radiation parameters. The 3D results are validated with the available 2D results or results with pure radiation problems as limiting cases.     

Blast waves in inhomogeneous atmospheres with counterpressure and heat transfer effects

The study on blast waves in cold exponential atmospheres by Bach, Kuhl, and Oppenheim is extended to provide a uniformly valid numerical solution of a point explosion problem in isothermal exponential atmospheres with finite temperature at the centre. This is achieved initially by solving the equations of motion with the help of a perturbation technique which takes into account thermal radiation and heat conduction. Whereas the extended perturbation solution for the strong shock regime (i.e. short times after initiation) serves as a starting solution for the numerical integration, the solution using the method of characteristics is valid for the whole flow field since counterpressure effects and energy losses at the front are not neglected.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

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.     

高超声速高焓条件下的内嵌式温敏漆测量方法

热流密度点测量结果并不能完全反映详细的热流分布特征, 尤其是针对热流梯度较大、热流分布复杂的区域, 需要热流密度场测量技术以获取全场精细的热流分布特征. 应用温敏漆测量热流密度场的方法得到了广泛应用, 但实验条件来流总温较低, 与真实飞行环境存在明显差异, 真实飞行条件下的辐射效应严重限制了温敏漆技术的应用. 针对高超声速高焓条件下缺乏热流密度场测量方法的难题, 提出了内嵌式温敏漆测量方法, 基本思想是利用温敏漆测量内壁面温度的变化历程结合热传导反问题的求解确定热流密度. 本文详细介绍了内嵌式温敏漆测量方法的测量原理、测量系统构成、数据处理方法、设计原则及该测量方法的优势. 针对高超声速风洞实验中常见的阶跃、线性和局部突变等热流密度分布进行了数值验证, 验证了内嵌式温敏漆测量方法的可行性, 并分析了风洞实验温度测量精度及噪声对测量结果的影响. 内嵌式温敏漆测量方法可用于测量高超声速真实飞行环境下细致的气动热特征, 扩展了温敏漆测量方法的应用范围, 解决了高超声速高焓条件下缺乏热流密度场测量方法的难题.      

A radiation and convection fluxmeter for high temperature applications

Heat flux is an essential parameter for the diagnostic of thermal systems. In high temperature industrial environment, there are difficulties in measuring incident radiation heat flux as well as in differentiating between the convective and radiative components of heat flux on the heat transfer surface. A new method for heat flux measurement is being developed using a porous sensing element. The gas stream flowing through the porous element is used to measure the heat received by the sensor surface exposed to the hot gas environment. A numerical model of sensor with appropriate boundary condition has been developed in order to perform analysis of possible options regarding its design. The analysis includes: geometry of element, physical parameters of gas and solid and gas flow rate through the porous element. For the optimal selection of parameters, an experimental set-up was designed, including the sensor element with respective cooling and monitoring systems and a high temperature radiation source. The experimental set-up was used to obtain calibration curves for a number of sensors. The linear dependency of the heat flux and respective temperature difference of the gas were verified. The accuracy analysis of the sensor reading has proved high linearity of the calibration curve and accuracy of ±5%.     

Analysis of the transpiration cooling of a thin porous plate in a hot laminar convective flow

This paper deals with the asymptotic and numerical analysis for the steady-state transpiration cooling of a thin porous flat plate in a laminar hot convective flow, taking into account the streamwise heat conduction through the plate. For high conductivity plates, a regular perturbation analysis has been carried out, yielding a three-term asymptotic solution for the distribution of plate temperature. In the limit of a very poorly conducting plate, a singular perturbation technique, based on matched asymptotic expansions, is employed to solve the governing equations. We also solved the equations numerically using a quasilinearization technique. The numerical results are in good agreement with the asymptotic solution close to the asymptotic limits studied.     

Transient heat conduction in a solid slab using multiple-scale analysis

In this paper we study the unsteady heat conduction due to a sudden temperature step in the external surfaces of a solid slab. In order to estimate the temperature profile in the solid, we applied the multiple-scale perturbation technique by identifying the “early” and “late” transient regimes for small values of the Biot number, Bi. In this sense, we have re-visited the classical lumped method, incorporating this particular case as an asymptotic limit, which is fully described by the “late” regime for small values of Bi. Once the temperature distribution is analytically predicted, this solution is compared against the exact solution and with other analytical results obtained by using regular perturbation techniques, for different values of the Biot number Bi. Observing a good agreement between the corresponding comparisons, we obtain a very simple and useful formula to predict the nondimensional temperature of the solid slab.     

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 in an exponentially graded slab

The present article investigates one-dimensional non-Fourier heat conduction in a functionally graded material by using the differential transformation method. The studied geometry is a finite functionally graded slab, which is initially at a uniform temperature and suddenly experiences a temperature rise at one side, while the other side is kept insulated. A general non-Fourier heat transfer equation related to the functionally graded slab is derived. The problem is solved in the Laplace domain analytically, and the final results in the time domain are obtained by using numerical inversion of the Laplace transform. The obtained results are compared with the exact solution to verify the accuracy of the proposed method, which shows excellent agreement.     

Numerically gas radiation heat transfer modeling in chemically nonequilibrium reactive flow

A numerical method for calculation of strong radiation for 2D reactive air is developed. Governing equations are taken to be 2D, compressible Reynolds-average Navier–Stokes and species transport equations. Also, radiation heat flux is evaluated using a model of discrete ordinate method. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method.     

Rewetting of an infinite tube with a uniform heating

 The two-dimensional quasi-steady conduction equation governing conduction controlled rewetting of an infinite tube, with outer surface flooded and the inside surface subjected to a constant heat flux, has been solved by Wiener–Hopf technique. The solution yields the quench front temperature as a function of various model parameters such as Peclet number, Biot number and dimensionless heat flux. Also, the dryout heat flux is obtained by setting the Peclet number equal to zero, which gives the maximum sustainable heat flux to prevent the dryout of the coolant. Received on 6 September 2000 / Published online: 29 November 2001     

基于遗传算法的混凝土三维非稳态温度场反分析

大体积混凝土结构施工期间的合理温度控制问题非常重要，而精确进行温度计算所需的一些材料参数往往不易直接测得，需要根据一些易测得的量进行反求。本文基于三维瞬态温度场有限元求解理论与反问题理论，建立了混凝土三维瞬态温度场反问题求解数值模型。运用遗传算法寻求非线性反演问题全局最优解，只需要若干点温度实测值便可实现混凝土多个热学参数如绝热温升、导温、导热系数及热交换系鼓等的同时反演，算例对本文反演方法的反演精度及数值稳定性给出了满意的证明。     

大型空间结构的热-结构动力学分析

空间结构在辐射换热条件下的热诱发振动是导致空间结构失效的一种典型模式。弄清热诱发振动的机理是理解热诱发振动失效的基础。本文针对常见的空间薄壁杆件结构，提出了一种能够对复杂结构及加热条件进行比较准确的温度场和热诱发振动分析的有限元方法。首先利用一种Founer-有限元方法，同时考虑杆截面内平均温度和温差，求解了包含辐射非线性的瞬态热传导问题，并推荐了一种有效降低求解规模的减缩近似方法-Lanczos方法。在此基础上，用有限元法求解了杆件结构的热诱发振动问题，并就杆截面内平均温度和温差对结构振动的影响以及最大动静态响应的比值分别进行了讨论．合理地解释了一类常见的热诱发振动现象，本文的数值算例说明了这点。