Finite difference modeling of heat distribution in multilayer soils with time-spatial hydrothermal properties

In this study, the heat distribution throughout the profile of unsaturated multilayered soil is determined using finite difference method while its thermal diffusivity varies with time and depth. First, the input parameters such as water content, dry density and sand content of the soil profile are provided. These data are coupled with the theoretical approaches to estimate thermal properties of soil such as thermal conductivity and thermal diffusivity of multilayered soil. Second, finite difference method is used to model heat distributions in soil profile taking into account the initial and boundary conditions. A continuity of heat flux between each layer is performed as a condition in the numerical model. A comparison of estimated temperature within time throughout the profile with the thermal probe measurements shows a satisfactory capacity of the numerical model. Finally, different cases of nonhomogeneous and homogeneous soil show that thermal response of homogeneous and nonhomogeneous soils are almost similar at average value of thermal diffusivity where hydrothermal characteristics of each soil layer (such as water content, dry density, and soil texture) are required to calculate this average value.     

激光脉冲法测量半透明材料的热扩散率

激光脉冲法测量半透明材料导热性能时,包含了热辐射传热的贡献。提出了一个新的物理模型,将传导和热辐射的耦合传热分开,通过对相关参数的估计,使模型模拟曲线与实际探测曲线一致,此时计算得出的热扩散率为半透明材料的传导热扩散率,所得结果与采用反射层去除热辐射的方法所得结果吻合。方法可大大简化激光脉冲法测量半透明材料的实验镀膜工艺,可减小测量薄膜材料时镀膜带来的偏差。     

Estimation de la résistance thermique de contact durant la solidification du verre

Estimation of the thermal contact resistance during glass solidification. This paper presents an experimental study of thermal contact conditions during glass moulding. Our goal was to develop an experimental setup to simulate the real contact conditions during the glass solidification and to build a numerical procedure to estimate the thermal parameters characterizing heat transfer at the contact interface (mould–glass). The semi-transparent character of glass was taken into account when building the theoretical heat transfer model. Thus a heat radiation–conduction model was built to simulate heat transfer at the interface during the glass cooling. The study shows that when the coupled conduction–radiation effect is taken into account, the parameter estimation is better. Thermal contact resistance mold–glass was estimated and the quality of heat transfer at the interface was analyzed.     

Triple vacuum glazing: Heat transfer and basic mechanical design constraints

Given the major role played by windows with regard to energy losses from buildings in cold climates, low thermal transmittance is an indispensable property of glazing in low-energy buildings. Evacuation offers the only means of achieving negligible gaseous conduction in glazing cavities. Application of low-emittance coatings to glass sheet surfaces inside the cavity reduces the radiative heat transfer. The feasibility of double vacuum glazing using arrays of support pillars between the glass sheets has been shown by other authors. This type of glazing is commercially manufactured today. Based on these achievements, our study set out to investigate heat transfer in triple vacuum glazing by means of (i) an analytical thermal network model and (ii) a numerical finite difference model. The study focused on the impact of the following parameters on thermal transmittance: emittances of glass sheet surfaces inside the cavity, support pillar radius, support pillar separation and thermal conductivity of support pillar material. The design procedure for triple vacuum glazing taking into account not only thermal but also mechanical stresses due to atmospheric pressure, i.e., to enable identification of favourable parameter sets, is presented. Our findings suggest that use of the triple vacuum glazing concept can significantly reduce the thermal transmittances achieved by the best insulation glazing units currently on the market. E.g., a centre-of-glazing thermal transmittance of less than 0.2 W m⁻² K⁻¹ is achievable using stainless steel support pillars, 6 mm/4 mm/6 mm sheets of untempered soda-lime glass and four low-emittance coatings (ε = 0.03).     

宽温域中碳纤维导热特性研究

碳纤维作为一种被广泛应用的微纳米材料,对其导热性能的测量研究一直被作为对碳纤维性能研究的重要内容。在利用氦气的气体液化基础上搭建的超低温实验环境中,基于瞬态电热法对处于290到10 K温度内的碳纤维样品的导热性能进行研究。实验发现,当实验温度低于某一特定温度后,材料的热扩散率表现出与声子散射分析相反的实验结果。通过引入热扩散系数倒数这一理论研究声子热阻在低温下的变化,分析得出,当实验环境温度低于某一特定温度后,低温会造成碳纤维材料内的石墨微晶体结构发生变化,从而造成材料热扩散率下降。     

Development of an algorithm to extract thermal diffusivity for the radial converging wave technique

The usual equation for the converging wave method [P. Cielo, L.A. Utracki, M. Lamontagne, Thermal diffusivity measurements by the converging thermal-wave technique, Canad. J. Phys. 64 (1986) 1172-1177] for thermal diffusivity measurements assumes idealised conditions that are difficult to achieve in a real experimental situation and this hinders the extraction of diffusivity values. A model for thermal transport is described here that takes into account errors due to heat losses and is relatively insensitive to detection position inaccuracy. A simple polynomial equation is derived from the model and it is used to generate initial guesses for the Levenberg-Marquardt algorithm, which uses these initial guesses to avoid a local minimum problem and ultimately produces a value for radial thermal diffusivity.     

MHD nonlinear natural convection from a uniformly moving porous vertical plate with constant heat and mass flux in the presence of thermal radiation,diffusion-thermo,heat sink,and chemical reaction

An attempt has been made to investigate the problem of nonlinear free convection heat and mass transfer flow past an infinite vertical porous plate embedded in a porous medium by taking into account thermal radiation and heat sink with constant heat and mass flux. Transversely oriented and of uniform strength $B_0$, a magnetic field has been introduced to the fluid area. The nonlinear density variation with temperature as well as concentration are the basis for the current physical situation, which is explained by this mathematical model. Exact solutions are derived for momentum equation, energy equation, and species continuity equation under the relevant boundary conditions. The dimensionless governing equations are analytically solved. The influence of various physical parameters, such as Dufour number, Schmidt number, thermal Grashof number, magnetic parameter, mass Grashof number, heat sink, thermal radiation, Prandtl number, chemical reaction parameter on the flow, and transport characteristic, has been presented graphically and in tabular form. The novelty of the present investigation is that here both constant heat and mass flux at the plate are taken into account in addition to thermal radiation and heat sink. The findings of the mathematical study demonstrate that velocity, temperature, and skin friction intensify with a rise in the Dufour number this is due to the fact that the convection current becomes stronger as the Dufour number rises. Fluid's concentration declines as the Schmidt number grows, or the concentration rises as the mass diffusivity rises. Fluid temperature is enhanced with high thermal diffusivity. Frictional resistance on the plate hikes due to thermal buoyancy force.     

High‐temperature stability in yttria‐stabilized zirconia

Yttria‐stabilized zirconia has been studied as a candidate standard reference material for the determination of thermal properties. This study evaluated the high‐temperature stability, which is important for yttria‐stabilized zirconia to be used for a standard reference material, using a common material of fine ceramics, Referceram ZR1 (zirconia). The high‐temperature stability was evaluated by measuring the change in the thermal diffusivity before and after heat treatment at temperatures between 200 ^°C and 1500 ^°C. No change in the thermal diffusivity was observed when the samples were treated at temperatures equal to or below 900 ^°C. However, it was revealed that the changes in the thermal diffusivity were caused by the transformation and separation of the crystal phase and the cracks that occur at grain boundaries when the samples were treated at temperatures equal to or above 1000 ^°C. From these results, we confirmed that Referceram ZR1 is sufficiently stable for use as a reference material at temperatures equal to or below 900 ^°C. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(2): 57–67, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20193     

Diffusivity measurement of semi-transparent media: model of the coupled transient heat transfer and experiments on glass, silica glass and zinc selenide

The aim of this theoretical and experimental study is to provide a complete methodology to estimate the intrinsic diffusivity of semi-transparent media from flash method experiments. A semi-analytical model describes the coupled conductive-radiative transient heat transfer in a slab. The relevance of the model used for the inversion is then investigated. Experimental results are presented for several semi-transparent samples: float glass, SiO₂ and ZnSe. Measurements of rear face temperature are obtained by optical way (infrared detection) for a wide temperature range (293-700 K), for several radiation boundary conditions (black or gold coatings). The results are compared with those obtained through an other set-up and an other experimental procedure.     

Simultaneous measurements of thermal conductivity and thermal diffusivity of insulators,fluids and conductors using the transient plane source (TPS) technique

Simultaneous measurements of thermal conductivity and thermal diffusivity of composite red-sand bricks, glycerine and mercury have been made at room temperature by the recently developed transient plane source (TPS) technique. This paper describes, in brief, the theory and the experimental conditions for the simultaneous measurements of thermal conductivity and thermal diffusivity of insulators, fluids and metals. The source of heat is a hot disc made out of bifilar spirals. The disc also serves as a sensor of temperature increase in the sample. The measured values of the thermal conductivity and thermal diffusivity of these samples are in agreement with the values reported earlier using other methods. The advantage of the TPS technique is the simplicity of the equipment, simultaneous information on thermal conductivity and thermal diffusivity, and also the applicability of the technique to insulators, fluids and metals.     

Transient Radiation-Conductive Heat transfer Problems: "The Quadrupole Method

This paper presents a statement of the works performed in L.E.M.T.A by the members of the thermal and mechanical heterogeneous media research group during the last six years concerning the solving of coupled conductive and radiative heat transfers within a multilayer and semi-transparent "wall". Out of the authors, this paper allows to take inspiration from the works of D. Maillet, M. Lazard and V. Manias119'20'21]. The aim of these works is to represent in a macroscopic way, with the minimum number of thermophysical parameters, the heat transfers in a plane system composed of semi-transparent media. The approach we propose is semi-analytic (Kernel substitution technique, Laplace transformation) and allow to obtain in the Laplace domain an analytical solution that can be easily used. This method can be applied in two main scopes of applications: the estimation of thermophysical properties (phononic conductivity, optical thickness, Planck number for instance) of semi-transparent materials (glasses, crysta     

Numerical simulation of a multi-layer latent heat thermal energy storage system

A computational model for the prediction of the thermal behaviour of a compact multi-layer latent heat storage unit is presented. The model is based on the conservation equations of energy for the phase change material (PCM) and the heat transfer fluid (HTF). Electrical heat sources embedded inside the PCM are used for heat storage (melting) while the flow of an HTF is employed for heat recovery (solidification). Parametric studies are performed to assess the effect of various design parameters and operating conditions on the thermal behaviour of the unit. Results indicate that the average output heat load during the recovery period is strongly dependent on the minimum operating temperature, on the thermal diffusivity of the liquid phase, on the thickness of the PCM layer and on the HTF inlet mass flowrate and temperature. It is, on the other hand, nearly independent of the wall thermal diffusivity and thickness and of the maximum operating temperature. Correlations are proposed for the total energy stored and the output heat load as a function of the design parameters and the operating conditions. © 1998 John Wiley & Sons, Ltd.     

同轴地埋管换热器岩土热响应试验研究

岩土热物理性质是影响地源热泵系统设计和运营的关键因素,对位于武汉市洪山区的2口不同深度的同轴地埋管换热孔分别进行48 h的热响应试验,并对同轴地埋管换热器内外管之间环形空间中的平均流体温度进行测试.根据同轴地埋管换热器的几何特性,以简便实用的方式测量同轴地埋管换热器环状空间传热流体的平均温度,结合同轴地埋管换热器钻孔热...     

Transient radiation-conductive heat transfer problems: “The quadrupole method”

This paper presents a statement of the works performed in L.E.M.T.A by the members of the thermal and mechanical heterogeneous media research group during the last six years concerning the solving of coupled conductive and radiative heat transfers within a multilayer and semi-transparent “wall”. Out of the authors, this paper allows to take inspiration from the works of D. Maillet, M. Lazard and V. Manias^{[19, 20, 21]}. The aim of these works is to represent in a macroscopic way, with the minimum number of thermophysical parameters, the heat transfers in a plane system composed of semi-transparent media. The approach we propose is semi-analytic (Kernel substitution technique, Laplace transformation) and allow to obtain in the Laplace domain an analytical solution that can be easily used. This method can be applied in two main scopes of applications: the estimation of thermophysical properties (phononic conductivity, optical thickness, Planck number for instance) of semi-transparent materials (glasses, crystals, glass wool, semi-conductors, synthetic diamonds, vitroceramics and so on) and the modelling of processes with semitransparent walls (for instance bottles forming, flat glass production, drying of paper). The method will be first presented and validated and two examples of applications will be then given. This method can be applied to semitransparent walls that emit, absorb and scatter the radiant energy (participating medium). It appears from the principle of a Kernel substitution technique applied to the radiative flux expression and initially introduced by Lick^[1] that allows to change the character of the governing heat equation from the integro-differential form to a purely differential one. In the case of limiting cases of purely scattering and purely absorbing media, the solution of the radiative transfer equation is exact. In the general case, we make a two-flux approximation. In all cases, we assume a linear transfer and use the Laplace transform. The method can be applied to grey or grey by bands media, with isotropic or anisotropic scattering. The advantage of the method is fast computational times for good precision.     

光学热带法测量固态材料热物性研究

针对接触式瞬态热带法测量导热系数时,加热丝和样品间接触热阻,会影响实验测量结果以及对固体样品形状大小要求较高的现状,根据瞬态热带法原理,本文提出了一种光学瞬态热带法来测量固体材料的导热系数。采用连续激光为加热源,通过透镜将光斑放大并聚焦照射在样品表面,实现样品非接触式测量。构建二维导热模型,采用红外热像仪记录样品表面温升随时间的变化关系,根据导热理论模型求出待测样品的热扩散系数及导热系数。以K9和石英玻璃为样品对本套测量方法进行验证,制备并测量了纯石蜡、0.5%和1%石墨烯-石蜡的固态复合相变材料的导热系数,探讨了影响实验结果的潜在因素。     

Some new developments on coupled radiative-conductive heat transfer in glasses—experiments and modelling

The difficulty in obtaining reliable phonic thermal conductivity of glasses at high temperature leads the authors to propose a methodology based on an experimental and numerical investigation, in order to separate the conductive and radiative part in a combined heat transfer in semi-transparent materials. The thermal conductimeter is composed of a guard plane plate and a Mach-Zehnder interferometer, supplying the total heat flux and the temperature distribution. With such a device no contacts are needed between sample and hot plate or heat sink. These measurements are treated numerically by a nodal analysis modelling of simultaneous conductive-radiative heat transfer. A monodimensional (non-diffusing) non-gray analysis including multireflections was considered. Determinations of the temperature derivative of the refractive index and the infrared spectra of materials at high temperature have been carried out. Values of the phonic conductivity of silica glass up to 900 K and borosilica glass up to 750 K for samples with different thicknesses and frontier's emissivities have been obtained by an identification process. Results are in agreement with literature data.     

Influence of thermal sensitivity of the materials on temperature and thermal stresses of the brake disc with thermal barrier coating

The time-dependent frictional heating of a disc with applied thermal barrier coating (TBC) on its working surface was investigated. To determine the temperature fields in the coating and the disc a one-dimensional friction heat problem during braking was formulated, with taking into account the dependence of thermal properties of materials from temperature. A model was adopted for materials with a simple non-linearity, i.e. materials whose thermal conductivity and specific heat are temperature dependent, and their ratio – thermal diffusivity is constant. The linearization of the corresponding boundary-value heat conduction problem was made by the Kirchhoff transformation and the linearizing multipliers method. A numerical-analytical solution to the obtained problem was found by Laplace transform method. Knowing the temperature distributions, quasi-static thermal stresses in the strip (TBC) with taking into account change in temperature mechanical properties, were determined. The distribution of temperature and thermal stresses in the strip made from ZrO₂ deposited on the UNS G51400 steel disc, was investigated.     

An exact modelling for thermal diffusivities of solid objects exposed to heating

A new simple model for determining the thermal diffusivities of solid geometrical objects (i.e., infinite slab, infinite cylinder, and sphere) being heated in a heating medium is proposed. In the unsteady-state heat transfer modelling, the lag factor and heating coefficient for heating applications were well-defined as being in a cooling process. In addition, new characteristic equations for the case of 0 < Bi < 100 in the transient heat transfer were developed instead of the existing complicated equations, and these were employed. In order to test the present model, the literature heat transfer data were used as an example and the use of the model was described in detail. The results of this study indicate that the heating coefficient has a direct influence on the thermal diffusivity and that the present model permits the determination of the thermal diffusivity values of solid geometrical objects in a simple and accurate manner.     

Measurement of the thermal diffusivity of thin materials using an infrared thermal wave imaging technique

A thermal wave imaging technique was developed for the evaluation of thermal properties. In this paper we report both theoretical and experimental studies on an infrared thermal wave imaging method for thermal diffusivity measurements of thin materials in the direction parallel to the surface. © 1999 Scripta Technica, Heat Trans Asian Res, 28(2): 89–94, 1999     

水合物导热系数和热扩散率实验研究

基于Hot Disk热常数分析系统的单面测试功能,建立了一套新的天然气水合物热物性测试系统,并实验研究了I型水合物（甲烷）、H型水合物（甲烷和甲基环己烷）的导热系数和H型水合物的热扩散率。结果显示甲烷水合物样品导热系数随温度的变化非常小,平均导热系数约为0.53 W/(m•K)。结合文献报道和实验分析发现零孔隙率甲烷水合物的导热系数大约为0.7 W/(m•K),水合物样品在压缩过程中虽然减少了孔隙,但是却引起晶体破碎,导致导热系数与理想值差距较大。水合物的导热系数与水合物的类型及客体分子有关,大体顺序为I型 > II型 > H型 > 半笼型水合物。甲烷−甲基环己烷生成的H型水合物热扩散率为0.205 ~ 0.26 mm2/s,和其他类型的水合物相当;水合物的热扩散率大约为水的两倍,而导热系数和水相近。