Laser Flash Experiments 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.

Digital twin of a laser flash experiment helps to assess the thermal performance of metal foams

Metal foams are a class of materials with immense potential. The complex topology in these lightweight systems is responsible for their outstanding mechanical and thermal properties. Furthermore, this is the same reason why thermal assessment of metal foams is challenging. While conventional analytical techniques provide useful data, modern-age technology allows to explore thermal transfer in metal foams in great detail by building a digital twin of the thermal characterisation experiment. In this work, high-accuracy measurements with a laser flash analysis instrument, processed with two effective-medium heat conduction models, are compared to a digital twin built with computed tomography and finite element analysis. This combination helps resolving complexity in analysing AlSi7Mg open-cell foams. Evidence of non-Fourier macroscopic heat conduction is found, which makes standard laser-flash analysis non-scalable.

Avoiding Natural Convection in Laser-Flash Experiments

Avoiding Natural Convection in Laser-Flash Experiments

Modeling research on laser quenching process of GCr15 bearing steel basing on material properties obtained with experimental methods

A combination of temperature and microstructure prediction models for the laser quenching process of GCr15 bearing steel was established. The thermo-physical parameters and austenitizaiton kinetics of GCr15 bearing steel were obtained with the laser flash and dilatometer experiments, respectively, to improve the prediction accuracy of the model. The dilatometric experiment results for the austenitization kinetics for high heating rates were fitted with the isochronal JMA relationship. Basing on the experimental results, the temperature and microstructure evolutions of GCr15 bearing steel during the laser quenching processes were simulated. According to the simulation results, optimized technological parameters for the laser quenching process were proposed.

Complexity matters: Highly-accurate numerical models of coupled radiative–conductive heat transfer in a laser flash experiment

Opaque and fully dense solids respond to a laser pulse by absorbing its energy, causing non-uniform heating and thus creating a thermal gradient. Thermalisation by thermal conduction acts to minimise that gradient; monitoring this process as a function of time enables to infer the material properties such as thermal diffusivity. For samples with transparency in the near-infrared region (semi-transparent samples), heat within the sample volume is carried both by radiation and conduction, requiring appropriate adjustments to data processing in laser flash analysis. In experiments where a high-emissivity coating is applied to both faces of a semi-transparent sample, an unconstrained diathermic model is conventionally used, allowing to separate conductive and radiative heat fluxes. At high temperatures, materials with strong anisotropic scattering produce a sharp initial peak on the temperature curve, which this simple model fails to reproduce. A more complex coupled radiative–conductive problem needs to be considered instead. Although the general methods for solving radiative transfer problems had been formulated many decades ago, their numerical implementation is not always straightforward. This paper presents the complete set of algorithms for solving the coupled problem allowing to increase the measurement accuracy. The constituent numerical techniques are cross-verified, and the computational method is validated on a set of experimental data collected from a synthetic alumina sample.

Improving Thermal Diffusivity Measurements by Including Detector Inherent Delayed Response in Laser Flash Method

Laser flash experiments are a widely used to determine thermal diffusivity of matter. Especially for thin samples or high diffusive materials, the laser pulse-time delay and its shape may become crucial for precise measurements (“finite pulse-time effect”). An additional delayed response and modification of the shape of the signal can be caused by time delays of detectors and electronic components (e.g., electronic filters) and may be inherent to Laser Flash Apparatuses (LFA). Similar to the correction of the finite pulse-time effect, this detector system inherent delayed response needs to be taken into account, especially for thin or high diffusive materials. To correct for this additional delay, detector signals of direct laser pulses were measured and for correction of this systematic errors a transfer function is derived. It reproduces the detector signal using the pulse shape measured by a diode within the apparatus and thus takes into account the actual laser pulse shape and detector behavior. For the used experimental setup, systematic errors caused by this effect are in the same range than the often considered finite pulse-time effect. As the detector related time delay is system inherent, the developed transfer function can be used to effectively eliminate both, the finite pulse-time delay and the detector inherent delayed response. Besides experimental determinations, synthetic temperature response data are used to quantify the systematic errors related to the additional detector inherent retardation for various thermal diffusivities and sample thicknesses. By not taking the additional delay into account systematic errors > 10 % may arise for both, high and low temperature detectors, indium antimonide (InSb) and MCT (HgCdTe), respectively.

Rear-surface integral method for calculating thermal diffusivity: Finite pulse time correction and two-layer samples

We study methods for calculating the thermal diffusivity of solids from laser flash experiments. This experiment involves subjecting the front surface of a small sample of the material to a heat pulse and recording the resulting temperature rise on the opposite (rear) surface. Recently, a method was developed for calculating the thermal diffusivity from the rear-surface temperature rise, which was shown to produce improved estimates compared with the commonly used half-time approach. This so-called rear-surface integral method produced a formula for calculating the thermal diffusivity of homogeneous samples under the assumption that the heat pulse is instantaneously absorbed uniformly into a thin layer at the front surface. In this paper, we show how the rear-surface integral method can be applied to a more physically realistic heat flow model involving the actual heat pulse shape from the laser flash experiment. New thermal diffusivity formulas are derived for handling arbitrary pulse shapes for either a homogeneous sample or a heterogeneous sample comprising two layers of different materials. Presented numerical experiments confirm the accuracy of the new formulas and demonstrate how they can be applied to the kinds of experimental data arising from the laser flash experiment.

Rear-surface integral method for calculating thermal diffusivity from laser flash experiments

The laser flash method for measuring thermal diffusivity of solids involves subjecting the front face of a small sample to a heat pulse of radiant energy and recording the resulting temperature rise on the opposite (rear) surface. For the adiabatic case, the widely-used standard approach estimates the thermal diffusivity from the rear-surface temperature rise history by calculating the half rise time: the time required for the temperature rise to reach one half of its maximum value. In this article, we develop a novel alternative approach by expressing the thermal diffusivity exactly in terms of the area enclosed by the rear-surface temperature rise curve and the steady-state temperature over time. Approximating this integral numerically leads to a simple formula for the thermal diffusivity involving the rear-surface temperature rise history. Using synthetic experimental data we demonstrate that the new formula produces estimates of the thermal diffusivity – for a typical test case – that are more accurate and less variable than the standard approach. The article concludes by briefly commenting on extension of the new method to account for heat losses from the sample.

Surrogate accelerated Bayesian inversion for the determination of the thermal diffusivity of a material

Determination of the thermal properties of a material is an important task in many scientific and engineering applications. How a material behaves when subjected to high or fluctuating temperatures can be critical to the safety and longevity of a system’s essential components. The laser flash experiment is a well-established technique for indirectly measuring the thermal diffusivity, and hence the thermal conductivity, of a material. In previous works, optimization schemes have been used to find estimates of the thermal conductivity and other quantities of interest which best fit a given model to experimental data. Adopting a Bayesian approach allows for prior beliefs about uncertain model inputs to be conditioned on experimental data to determine a posterior distribution, but probing this distribution using sampling techniques such as Markov chain Monte Carlo methods can be incredibly computationally intensive. This difficulty is especially true for forward models consisting of time-dependent partial differential equations. We pose the problem of determining the thermal conductivity of a material via the laser flash experiment as a Bayesian inverse problem in which the laser intensity is also treated as uncertain. We introduce a parametric surrogate model that takes the form of a stochastic Galerkin finite element approximation, also known as a generalized polynomial chaos expansion, and show how it can be used to sample efficiently from the approximate posterior distribution. This approach gives access not only to the sought-after estimate of the thermal conductivity but also important information about its relationship to the laser intensity, and information for uncertainty quantification. Moreover, this approach leads to significant speed up over traditional methods by orders of magnitude. We also investigate the effects of the spatial profile of the laser on the estimated posterior distribution for the thermal conductivity.

Analytic solution of Guyer-Krumhansl equation for laser flash experiments

The existence of non-Fourier heat conduction is known for a long time in small and low temperature systems. The deviation from Fourier’s law has been found at room temperature in heterogeneous materials like rocks and metal foams (Both et al., 2016; Ván et al., 2017). These experiments emphasized that the so-called Guyer-Krumhansl equation is adequate for modeling complex materials. In this paper an analytic solution of Guyer-Krumhansl equation is presented considering boundary conditions from laser flash experiment. The solutions are validated with the help of a numerical code (Kovács et al., 2015) developed for generalized heat equations.

Investigation of thermophysical properties of thin-layered paint

The present study reports an investigation of the thermophysical properties of a camouflage coating paint (brand name: EC Paint) applied in thin layers onto a sample substrate. Since the thin-film form of the specimen substantially impedes traditional thermophysical measurements, a dedicated investigation procedure was developed to address this issue. This tailored approach comprises: SEM characterisation; density determination; DSC measurements; laser flash experiments; and a numerical parameter estimation procedure for determining thermal conductivity/diffusivity transversal to the coated surface. Experimental studies were carried out on multi-layered specimens of the EC Paint deposited onto molybdenum (Mo) or aluminium (Al) foil substrates of known thermophysical properties. The key measurements of thermal transport properties were performed on paint layers of varying thickness. In addition, the supporting gravimetric and calorimetric experiments were performed at temperatures ranging from about 20–120 °C. The resultant values of thermophysical properties of the EC Paint layer fall within the range typical for insulators. Furthermore, the study also revealed the presence of a moisture sorption effect, which has been further characterised. Finally, the obtained qualitative and quantitative results confirmed the correctness and effectiveness of the elaborated procedures.

Isolating lattice from electronic contributions in thermal transport measurements of metals and alloys above ambient temperature and an adiabatic model

From femtosecond spectroscopy (fs-spectroscopy) of metals, electrons and phonons reequilibrate nearly independently, which contrasts with models of heat transfer at ordinary temperatures ([Formula: see text] K). These electronic transfer models only agree with thermal conductivity [Formula: see text] data at a single temperature, but do not agree with thermal diffusivity [Formula: see text] data. To address the discrepancies, which are important to problems in solid state physics, we separately measured electronic (ele) and phononic (lat) components of [Formula: see text] in many metals and alloys over [Formula: see text]290–1100 K by varying measurement duration and sample length in laser-flash experiments. These mechanisms produce distinct diffusive responses in temperature versus time acquisitions because carrier speeds [Formula: see text] and heat capacities [Formula: see text] differ greatly. Electronic transport of heat only operates for a brief time after heat is applied because [Formula: see text] is high. High [Formula: see text] is associated with moderate [Formula: see text], long lengths, low electrical resistivity, and loss of ferromagnetism. Relationships of [Formula: see text] and [Formula: see text] with physical properties support our assignments. Although [Formula: see text] reaches [Formula: see text] near 470 K, it is transient. Combining previous data on [Formula: see text] with each [Formula: see text] provides mean free paths and lifetimes that are consistent with [Formula: see text] K fs-spectroscopy, and new values at high [Formula: see text]. Our findings are consistent with nearly-free electrons absorbing and transmitting a small fraction of the incoming heat, whereas phonons absorb and transmit the majority. We model time-dependent, parallel heat transfer under adiabatic conditions which is one-dimensional in solids, as required by thermodynamic law. For noninteracting mechanisms, [Formula: see text]. For metals, this reduces to [Formula: see text] above [Formula: see text]20 K, consistent with our measurements, and shows that Meissner’s equation [Formula: see text] is invalid above [Formula: see text]20 K. For one mechanism with multiple, interacting carriers, [Formula: see text]. Thus, certain dynamic behaviors of electrons and phonons in metals have been misunderstood. Implications for theoretical models and technological advancements are briefly discussed.

Photochemistry of Fe(III) complexes with salicylic acid derivatives in aqueous solutions

Abstract The photochemistry of a series of 1:1 Fe(III) complexes with salicylic acid derivatives (SADs) in aqueous solution has been investigated, using the following model compounds: salicylic acid (SA), 5-sulfoSA (5SSA), 4-hydroxySA (2HSA), 6-hydroxySA (6HSA), 4-nitroSA (4NSA) and 5-nitroSA (5NSA). The results of optical spectroscopy, steady-state and nanosecond laser flash photolysis experiments show that all Fe(III)–SAD complexes exhibit good photochemical stability upon 355 nm excitation (quantum yields of photolysis do not exceed 0.01). No evidence of hydroxyl radical formation was observed in laser flash experiments. Therefore, the primary photoprocess was assumed to be an electron transfer from coordinated SAD to the Fe(III) ion in the excited complex, leading to the formation of Fe(II) and the corresponding SAD phenoxy radical. SADs containing electron-withdrawing groups (4NSA, 5NSA, 5SSA) exhibit the smallest quantum yields of photolysis of the series, whereas the highest values were observed for SA and SADs containing electron-donating groups (4HSA, 6HSA). Therefore, in contrast to Fe(III)-complexes with aliphatic carboxylates, sunlight photolysis of Fe(III)–SAD complexes cannot be an effective way for the degradation of SADs in natural water systems.

Transient heat conduction within periodic heterogeneous media: A space-time homogenization approach

Composite materials generally exhibit a highly anisotropic thermal behavior (due to the orientation of fibers), leading to strong difficulties to determine the thermal conductivity tensor. Two approaches can be developed for its evaluation. The first one is to carry out experimental measurements with one or several devices to get all the components of the tensor. The second one is to use predictive models based on homogenization theories from the properties and the arrangement at the microscopic scale of each component of the composite material.Following this second approach, a space-time homogenization based on the multi-scale asymptotic expansion method is first developed to model the transient heat conduction problem within periodic heterogeneous structures. The introduction of additional terms to correct the edge effects (i.e. close to the boundaries of the macroscopic domain) in the transient state is considered. We show how these transient correcting terms can be introduced and calculated, depending on the classical boundary conditions in conduction heat transfer problems. Moreover, we underline that correcting terms have also to be added to take into account “short time” effects.Furthermore, we propose to discuss numerical results of the heat transfer modeling in a Laser Flash experiment. We specifically show how the effective thermal diffusivity may be biased when edge effects are neglected in the homogenized model.

Characterization of microstructure and thermal properties of YCSZ coatings obtained by suspension plasma spraying

The paper describes the procedure of determination of thermal properties (thermal diffusivity and thermal conductivity) of yttria/ceria stabilized zirconia coatings. The coatings were deposited by suspension plasma spraying method using SG-100 torch. The commercial powder with a chemical composition ZrO2+24wt.% CeO2+2.5wt.% Y2O3 was used and coatings were sprayed onto stainless steel substrates. The suspensions consisted of zirconia powder, water, ethanol and small addition of dispersant. The design of spray experiments included the following variable process parameters: (i) spray distance; and (ii) torch scan linear speed. The microstructure of coatings was determined by scanning electron microscopy (SEM) and X-ray diffraction (XRD). The phase composition and the crystallite size of coatings were estimated by Rietveld method. The different methods were used to find out the thermal properties values up to 573K. Firstly, thermal diffusivity of YCSZ coatings was determined by using a commercial setup and the obtained results were used to calculate the values of thermal conductivity. Then, to check the validity of the measurements and calculations, the simulations of laser flash experiment were made using COMSOL Multiphysics software. The least square method enabled to find the optimized value of thermal conductivity. Finally, the use of another setup enabled to find out the thermal transport properties in the temperature up to 873K.

Cell-Wide Coordination of ROS-Induced ROS Release by Hydrogen Peroxide in Mitochondrial Networks

Mitochondrial depolarizations of membrane potential (ΔΨm) can decrease electrical excitability of the cardiomyocyte, and ultimately lead to cardiac arrhythmia. Mitochondrial reactive oxidative species (ROS) induced ROS release (RIRR), has been shown to be the mechanism behind cell wide mitochondrial oscillations of ΔΨm. While the superoxide production/scavenging system is a key component to this mechanism, the contribution of H2O2 production/scavenging to RIRR is unknown. Current mitochondrial models do not take into account the role of H2O2, which diffuses over a larger distance than superoxide, in modulating the vulnerability of the network to ΔΨm oscillation. The objective of this study was to characterize the interplay between the different ROS production/scavenging systems in a model of the mitochondrial network that reproduces the kinetics and synchronization of ΔΨm depolarization and repolarization. We hypothesized that accumulation of H2O2, which can easily diffuse into the mitochondrial matrix and inhibit superoxide scavenging, is responsible for increasing the oscillatory vulnerability of the mitochondrial network. We employed a 1D model of mitochondrial network dynamics that includes the RIRR mechanism via the superoxide-sensitive inner membrane anion channel, and diffusion of superoxide and H2O2 between mitochondria. Localized oxidative stress was simulated by increasing superoxide production. ΔΨm depolarization/repolarization wave patterns of the network, with and without H2O2 diffusion, were compared. H2O2 diffusion from the oxidatively-stressed mitochondrion, was found necessary to gradually extend the oscillatory region to the rest of the network, as observed over time in laser flash experiments. Thus, H2O2 is the key messenger molecule in bringing the mitochondrial network into the oscillatory state. The model results suggest that H2O2 diffusion is an important player in bringing the network close to criticality, both by depleting the antioxidant defenses and by accentuating the inhibition of superoxide scavenging in the matrix.

Effect of Thermal Interface on Heat Flow in Carbon Nanofiber Composites

The thermal transport process in carbon nanofiber (CNF)/epoxy composites is addressed through combined micromechanics and finite element modeling, guided by experiments. The heat exchange between CNF constituents and matrix is studied by explicitly accounting for interface thermal resistance between the CNFs and the epoxy matrix. The effects of nanofiber orientation and discontinuity on heat flow and thermal conductivity of nanocomposites are investigated through simulation of the laser flash experiment technique and Fourier's model of heat conduction. Our results indicate that when continuous CNFs are misoriented with respect to the average temperature gradient, the presence of interfacial resistance does not affect the thermal conductivity of the nanocomposites, as most of the heat flow will be through CNFs; however, interface thermal resistance can significantly alter the patterns of heat flow within the nanocomposite. It was found that very high interface resistance leads to heat entrapment at the interface near to the heat source, which can promote interface thermal degradation. The magnitude of heat entrapment, quantified via the peak transient temperature rise at the interface, in the case of high thermal resistance interfaces becomes an order of magnitude more intense as compared to the case of low thermal resistance interfaces. Moreover, high interface thermal resistance in the case of discontinuous fibers leads to a nearly complete thermal isolation of the fibers from the matrix, which will marginalize the contribution of the CNF thermal conductivity to the heat transfer in the composite.

Thermophysical Model to Numerically Determine the Diffusivity of Highly Excited Nuclear Matter with an Instantaneous, Internal Pulse Method

We have studied thermalization of binding energy released as an instantaneous, internal heat pulse in a sphere. This resembles transient heat transfer in laser flash experiments, where thermal diffusivity is determined from temperature evolution measured on front or rear surfaces of thin films. Here, instead, we are interested in the long term behavior of sample temperature when it approaches thermal equilibrium. The method is applied to a nucleus. Therefore, not only energy source, time scale, and sample geometry but also materials, properties, and boundary conditions in the present article are completely different from conventional matter and standard laser flash methods. However, the principle by which determination of diffusivity is made is conserved. Diffusivity, κ, of the nucleus is estimated from kinetic gas theory to be κ/[10−8 m2·s−1] = 9.35 ± 2.97. Second, numerical simulation yields the time, tE, needed for thermalization after the disturbance. From comparison of tE with lifetime resulting from the uncertainty principle, the diffusivity can be extracted. Both results for κ agree within 10 %, but κ depends on energy level density (or excitation energy), a dependence that is not reported in previous literature. Thermalization in nuclear matter is confirmed to proceed by diffusion. The new internal source method could be transformed to experiments on a laboratory scale.

Computer simulations of non-congruent melting of hyperstoichiometric uranium dioxide

Detailed models of UO2+x at very high temperatures incorporating the effects of non-congruent melting have been developed to support the design and analysis of experimental work related to nuclear safety. Models based on both the Stefan formulation and phase field approach are implemented using recently published material properties. Simulations compare well with laser flash experiments performed on UO2+x. This work has application in modelling centreline melting of defective fuel which may occur due to the reduced thermal conductivity and lower incipient melting temperature associated with fuel oxidation.

Inference of high thermal transport in the lower mantle from laser-flash experiments and the damped harmonic oscillator model

Contact-free, laser-flash analysis (LFA) accurately (±2%) measures lattice thermal diffusivity (D) at high temperature (T). Conventional measurements of minerals underestimate D by ∼20% near 298 K due to interface resistance, although simultaneously existing direct radiative transfer artificially elevates D as T rises. Pressure (P) determinations possess these and other problems; however, reproduced values of ∂D/∂P agree the damped harmonic oscillator model. Models combined with new LFA data on perovskite compounds show that lattice thermal conductivity (klat) is high and independent of T, increasing from 7.5 to 30 W/m K (±25%) across the lower mantle (LM) due to compression. Diffusive radiative transfer is estimated from a recent model: For expected fine grain-size, spectral characteristics do not play a strong role, indicating that krad increases from ∼1 to ∼5 W/m K across the LM, estimated from olivine spectra. Although greater accuracy through improved measurements is needed, our results demonstrate that the LM is an efficient conductor of heat. Even a low, adiabatic temperature gradient can carry the power inferred to run the dynamo. Mantle convection may be limited to above 670 km.