Thermal Diffusivity Of Solid Materials Research Articles

Analytical formulas for calculating the thermal diffusivity of cylindrical shell and spherical shell samples

Calculating the thermal diffusivity of solid materials is commonly carried out using the laser flash experiment. This classical experiment considers a small (usually thin disc-shaped) sample of the material with parallel front and rear surfaces, applying a heat pulse to the front surface and recording the resulting rise in temperature over time on the rear surface. Recently, Carr and Wood [Int J Heat Mass Transf, 144 (2019) 118609] showed that the thermal diffusivity can be expressed analytically in terms of the heat flux function applied at the front surface and the temperature rise history at the rear surface. In this paper, we generalise this result to radial unidirectional heat flow, developing new analytical formulas for calculating the thermal diffusivity for cylindrical shell and spherical shell shaped samples. Two configurations are considered: (i) heat pulse applied on the inner surface and temperature rise recorded on the outer surface and (ii) heat pulse applied on the outer surface and temperature rise recorded on the inner surface. Code implementing and verifying the thermal diffusivity formulas for both configurations is made available.

Determination of thermal diffusivity of thin films by applying Fourier expansion analysis to thermo-reflectance signal after periodic pulse heating

The flash methods, which are the most popular transient methods for measuring the thermal diffusivity of solid materials, have evolved into ultrafast laser flash methods by using picosecond or nanosecond pulse lasers as a heating source and a thermo-reflectance technique such as high-speed thermometry. In conventional ultrafast laser flash methods, thermal diffusivity is determined by fitting an analytical equation after single pulse heating to observe thermo-reflectance signals, although actual thermo-reflectance signals are observed after periodic pulse heating. This paper presents an exact analytical solution of the temperature response expressed by Fourier series for one-dimensional heat diffusion after periodic pulse heating. These Fourier coefficients are directly related to the Laplace transformation of the temperature response after single pulse heating. The signal observed for a 100 nm thick platinum thin film on a fused quartz substrate was analyzed by this Fourier expansion analysis and fitted by analytical equations with three parameters: heat diffusion time across thin film, the ratio of heat effusion of the substrate to thin film, and the amplitude of the signal over the entire range of pulse interval in the time domain. Robustness in determining the thermal diffusivity of the thin film by the ultrafast laser flash method can be improved by this new analysis approach.

A New Efficient Formula for the Thermal Diffusivity Estimation from the Flash Method Taking into Account Heat Losses in Rear and Front Faces

The flash method is a commonly used technique for estimating the thermal diffusivity of solid materials. In this work, we develop a new efficient formula for the thermal diffusivity calculation to process the flash method data in the case of heat losses at the rear and front faces. First, the transient heat equation is analytically solved using the Green functions under time-dependent convection boundary conditions. The property of the descending part of the analytical solution, containing series which converges very quickly for long times, allows to express the thermal diffusivity as a function of the slope of the natural logarithm of the temperature rise and the Biot numbers related to heat losses at the rear and front faces. These Biot numbers are calculated from the ratio between the integrals of the complete temperature trends of the two faces. For this purpose, we developed a novel way to evaluate these integrals using the analytical solutions in Laplace domain. To verify the accuracy of these formulas, we simulated experimental data adding a Gaussian noise to the theoretical temperature results of the flash method data.

Effects of sample holder characteristics on thermal diffusivity measurement using the laser flash method

The laser flash method is commonly adopted to measure the thermal diffusivity of solid material since its advantages, such as a wide measuring range of thermal diffusivity, a small amount of samples, a high measuring temperature, and so on. However, the sample holders used by this method are limited and costly, which seriously affects the convenience and economy of this method. So, in order to develop and design more kinds of sample holders, it is necessary to study the effects of sample holder characteristics on measuring results. A transient flow and heat transfer calculation model was developed to analyse effects of pulse energy, pulse time, laser beam area, protective gas flow and sample holder materials on the thermal diffusivity measurement. It is found that the temperature increase of the sample upper surface ΔT obviously increases with pulse energy, pulse time and laser beam area increasing, but the half heating up time t50 slightly decreases with theses parameters increasing. ΔT and t50 are independent to the volume flow rate of protective gas. The heat transfer process and mechanism between sample and holders with various materials were analysed. The heat loss of samples depends on the heat conduction and radiation between sample and holder, the heat convection and radiation from sample to protective gas. The thermal conductivity, specific heat and emissivity of holder materials can affect the heat conduction and radiation between sample and holder slightly. So the ΔT and t50 are nearly independent to the holder material properties. Based on these conclusions, a new SUS310 holder was made, and the thermal diffusivity of a sample was experimentally measured using the new holder. As a result, the measuring error is less than ±3%.

Determination of Thermal Diffusivity of Austenitic Steel Using Pulsed Infrared Thermography

Abstract The simple method of determining thermal diffusivity of solid materials at room temperature using the pulsed infrared thermography (IRT) is proposed. The theoretical basis of the method and experimental results are presented. The study was conducted on austenitic steel 316L. Theobtained results show that the thermal diffusivity value of the tested steel determined by means of pulsed infrared thermography is very approximate to the values given in the literature, obtained by using more complicated methods. The differences between these values are 0.5%.

Characterization of Thermal Transport in One-dimensional Solid Materials

The TET (transient electro-thermal) technique is an effective approach developed to measure the thermal diffusivity of solid materials, including conductive, semi-conductive or nonconductive one-dimensional structures. This technique broadens the measurement scope of materials (conductive and nonconductive) and improves the accuracy and stability. If the sample (especially biomaterials, such as human head hair, spider silk, and silkworm silk) is not conductive, it will be coated with a gold layer to make it electronically conductive. The effect of parasitic conduction and radiative losses on the thermal diffusivity can be subtracted during data processing. Then the real thermal conductivity can be calculated with the given value of volume-based specific heat (ρcp), which can be obtained from calibration, noncontact photo-thermal technique or measuring the density and specific heat separately. In this work, human head hair samples are used to show how to set up the experiment, process the experimental data, and subtract the effect of parasitic conduction and radiative losses.

Contact measurement of thermal conductivity and thermal diffusivity of solid materials: Experimental validation of feasibility with a prototype sensor

A contact method has been proposed for measuring thermal transport properties of solids including soft materials. The method has an advantage of potential utilization for in-situ measurement without preparing a sample specimen. A unique feature of the method is to prepare a shallow cavity around a film sensor for a layer of a gel that is used to eliminate the thermal contact resistance between the sensor and the sample. A prototype sensor, 3mm in diameter, was fabricated on the surface of 0.16-mm thick glass substrate, and used with a 50-μm thick silicon rubber sheet as a spacer for the gel. The transient temperature rise of the sensor was determined from the electrical resistance after heating the sensor at a constant current. The thermal conductivity and the thermal diffusivity of a sample as well as the thickness of the gel layer were then determined from an iteratively obtained theoretical temperature rise that agreed with the measured temperature rise. The results obtained by the experiments with four different materials indicated that the thermal conductivity could be determined within 10% errors. The present study therefore demonstrated feasibility of the method, while improvement is still needed to reduce the error particularly in the thermal diffusivity.

Measurement of Thermal Conductivity and Thermal Diffusivity of Solid Materials Using a Novel Stamp Sensor: A Feasibility Study with Numerical Analysis

Measurement of Thermal Conductivity and Thermal Diffusivity of Solid Materials Using a Novel Stamp Sensor: A Feasibility Study with Numerical Analysis

Thermal characterization of liquids and pastes using the flash technique

For decades, flash methods [W.J. Parker, R.J. Jenkins, C.P. Butler, G.L. Abbott, J. Appl. Phys. 32 (1961) 1679–1684] have been well-known for characterizing the thermophysical properties such as the thermal diffusivity of solid materials. Fast measurement times, easy sample preparation and high accuracy are only some of the advantages of this non-contact, non-destructive measurement technique. Furthermore, the method can easily be adapted to the analysis of multi-layer samples as long as appropriate mathematical models are employed for the analysis of the detector curves. Nowadays, characterization of liquids, pastes and melts is becoming increasingly important for industrial applications. Presented in this work are principle details regarding newly developed sample holders for such applications. Furthermore, reliability tests (on water and ethylene glycol) are presented and compared to literature values. Additionally, some application examples on pastes and polymer melts are shown.

Method of Nondestructive Determination of Thermophysical Properties of Solid Materials

A method of nondestructive determination of the thermal conductivity and thermal diffusivity of solid materials by a section of the thermogram, which is characterized by regularization of heat fluxes, with account for registration of the time interval during which the studied object can be thought of as semi‐bounded is considered.

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.

광열변위법의 변형각을 이용한 열확산계수 측정

A new method of measuring the thermal diffusivity of solid material at room temperature using photothermal displacement is proposed. The influence of the parameters, such as radius and modulation frequency of the pump beam and the sample thickness, was studied. In previous works, thermal diffusivity was determined by the deformation angle and phase angle as the relative position between the heating and probe beams. In this study, however, we proposed the new analysis method based on the real part of deformation angle as the relative position between two beams. From the zero-crossing position of real part of deformation angle with respect to the pump beam, the thermal diffusivity of the materials can be obtained. The experimental values for different samples obtained by applying the new method are in good agreement with the literature values.

Measurement of Thermal Diffusivity Using Minimum Phase Based on the Photothermal Displacement

A new method of measuring the thermal diffusivity of solid material at room temperature using photothermal displacement is proposed. The influence of the parameters, such as radius and modulation frequency of the pump beam and the sample thickness, was studied. From the minimum position of phase of measured deflection with respect to the pump beam, the thermal diffusivity of the materials can be obtained. The position where phase has the minimum value is determined using multiparameter least-square regression fitting. The experimental values for different samples obtained by applying the new method are in good agreement with the literature values.

Method of Measuring Thermal Diffusivity of Composites with Thick Fillers and Reinforced Rubbers

The thermal diffusivity is a property of materials necessary for the mathematical modelling of unsteady heat transfer proceeding during their processing. A new method of measuring thermal diffusivity of solid materials was developed. In estimating the thermal diffusivity of solid materials by this method the experimental temperature field of the sample must be analysed. The values of the thermal diffusivity at different temperatures are obtained by solving the equation of unsteady heat conduction for time variable boundary condition. This method can be applied for composites with thick fillers and reinforced rubbers and enables us to determine the thermal diffusivity of elastomers and reinforced rubbers at temperatures ranging from 20 to 200°C.

Measurement of thermal diffusivity based on the photothermal displacement technique using the minimum phase method

A method of measuring the thermal diffusivity of solid material at room temperature using photothermal displacement is proposed. The influence of the parameters, such as the radius and modulation frequency of the pump beam and the sample thickness, was studied. From the minimum position of phase of measured deflection with respect to the pump beam, the thermal diffusivity of the materials can be obtained. The position where phase has the minimum value is determined using multiparameter least-square regression fitting. The experimental values for different samples obtained by applying the method are in good agreement with the literature values.

Thermal Diffusivity of Nickel Manganite Compound Using a Photoacoustic Method

A two-beam photoacoustic method to find the thermal diffusivity of solid materials by using a specially designed photoacoustic cell having the provision of front and rear surface illumination of the sample has been described. Thermal diffusivities of aluminium, polycrystalline silicon, and nickel manganite samples obtained from phase-lag measurements of the photoacoustic signal generated by front and rear surface illuminations of the sample as a function of the modulation frequency of the argon ion laser radiation are reported.

Photothermal radiometry measurement of thermal diffusivity

A method of measuring the thermal diffusivity of solid material at room temperature with photothermal radiometry is described. By measuring the amplitude and phase frequency characteristics of the photothermal signal, the thermal diffusivity is calculated and compared with the value obtained by the pulsed laser conductometer method.

Photothermal deflection applied to thermal diffusivity measurements of ceramic (ferrite) materials

The photothermal deflection method for the measurement of the thermal diffusivity of solid materials is discussed. Measurements on ferrites of different compositions are presented.

A laser interferometric method applied to thermal diffusivity measurements of ferrites

A laser interferometric method for the measurement of thermal diffusivity of solid materials is discussed. Measurements on ferrites of different composition are presented.

Determination of thermal diffusivity of solid materials near the melting point

The paper deals with the determination of the thermal diffusivity of solid materials near the melting point by studying the unidirectional propagation of a solidification front through the melts. The method is based on Neumann's thermal analysis of the liquid/solid interface during a solidification process. Measurements are given and the thermal diffusivity is determined for ice, mercury, and aluminum. The results are in fair agreement with reference data. An attempt is also made with data from the literature to calculate thermal diffusivity in very rapidly quenched metals, namely, tin, lead, and zinc. The calculated values are substantially lower than for the solid metals under normal conditions, a result that may reflect the glassy structure of the materials attained by quenching.