On estimating thermal diffusivity using analytical inverse solution for unsteady one-dimensional heat conduction

A modified procedure for calculating the thermal diffusivity of solids based on temperature measurements at two points and the semi-infinite boundary condition is presented. The method makes use of a solution to the unsteady one-dimensional inverse heat conduction problem for the semi-infinite solid. The procedure gives accurate results based on temperature changes produced by an arbitrary fluctuating heat flux source at the boundary.     

Measurement of thermal conductivity, thermal diffusivity and heat capacity of highly porous building materials using transient plane source technique

This paper presents both experimental and theoretical works concerning evaluation of the thermal conductivity, thermal diffusivity and heat capacity of wood composites. Moreover, the aim of this study is to show that the transient plane source technique originally used for measuring thermal properties of isotropic materials can be spread worthy of heat capacity, thermal conductivity and thermal diffusivity measurements of highly porous materials. Measurements of the thermal conductivity, thermal diffusivity and heat capacity have been performed at room temperature (20 ± 0.5°C) and normal pressure. An attempt has been made to predict the thermal diffusivity of wood composites from the predicted values of thermal conductivity using a Verma et al's model based on Ohms law and the calculated values of heat capacity using the enthalpy concept. The predicted values by the proposed model are compared with the values of the thermal diffusivity measured using the TPS method. A comparison shows a good agreement.     

Simple measurement of thermal diffusivity and thermal conductivity using inverse solution for one-dimensional heat conduction

A new method is proposed for measuring thermal diffusivity and thermal conductivity simultaneously using the inverse solution for one-dimensional unsteady heat conduction. Unlike previous method proposed by authors, the new procedure does not require the temperature measurement for a long time duration after the temperature starts changing at a sensor position; and then a selection of time duration can be chosen such that the measured temperature change becomes large enough to ensure a required accuracy for the estimated values of thermal diffusivity and thermal conductivity. The measurement is usually completed within 3 min until the temperature rise at the thermocouple position reaches a certain temperature level, for example 1% of an error level. This method has the additional advantage of being independent of the surface condition, except for the requirement of two or three sensing positions in the material. The accuracy of the estimated values is also similar to the error level of the sensor at these positions.     

Non-steady-state methods for determining the moisture diffusivity of porous materials

Two non-steady-state methods for determining the moisture diffusivity of porous materials in a dependence on the moisture content are developed in the paper. The methods are verified using an artificial example for which an exact solution is known, and compared to other approaches commonly used in the practice. The results of the comparisons show that both new methods increase remarkably the accuracy of determining the moisture diffusivity. The integral method can be used quite generally, while the modified Matano method is limited to the short time regime when the boundary condition on the remote end of the sample does not play any significant role. The newly developed methods can also be used with only little modifications for determining the thermal conductivity and thermal diffusivity.     

Influence of gas emission on heat transfer in porous ceramics

It is known that thermal diffusivity, a, of several types of porous ceramic and refractory materials decreases with decreasing gas pressure. However, a of several ceramics (e.g., magnesite refractories with porosity about 25%) measured in vacuum by the monotonous heating exceeds the comparable data registered at atmospheric pressure. A similar effect was found for thermal diffusivity of several insulating materials. However, for some porous ceramics this phenomenon is absent or less prominent.It had been known that several heterogeneous physico-chemical processes take place on pore surfaces of ceramic materials. These processes include heterogeneous chemical reactions accompanied by emission of gaseous products. It had been conjectured that these processes affect thermophysical properties of ceramic materials, especially during fast heating or cooling.In this paper we substantiate this conjecture. Namely, we develop a quantitative model for the apparent thermal diffusivity, as measured by the nonstationary monotonous heating method. It takes into account the emission and adsorption of the gas on the opposite pore sides along the temperature gradient, the diffusive gas motion inside the pores and its removal from the pores due to the material gas permeability. The effect of these processes is shown to produce an additional heat flux inside the pore or crack and, hence, to increase the measured thermal diffusivity.In the presence of the passive gas, the rates of gas emission and its transport within the pore are significantly reduced, which leads to diminution of the effect of gas emission-adsorption on the heat transfer across the pore. Consequently, we show that this leads to a situation (observed in experiment) where thermal diffusivity of a material measured at high temperature in vacuum may exceed the comparable property at atmospheric pressure.When the reaction terminates due to the full conversion of the available solid reactant, the additional heat flow due to the gas emission and adsorption terminates, and the measured thermal diffusivity decreases. The rates of gas removal and of chemical conversion depend on the amount of reactant available within the specimen and on the heating rate. We show that as a result of this, the measured thermophysical properties depend on the material thermal history and heating parameters, and, hence, cannot be regarded as true material properties.     

Temperature dependence of thermal conductivities and thermal diffusivities of composites using transient hot-strip method

Simultaneous measurements of the thermal conductivity and thermal diffusivity of four composite building materials, namely black marble stone, normal building stone, red sand brick and cement brick have been made at room temperature using the transient hot-strip method. The power supplied to these samples is quite large compared with that for loose building materials owing to their composite (brick) nature. The temperature dependence of thermal conductivity and thermal diffusivity of these materials has also been investigated in a temperature range from 10 to 60°C. Temperature stability is assured within 0.1°C by using a platinum resistance thermometer in the chamber containing samples and a digital voltmeter to record any variation in resistance. The results of these experiments show that there is a very slight variation in thermal conductivity and thermal diffusivity of these materials in this temperature range.     

Measuring and modeling vapor boundary layer growth during transient diffusion heat and moisture transfer in cellulose insulation

In this paper, an experimental test facility that permits continuous measurements of transient heat and moisture transfer in porous media is applied to study the vapor boundary layer in cellulose insulation. The experiment measures the relative humidity, temperature and moisture accumulation within the cellulose specimen with a fully developed flow of air at a controlled temperature and humidity provided above the surface. These experimental results are used to verify a mathematical model, which is used to develop an expression for moisture diffusivity (α_m) that is analogous to thermal diffusivity, and takes into consideration moisture storage. The moisture diffusivity is used to calculate the vapor density in the boundary layer and the size of vapor boundary layer in cellulose insulation. It is found that the moisture storage effect has a very significant effect on the vapor boundary layer and cannot be ignored. For cellulose insulation, the size of the vapor boundary layer may be over predicted by a factor of ten when moisture storage is neglected.     

Thermoelastic Analysis of an Annulus Using the Green-Naghdi Model

ABSTRACT

The linear theory of thermoelasticity of Green-Naghdi (GN) types II and III for homogeneous and isotropic materials are employed to study the thermal and mechanical waves in an annulus domain. The disturbances are generated by sudden application of temperature to the boundary. The nondimensional form of the governing equations are solved utilizing the Laplace transform method. Locally transversal linearization (LTL) technique, and a numerical inverse Laplace transform method are used to obtain the temperature, displacement, and stress fields in the physical time domain. The thermomechanical wave propagation and reflection from the boundary are investigated and the influence of the damping parameter on temperature, displacement, and stress fields in the Green-Naghdi type III is discussed.     

Measurements of thermal properties of insulation materials by using transient plane source technique

The paper reports on the measuring technique and values of the measured thermal properties of some commonly used insulation materials produced by local manufacturers in Saudi Arabia. Among the thermal properties of insulation materials, the thermal conductivity (k) is regarded to be the most important since it affects directly the resistance to transmission of heat (R-value) that the insulation material must offer. Other thermal properties, like the specific heat capacity (c) and density (ρ), are also important only under transient conditions. A well-suited and accurate method for measuring the thermal conductivity and diffusivity of materials is the transient plane source (TPS) technique, which is also called the hot disk (HD). This new technique is used in the present study to measure the thermal conductivity of some insulation materials at room temperature as well as at different elevated temperature levels expected to be reached in practice when these insulations are used in air-conditioned buildings in hot climates. Besides, thermal conductivity values of the same type of insulation material are measured for samples with different densities; generally, higher density insulations are used in building roofs than in walls. The results show that the thermal conductivity increases with increasing temperature and decreases with increasing density over the temperature and density ranges considered in the present investigation.     

THERMAL BOUNDARY RESISTANCE MEASUREMENTS USING A TRANSIENT THERMOREFLECTANCE TECHNIQUE

A transient thermoreflectance technique, using a 200-fs laser pulse, is demonstrated as a nondestructive method for measuring the thermal boundary resistance between a thin metallic film and dielectric substrate. Experimental results are presented for Au deposited on silicon and silicon dioxide substrates taken at room temperature and compared to a thermal model. The relevant thermal properties of the metal film and the substrate are known, leaving the thermal boundary resistance as the only free parameter in the least-squares fitting routine. It is shown that the sensitivity of this technique is related directly to the thermal diffusivity of the substrate. A comparison between the diffuse mismatch model, the phonon radiation limit, and the experimental results indicates that the phonon dispersion relations of the materials can be utilized to give a qualitative prediction of the thermal boundary resistance.     

Inverse analysis with integral transformed temperature fields: Identification of thermophysical properties in heterogeneous media

The objective of this work is to introduce the use of integral transformed temperature measured data for the solution of inverse heat transfer problems, instead of the common local transient temperature measurements. The proposed approach is capable of significantly compressing the measured data through the integral transformation, without losing the information contained in the measurements and required for the solution of the inverse problem. The data compression is of special interest for modern measurement techniques, such as the infrared thermography, that allows for fine spatial resolutions and large frequencies, possibly resulting on a very large amount of measured data. In order to critically address the use of integral transformed measurements, we examine in this paper the simultaneous estimation of spatially variable thermal conductivity and thermal diffusivity in one-dimensional heat conduction within heterogeneous media. The direct problem solution is analytically obtained via integral transforms and the related eigenvalue problem is solved by the Generalized Integral Transform Technique (GITT). The inverse problem is handled with Bayesian inference by employing a Markov Chain Monte Carlo (MCMC) method. The unknown functions appearing in the formulation are expanded in terms of eigenfunctions as well, so that the unknown parameters become the corresponding series coefficients. Such projection of the functions in an infinite dimensional space onto a parametric space of finite dimension also permits that several quantities appearing in the solution of the direct problem be analytically computed. Simulated measurements are used in the inverse analysis; they are assumed to be additive, uncorrelated, normally distributed, with zero means and known covariances. Both Gaussian and non-informative uniform distributions are used as priors for demonstrating the robustness of the estimation procedure.     

Estimation des propriétés thermiques à l'échelle millimétrique par méthodes périodiques: Résolution du problème direct et du problème inverse

Estimation of thermal properties by periodic methods: direct problem and inverse problem solving. This article presents two processes of thermal diffusivity measurement for homogeneous material. The experimental bench uses a periodic method dedicated to millimeter scale study. Simulation of this experimental method is studied in detail. The case of a homogeneous material of unknown diffusivity to be measured is studied. Sensitivity coefficient and calculus of Cramer–Rao bounds (BCR) prove the good conditioning of diffusivity estimation and illustrate the action of thermal losses. Simulations of Monte Carlo compare performances of least squares estimator to optimal performances defined by the BCR. Two experimental processes are validated by a study of the iron ARMCO chosen as material of reference.     

Temperature dependence of thermal conductivity and thermal diffusivity of some composites using the transient plane source technique

The recently developed transient plane source (TPS) technique has been applied for the simultaneous measurement of thermal conductivity and thermal diffusivity of two composite materials namely, marble and magnesium oxychloride cement in the range of temperatures from 30 to 150°C. The experimental results of these samples show that there is very slight variation in thermal conductivity and thermal diffusivity of these materials in this range of temperature. An effort has been made to express this variation of thermal conductivity and diffusivity with temperature by a linear relation, in these materials.     

Determination of thermal contact resistance from transient temperature measurements

The temperature distribution in combustion engine components is highly influenced by thermal contact resistance. For the prediction and optimisation of the thermal behaviour of modern combustion engines knowledge about the contact heat transfer is crucial.Available correlations to predict the contact resistance are simplifications of the real geometric conditions and only tested for moderate pressures up to 7 MPa. Typical combustion engine applications include contact pressures up to 250 MPa.The experimental approach presented here to derive the thermal contact resistance in terms of contact heat transfer coefficients for high temperature and high pressure conditions is based on transient infrared temperature measurements. Two bodies initially at two different temperatures are brought in contact and the surface temperature histories are recorded with a high-speed infrared camera. The contact heat flux is calculated by solving the related inverse problem. From the contact heat flux and from the measured temperature jump at the interface the contact heat transfer coefficient is calculated.The inverse method used for the calculation of the heat flux is based on the analytical solution for a semi-infinite body and a step response to a Neumann boundary condition. This method provides an algorithm that is used in a sequential manner. The use of “future” temperature data greatly improve the stability of the governing equations and reduce the sensitivity to measurement errors.     

Effective thermal parameters of layered films: An application to pulsed photothermal techniques

Pulsed photothermal techniques provide useful methods based on linear relations between measurable quantities to obtain the thermal diffusivity and thermal conductivity of homogeneous materials. In this work, the effective thermal parameters of two-layered films are defined starting from an homogeneous layer which at the surfaces, produces the same temperature fluctuations and the same photothermal signal that the composite heated by a fast pulse-laser. Our theoretical model predicts that the effective thermal parameters of the layered system can only be calculated in the limit when the laser pulse duration is smaller tan the characteristic time of each layer, respectively. The temperature distribution is calculated in each layer by using the Fourier integral and the time-dependent one-dimensional heat diffusion equation with appropriate boundary conditions according to the experimental conditions. Within this approximation, we found an analytical expression for both, the effective thermal diffusivity and thermal conductivity which depend significantly on the thickness and the thermal parameters of each film.     

The Lock-in Heating-Cooling Method for the Measurement of the Thermal Diffusivity of Solid Materials

A new test method is presented for the on-field nondestructive measurement of the thermal diffusivity of solid materials. A periodic thermal disturbance is supplied to the inspected material by a thermoelectric source based on the Peltier effect. This can alternate heating and cooling stages and provide, if properly controlled, a harmonic disturbance with null net heat flux. A steady-periodic temperature field can thus be induced within the specimen. The diffusivity of the material is then estimated by monitoring the propagation of the temperature cycles along the optically accessible surface of the specimen, adjacent to the thermal input surface area. A camera for infrared thermography is used for nonintrusive surface temperature measurement. At the current stage of development, the focus is on the accurate reproduction of the theoretical model on which the method is based. Ease of operation and portability of the test equipment are also pursued. However, tests on thin specimens of materials with known properties give measurements in encouraging agreement with the nominal values.     

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.     

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.     

An analytical analysis for the prediction of nonlinear inverse temperature profiles in solid explosives

A novel analytical method developed by Mansour and Hussein (11) has been used for the evaluation of critical thermal conditions for a non-linear inverse temperature distribution model of an explosive. The analytical results presented in this work have been compared with previously published numerical results and shown to be accurate. The advantage of this new method is that it can be easily applied to other inverse non-linear models arising in boundary layer, kinetics, electronics, vibration, combustion … etc.     

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。