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On the Use of Transient Plane Source Sensors for Studying Materials with Direction Dependent Properties
... The original Transient Plane Source (TPS) technique [1], [2], [3], [4] is based on a thin metal pattern, with the specific purpose of allowing the development of heat (by ohmic heating) in a controlled manner (e.g. equal heat generation per unit area, or unit length of the heating element). ...
... In case the probe pattern is designed in such a way that heat generation can be controlled inside the heated sample, and the average temperature increase can be accurately modelled by apreferably analyticalsolution to the general thermal conductivity equation [3], [4], [6], opens interesting possibilities: For such a situation, the test of a sample with a single step-wise heat pulse, and simultaneous recording of the average probe temperature increase Δ with time , renders a 2dimensional (Δ , ) plot. In some circumstances, often the (Δ , ) response can be modelled solely by parameters thermal conductivity (isotropic or tensor) and thermal diffusivity (isotropic or tensor), heating power 0 , and some additional parameters such as a near-constant parameter , representing the total thermal resistance between the metal pattern and the bulk sample surface (incorporating also thermal contact resistances), and a time correction . ...
... Correspondingly, for an anisotropic Hot Disk test, the free variables model-fitted in Eq. (1) would be ( , , = √ 1 2 and 2 = 2 2 κ 2 ⁄ ), where index 1 represents the normal direction, and index 2 represents the in-plane (radial) direction [3], [4], [6]. ...
The present work presents some results and considerations for testing the specific heat of large-size samples (dimensions up to 250 mm x 250 mm in-plane, and 75 mm in thickness).
Recent interest on testing thermal transport properties of anisotropic composite structures, including highly-anisotropic stacked structures such as Li-Ion batteries, or weave structures with graphite- or nanotube fillers, may involve individual layer thicknesses of significant size. To estimate the effective, or total, heat capacity of such a structure may be rather challenging with a test method such as DSC – since it is difficult to prepare a small-volume sample which would represent the averaged heat capacity of the total structure.
An experimental method on utilizing Hot Disk sensors have earlier been presented, whereby a high-conducting metal cell containing the sample, of thickness within 5 mm, and maximum diameter of around 20 mm. Two experiments are carried out: One in which a constant heating power is heating this cell – when empty – and the cell is located within an insulated environment (to minimize heat losses from the cell). Another corresponding experiment is performed in which identical experimental conditions (possibly with a higher heating power) – but applied to a cell with an internal sample. Heat losses (from the cell to the surrounding insulation) can be approximately accounted for, allowing the estimation of the heat capacity of the sample inside the cell – by comparing these two experiments.
Some example applications are demonstrated and discussed, from testing of anisotropic rock samples, to a full-size Li-Ion battery used for automobiles.
... Less work has been applied to consideration of the case of an orthotropic or a more generally anisotropic medium. The study of an anisotropic medium was considered with a strip geometry [11], for square planar geometry [10], and for a bifilar spiral geometry approximated as a series of nested rings [41], although questions have been raised about the validity of this last result in the consideration of highly anisotropic thermal conductors [42]. An analytical solution derived from first principles for the temperature field created by the interaction of a CHS with an orthotropic medium, on the other hand, has not yet been reported in the scientific literature to the knowledge of the authors. ...
... In the isotropic case where k r ¼ k z ¼ k and a r ¼ a z ¼ a, Eqs. (39)- (41) converge to the solution derived earlier for an isotropic semi-infinite medium, Eqs. (9) and (11). ...
... (10) and (11) for Pyrex (isotropic material), and Eqs. (40) and (41) for PMMA (anisotropic material). An excellent agreement is obtained in both cases. ...
... The simplification of reducing dimensions in F and Y to G and X can also be performed through approximation: when performing a socalled continuum approximation or continuum assumption of irreversible process N, vectors , cf. Appendix (apparent thermal conductivity (Gustafsson, 1991;Gustavsson, Karawacki & Gustafsson, 1994;Suleiman, Gustavsson, Karawacki & Lundén, 1997;Gustavsson & Gustafsson, 2001). The special case of 0 G proc no implies that a so-called linear phenomenological relation (cf. ...
... The Hot Disk technique (Gustafsson, 1991;Gustavsson et al., 1994;Suleiman et al., 1997;Gustavsson & Gustafsson, 2001), employing a thin, embedded doublespiral sensor, is capable of accurately recording the uniaxial anisotropic thermal transport properties of a solid structure in a single experiment. The geometric average value of the thermal conductivity in the radial (in-plane) and axial (through-plane) direction with respect to the circular sensor is recorded, together with the thermal diffusivity in the corresponding radial (in-plane) direction. ...
... The case of a stack sample structure of smooth Cu sheets, where heat has been allowed to penetrate more than 10 layers, is shown in Table A1 and A2, cf. (Gustavsson & Gustafsson, 2001). ...
For a general irreversible process, incorporating sub-processes, entropy change may be expressed as the vector product of a thermodynamic force-and flow vector. A fundamental hypothesis is introduced, whereby a general irreversible process or sub-process may be categorized as being of a non-residual type, or of a residual type. A non-residual irreversible process is typically associated with continuous, linear behavior, where true material properties represent model constants, and the principle of local equilibrium is valid. A residual irreversible process is typically associated with discrete-, non-continuous-, and often non-linear behavior, where model constants do not represent generally accepted material properties.
... The HOT-DISK technique has been used several times to report thermal conductivity measurements over a wide range of temperatures [4,[8][9][10]. A full complete description of the experimental capability regarding precision/accuracy and reproducibility of the measured data of various applications is given elsewhere [9]. ...
... Furthermore, the short measuring times (seconds) and small temperature gradient across the sample will prevent a non-uniform saturation distribution (thermo-migration phenomena) in the case of partially saturated samples. The data, stemming from the heat transport through the protective layer, the influence of contact resistance is avoided [8]. All of these measures will substantially reduce the possible errors that may result either due to the specific geometry or due to the physical nature of the available sample. ...
The HOT DISK technique is used to measure the thermal conductivity of dry and saturated samples of building materials at room temperature. This technique is also known as transient plane source technique (TPS). The technique uses a resistive heater pattern (TPS element) that is cut from a thin sheet of metal and covered on both sides with thin layers of an insulating material. The TPS element/sensor is used as both heat source and temperature sensor. Regarding measurements of saturated (wet) samples this technique has several advantages such as the short measuring time and the small temperature rise (few degrees) across the sample. These two advantages will prevent a non-uniform moisture distribution that may arise when a high temperature difference across the wet samples is maintained for a long time. Another advantage, the shape of TPS-element being flat and thin leads to a substantial reduction in contact resistance between the sample and the sensor. More details about the HOT DISK technique and its major characteristics will be discussed. The investigated samples are of different types of building materials with various water absorbing abilities. The thermal conductivity was measured both at dry and 40% by weight-wet conditions.
... The Hot Disk sensor is an electrically conducting metallic double spiral (nickel), covered by two thin layers of insulating material as shown in Stumpf et al. (2021). The Hot Disk equipment relies on the transient plane source method (Gustafsson 1991;Gustavsson and Gustafsson 2005), according to the Dansk Standard (2015) ...
... Anisotropy in thermal transport properties of materials is an increasingly important factor to consider. Equation 1 holds true for isotropic materials, however, if the material is anisotropic and if we assume that the thermal transport properties are constant in the radial direction, with respect to the plane of the sensor, but different from the thermal transport properties in the axial direction then equation 1, has to be modified as follows [9]: ...
... It is also possible to measure the properties of anisotropic materials, provided the substrate has a uniaxial structure and the probe is properly oriented. Assuming that the properties along the a-and b-axes are the same, but different from those along the c-axis, and also that the plane of the probe is mapped out by the a-and b-axes, then we have the following expression for the temperature increase [28]: ...
This experimental method was first proposed in 1991 and is presently being used for determining thermal conductivity, thermal diffusivity, thermal effusivity, and volumetric heat capacity of solids. Under special and well-controlled conditions, it is possible to measure thermal conductivity over approximately six orders of magnitude at temperatures ranging from 25 K up to 1500 K. A feature of this method is the possibility to obtain both the thermal conductivity and thermal diffusivity from one single transient recording and in that way to open up convenient measurements of thermal transport of certain anisotropic materials. A further advantage of using a transient method relates to the possibility to eliminate the influence of the contact resistances always present between the heating element, functioning also as the temperature recorder, and the surface of the substrate under investigation. This review will touch upon the limitations of the method with an estimation of the measuring uncertainty together with a discussion on the influence of the difference between the experimental arrangement and the assumption made in the development of the analytical theory used for analyzing the experimentally recorded data. The method has turned out to be useful not only in measurements of the thermal transport but also for special quality control situations. It is used in both academic institutions and in industrial laboratories and has so far generated some 5000 scientific papers in international journals.
... Thermal conductivity in the normal direction vs depth profile of the mica stack with defects at different locations. The constant black line represents the λ through-plane obtained using the anisotropic method.12 ...
A recently developed method for analyzing the thermal conductivity vs depth variation near a sample surface has been extended to include inhomogeneous samples with anisotropy. If not considered, the anisotropy ratio in the sample structure can distort the depth-position data of the original test method. The anisotropy ratio is introduced in the original computational scheme in order to improve the depth-position estimations for inhomogeneous structures with anisotropy. The proposed approach has been tested in experiments and shown to improve depth position mapping.
... capacity (temperature range: 10 K-10000 K), and thermal diffusibility with high accuracy (±3%) (Gustafsson, 1991). The experimental principle was the transient plane source (TPS) method (Gustavsson et al., 1994;Gustavsson and Gustavsson, 2005). The core component of the method was a probe with a spiral structure, which was etched into a 10 (±2)-μm-thick metal sheet that was insulated with a 4-100-μm film. ...
The Wugongshan area is rich in medium–low temperature convective geothermal resources, among which there are more than 10 geothermal fields in Wentang, Wanlongshan, Wenjia, Hongjiang, etc. There are few basic geothermal geological studies in the geothermal fields and their peripheral areas; thus far, no systematic research work into the thermophysical parameters has been carried out. In this paper, 85 rock samples were collected from the surface and boreholes covering the strata and magmatic rocks in the study area. The results show that the average radioheat generation rate, the average thermal conductivity, and the average specific heat are 0.24–5.49 (μW/m³), 1.995–4.390 (W/mK), and 1.318–4.829 (MJ/m³K), respectively. The average thermal diffusivity ranges from 1.115 to 1.611 × 10⁻⁶ m²/s. The highest radioheat generation rate is Jurassic granite, and the lowest is quartz vein. The largest thermal conductivity and specific heat is the siliceous quartzite, and the smallest is the quartz vein. The highest thermal diffusivity is Cambrian metamorphic mica schist, and the lowest is siliceous quartzite. The radioactive heat generation rate, thermal conductivity, specific heat, and thermal diffusivity are closely related to the chemical composition, mineral composition, rock fabric, porosity, water content, and temperature and pressure conditions of rocks in the whole area. There is a linear relationship between thermal conductivity (K) and thermal diffusivity (κ), and the correlation equation is K = −0.3144k + 3.2172. Combined with the characteristics of thermophysical parameters, the genetic theory of deep crust heat generation + structural heat accumulation + siliceous quartzite heat conduction + granite heat preservation is preliminarily proposed.
... In addition, it is flexible and only requires one or two pieces of the sample to characterize with only a single flat surface. The method is applicable to most materials types, including thin samples [224] and non isotropic materials [225]. It is standardized in ISO 22007-2 [226] since 2008. ...
The building sector has a major role to play in the mitigation of greenhouse gas emissions. Indeed, residential and non-residential buildings account for 40% total energy consumption in the European union. In addition, given that 80% of building energy demand come from heating, thermal insulation is a domain with great potential for energy savings.The estimation of the thermal performance of a building usually relies on theoretical calculations. When in situ measurements are performed, the results often show some discrepancies with predictions: this is the so-called “performance gap”. Thus, it is important to distinguish the contribution of each element of the building envelope to the overall energy losses. In particular, “thermal bridges” (insulation irregularities) generate locally additional heat losses. They may also alter the thermal comfort of inhabitants as well as lead to mould growth issues.This thesis proposes several methods for the in situ estimation of heat losses in a building wall or in a thermal bridge. The methodology consists in applying an artificial thermal load to the wall and to analyze its transient response. This “active” approach is usually faster and less sensitive to weather conditions than standard steady-state methods. In practice, the indoor air is heated, and both the temperature and heat flux are measured on the wall surface. An inverse method then estimates the thermal resistance of the wall by fitting a model (direct model) to these transient measurements. The well-posedness of the inverse problem is assessed thanks to several mathematical tools. Some model reduction steps are required for the parameters of the direct model to be estimable with the desired uncertainty.In the case of a homogeneous wall, temperatures and heat fluxes are measured with contact sensors at one specific location. For a non-homogeneous wall or a thermal bridge, these local contact measurements are extrapolated to the rest of the wall thanks to infrared thermography and the quantification of the total heat transfer coefficient. For this purpose, several methods were developed to measure this coefficient in situ. Thanks to this extrapolation procedure, the inverse method can estimate the thermal resistance (or thermal transmittance) of an equivalent homogeneous wall having the same behavior as the real wall.The methods developed were validated on four experimental campaigns. Measurements were carried out in laboratory, in a climate chamber, and in situ. Different types of wall (heavyweight internally insulated wall, lightweight insulated wall) were tested. Several types of material-related thermal bridges were also investigated (mainly high-conductive materials in insulation systems). The results were compared to reference values obtained from steady-state measurements. Indeed, several methods for the characterization of thermal bridges in steady-state were compared: some are inspired from the literature, others are original.
... This method has been used for a broad range of materials including bulk solids and thin films [8,[11][12][13], powders [14], and liquids [15,16]. Furthermore, Hot Disk can test isotropic as well as anisotropic samples [6,17], which is especially important for low-density fibrous or cellulous thermal insulating materials, where fiber alignment introduces differences in thermal conductivity in axial and radial directions [18]. ...
The transient plane source (TPS) technique, also referred as the Hot Disk method, has been widely used due to its ability to measure the thermal properties of an extensive range of materials (solids, liquids, and powder). Recently, it has been recognized that typical Hot Disk sensors can influence TPS results of thermally insulating materials and lead to an overestimation of thermal conductivity. Although improvements have been proposed, they have not yet been implemented in the commercial TPS, leaving researchers with non-standardized modifications or options provided by a commercial Hot Disk apparatus. An empirical study of thermally insulating materials such as extruded polystyrene (XPS) and aerogel blanket is conducted in order to address the factors that affect the reliability of thermal conductivity k obtained using the commercial TPS apparatus. Sensor size, input power, duration of the measurements, applied pressure, and, in the case of anisotropic materials, heat capacity are investigated, and the results are compared with those using a Heat Flow Meter apparatus. The effect of sensor size on the k value is ascribed to heat loss through connecting leads and is more pronounced in smaller sensors and in materials with lower k values. In the case of XPS and aerogel, the effect becomes minimal for sensors with a radius r ≥ 6.4 mm. The low input power yields a high scattering of the results and should be avoided. Applied contact pressure and the tested region of the specimen play an important role in experiments with low-density fibrous materials due to the large percentage of heat being transferred by radiation and the heterogeneous nature of the samples, respectively. Additionally, the sensitivity of anisotropic measurements to the value of the material’s volumetric heat capacity (ρCp) is shown, emphasizing the need for the precise determination.
... The thermal conductivity measurements were conducted in the laboratory using a thermal analyzer (model TPS 500 by Hot Disk) based on the Transient Plane Source (TPS) method with a Kapton-plastic coated sensor (Gustafsson 1991;Gustavsson and Gustafsson 2005). All the measurements were carried out at ambient pressure. ...
Abstract The Upper Rhine Graben (URG) has been extensively studied for geothermal exploitation over the past decades. Yet, the thermal conductivity of the sedimentary cover is still poorly constrained, limiting our ability to provide robust heat flow density estimates. To improve our understanding of heat flow density in the URG, we present a new large thermal conductivity database for sedimentary rocks collected at outcrops in the area including measurements on (1) dry rocks at ambient temperature (dry); (2) dry rocks at high temperature (hot) and (3) water-saturated rocks at ambient temperature (wet). These measurements, covering the various lithologies composing the sedimentary sequence, are associated with equilibrium-temperature profiles measured in the Soultz-sous-Forêts wells and in the GRT-1 borehole (Rittershoffen) (all in France). Heat flow density values considering the various experimental thermal conductivity conditions were obtained for different depth intervals in the wells along with average values for the whole boreholes. The results agree with the previous heat flow density estimates based on dry rocks but more importantly highlight that accounting for the effect of temperature and water saturation of the formations is crucial to providing accurate heat flow density estimates in a sedimentary basin. For Soultz-sous-Forêts, we calculate average conductive heat flow density to be 127 mW/m2 when considering hot rocks and 184 mW/m2 for wet rocks. Heat flow density in the GRT-1 well is estimated at 109 and 164 mW/m2 for hot and wet rocks, respectively. Results from the Rittershoffen well suggest that heat flow density is nearly constant with depth, contrary to the observations for the Soultz-sous-Forêts site. Our results show a positive heat flow density anomaly in the Jurassic formations, which could be explained by a combined effect of a higher radiogenic heat production in the Jurassic sediments and thermal disturbance caused by the presence of the major faults close to the Soultz-sous-Forêts geothermal site. Although additional data are required to improve these estimates and our understanding of the thermal processes, we consider the heat flow densities estimated herein as the most reliable currently available for the URG.
... The effect of this film and thermal contact resistances are also taken into account in the TPS method [11]. Different applications of the Hot Disc method are reported in literature [4,6,9,15,17,20]. ...
The Hot Disc method, also known as the transient plane source (TPS) technique, is an experimental approach to determine the thermal transport properties of materials. The core of the method is the Hot Disc sensor, an electrically conducting metallic strip, shaped as a double spiral clad with a protective polymer film. The mean temperature increase in the sensor has been approximated from various analytical approaches such as: the concentric ring sources model, the thermal quadrupoles formalism, and concentric circular strips structure approach. However, full numerical simulation of the sensor has not been addressed so far. Here we develop a 3D model of Hot Disc sensors and compare simulated mean temperature increase to experimental recordings. Joule heating coupled with heat transfer of solids (of COMSOL Multiphysics software) is used to simulate the working principle of the sensor. The volume mean temperature increase in the sensor from the simulations proves to be in a good agreement with the corresponding experimental recordings. The temperature distributions of the metallic strip are also evaluated and discussed with respect to the previous experimental findings. Furthermore, the current distribution across the strip is obtained. Such simulation can potentially be used in further optimizing geometry and parameter estimation.
... It should be noted that the direction perpendicular to the composite plates will be called transverse, while those parallel to the plate will be called longitudinal. The hot disk method [13,14] was also used to validate the values measured by thermography and to obtain the thermal conductivities in the principal directions. The measurements were performed with a TPS 2500 device by Hot Disk AB (Sweden). ...
Silica/phenolic composite materials are often used in thermal protection systems (TPS) for atmospheric re-entry. The present work aims to compare two different approaches to assess heat transfer properties of these materials: i) using standard and specific experimental methods, and ii) with the development of 3D thermal transfer multiscale model using 2D (microscopy) and 3D (tomography) images. The latter procedure, based on computations on images, is a two-step change of scale from microscopic scale to mesoscopic scale and then to the macroscopic one. Two silica/phenolic composites with different spatial organizations are studied and their thermal properties are compared. Several experimental methods have been used, including space-resolved diffusivity determinations. Numerical results are compared to experimental ones in terms of transverse and longitudinal thermal conductivities of the composites, and were found to be in good agreement. A discussion is made on the different possible sources of uncertainty for both methods.
... The thermal conductivity data presented in this article have been determined with the Transient Plane Source Technique also known as Hot Disk. The method including its theory has been approved and described in detail in numerous publications [5][6][7] [8]. ...
This article presents experimental results of thermal conductivity in metal foams. The thermal conductivity of cellular solids differs from those of their corresponding dense material. Therefore, the various pore size level effects contributing to the thermal conductivity are comprised by introducing an effective thermal conductivity. In this work we investigated metallic foams with a porosity ranging from 0.65 to 0.82 manufactured by the Slip Reaction Foam Sintering (SRFS) Process using a nickel-based powder. For the determination of the effective thermal conductivity at room temperature, we employed the Transient Plane Source Technique also known as Hot Disk. We verified the influence of the porosity and the thermal conductivity of the solid phase on the effective conductivity and compared the measured values of the effective conductivity with theoretical ones calculated using the thermal conductivity of the solid phase and the solid volume fraction. We present here a simple model that demonstrates the influence of the geometry of the grid elements qualitatively, discuss the applicability of the method to heterogeneous materials such as metallic foams and give an outlook about further investigations at higher temperatures.
Thermal conductivity of unsaturated silty clay in Shenyang was experimentally investigated during freezing process by HOTDISK method, using a new-developed device. Two prediction models based on the measured results were established and compared with 3 typical models. Efficiency of the new device was found to be about 13 times higher than that of air-cooled method. The influence of latent heat on thermal conductivity during measurement was preliminarily analyzed, the measurement error caused by latent heat was within an acceptable range. In the relatively dry state, thermal conductivity during the whole freezing process did not exhibit significant changes. However, thermal conductivity of wet soil increased by 20% ~ 50% at −1.5 ~ −5 °C. A linear and a power correction relationship corresponding to dry density and moisture content were established. When dry density and moisture content were small, predicted values were smaller in the positive temperature region and larger in the negative temperature region than measured results. However, as the dry density and moisture content increased, predicted values were larger than measured results. The two prediction models can predict thermal conductivity well (RMSE≈0.1 W·m-1·K-1, NSE > 0.95, AD≈-0.03 W·m-1·K-1, MAPE≈10%). Regarding the parameters beyond the scope of this experiment, the models should be further verified.
Die geringe Wärmeleitfähigkeit der Kunststoffmatrix limitiert die Wärmeleitung in polymeren Faserverbundwerkstoffen. Eine Erhöhung der Wärmeleitfähigkeit der Matrix kann dazu bei-tragen, die Wärme in einem Bauteil besser zu verteilen, thermische Spannungen zu reduzie-ren und damit die Lebensdauer zu erhöhen. Obwohl die Wärmeleitfähigkeit von kohlenstofffaserverstärkten Kunststoffen (CFK) eine wichtige Komponente zur Auslegung von Bauteilen ist, sind in der Literatur bisher einige we-sentliche Forschungsfragen offengeblieben. Erstens ist bisher ungeklärt, welchen Einfluss die Herstellungs¬temperatur und damit Morphologie der Fasern auf die transversale Wärmeleit-fähigkeit hat. Zweitens wurden in den letzten Jahren erste Ansätze zur Modifikation der Kunststoffmatrix mit leitfähigen Füllstoffen aufgezeigt, jedoch nicht systematisch untersucht. Drittens wurden bereits vor einigen Jahrzehnten Faserverbundwerkstoffe mit metallbe-schichteten Fasern untersucht; es wurden aber nur Faservolumengehalte von maximal 30 Vol.-% erreicht. Und viertens wurden die mechanischen Eigenschaften dieser Materialien in der Literatur bisher nur oberflächlich betrachtet, sind jedoch für die konstruktive Auslegung und damit für den Transfer in die industriellen Anwendungen von Bedeutung. Ziel der vorliegenden Arbeit ist es, die wesentlichen Einflussparameter auf die Wärme-leitfähigkeit von Faserverbundwerkstoffen, welche aus Kohlenstoff¬fasern und Epoxid¬harzen bestehen, zu analysieren. Zunächst wird der Einfluss der Herstellungstemperatur der Fasern auf die Wärme¬leitfähigkeit untersucht. Es ist bereits bekannt, dass die Herstellungstemperatur zu einem Wachstum der graphitischen Lamellen führt. Auch ist bekannt, dass die Herstellungstemperatur Zugmodul und Wärmeleitfähigkeit in Faserrichtung beeinflusst. In dieser Arbeit kann jedoch erstmalig gezeigt werden, dass die erhöhte Herstellungstemperatur auch zu einem Anstieg der trans-versalen Wärmeleitfähigkeit führt. Anschließend werden Faserverbundwerkstoffe mit einer graphitmodifizierten Epoxidharz-matrix untersucht. Hierbei kann eine deutliche Steigerung der Wärmeleitfähigkeit der Ver-bunde transversal zur Faser um 55 % als auch in Faserrichtung um 67 % erzielt werden. Fer-ner wird gezeigt, dass mit dem Einsatz von metallbeschichteten Fasern die transversale Wärmeleitfähigkeit des Faserverbunds auf das 5-fache und in Faserrichtung auf das 6,6-fache gesteigert werden kann. Bisher wurden in der Literatur die mechanischen Eigenschaften von Faserverbundwerkstof-fen mit erhöhter Wärmeleitfähigkeit meist vernachlässigt. Dabei sind diese für die Entwick-lung praktischer Anwendungen unerlässlich. Der Zusatz von Graphit zur Matrix führt zu einer Abnahme der Verbundfestigkeit, das Biegemodul hingegen steigt. Die bruchmechanischen Untersuchungen zeigen, dass der Einsatz der graphitmodifizierten Matrix mit einem Anstieg der Bruchzähigkeit in Mode I, jedoch einen Abfall in Mode II, einhergeht. Der Einsatz der Me-tallbeschichtung führt zu einem signifikanten Abfall der Biegefestigkeit und des Biegemoduls.
Stepwise transient (SWT) and transient plane source (TPS) methods were used to measure the thermal conductivity and diffusivity of soda-lime-silica glass and polymethylmethacrylate (PMMA). The results of measurement on silicate glass were in very good agreement, less than 1.2%. On the contrary, on PMMA the differences between results of both methods were exceeding 5%. The authors tried to explain this disagreement by an anisotropy of PMMA. The theory of TPS method for anisotropic materials were presented and applied to PMMA measurements. Under this assumption the difference between the results of both method were reduced to 1.8%
Ceramic insulations are often used to mitigate heat losses from high temperature systems. In the case of thermal batteries, insulation is exposed to high temperatures, high axial loads, shock and vibration scenarios, and alternate gaseous environments. All of these conditions influence the effective thermal conductivity of the material and subsequently the performance of the battery. To properly balance the thermal design of these systems, a model that can capture the influence of these variables on the effective thermal conductivity is necessary. A previous publication presented the development of an effective thermal conductivity model for two common materials used for thermal batteries. This paper investigates the application of this model to Min-K TE1400 board, whose microstructure interrupts gas phase conduction to minimize thermal conductivity. This necessitates modifications to the model to accurately represent effective thermal conductivity for this type of material.
Thermal conductivity was measured as a function of temperature and compression in air, helium, and partial vacuum environments using the Transient Plane Source (TPS) technique. The trends observed in the measured thermal conductivity are explained through pore size measurements of compressed samples. The effective medium model was tuned using this data and is shown to agree with experimental data. Lastly, the anisotropy of the material was evaluated using the TPS data and specific heat estimations. This showed that axial conductivity is consistently less than radial thermal conductivity, as is corroborated by X-ray CT analysis of the fiber orientations in the material. The results and implications of the anisotropic results are also discussed.
The temperature fields and heat fluxes created by a circular heat source (CHS) are derived for the case of a CHS embedded between two identical and isotropic semi-infinite media, when different thermal contact resistances (CRs) are present on each surface of the CHS. Three different temperature fields are derived: on the CHS surface and in each one of the media surrounding the CHS. The derivation of the three-dimensional heat flow solution uses first principles with no prior assumptions, and employs the Hankel and Laplace transforms. The analytical solution presented here is exact with no approximations, but is given in integral form, which requires a facile numerical evaluation. Finite element simulations performed with COMSOL Multiphysics are provided and validate the analytical solution. The application of the solution to thin film thermal conductivity virtual measurements is demonstrated. Regressions of the numerical results yield thin film resistances in excellent agreement with the actual values (all within 1.5% error), which can readily be translated into thin film thermal conductivities.
Ceramic fiber insulation materials are used in numerous applications (e.g. aerospace, fire protection, and military) for their stability and performance in extreme environments. However, the thermal properties of these materials have not been thoroughly characterized for many of the conditions that they will be exposed to, such as high temperatures, pressures, and alternate gaseous atmospheres. The resulting uncertainty in the material properties can complicate the design of systems using these materials. In this study, the thermal conductivity of two ceramic fiber insulations, Fiberfrax T-30LR laminate and 970-H paper, was measured as a function of atmospheric temperature and compression in an air environment using the transient plane source technique. Furthermore, a model is introduced to account for changes in thermal conductivity with temperature, compression, and ambient gas. The model was tuned to the collected experimental data and results are compared. The tuned model is also compared to published data sets taken in argon, helium, and hydrogen environments and agreement is discussed.
The thermal transport properties have been determined for titanium aluminide with nominal composition Ti-48Al-2W-0.5Si (at.%), cast to cylindrical bars with different gamma/(gamma + alpha (2)) microstructures. The amount of phases and the orientation of the lamellar plates vary from the core to the rim in each of the bars. Differences in the thermal conductivity of the two phases lead to anisotropy in the thermal transport properties, but with cylindrical symmetry in the bars. A newly developed, high-precision technique, the so-called transient plane source (TPS) technique, was used to resolve the anisotropy in a wide temperature range. Typically, the conductivity increases monotonously from about 12-14 W/m (.) K at room temperature up to about 20-22 W/m (.) K at 700 degreesC for the different materials, The anisotropy in both conductivity and diffusivity is about 15 % at all temperatures, but with fundamental differences between the different materials. The anisotropy of the transport properties is explained in terms of amounts of phases and directionality of the lamellar plates.
The objective of this work is to improve measurements of transport properties using the hot disk thermal constants analyzer. The principle of this method is based on the transient heating of a plane double spiral sandwiched between two pieces of the investigated material. From the temperature increase of the heat source, it is possible to derive both the thermal conductivity and the thermal diffusivity from one single transient recording, provided the total time of the measurement is chosen within a correct time window defined by the theory and the experimental situation. Based on a theory of sensitivity coefficients, it is demonstrated how the experimental time window should be selected under different experimental situations. In addition to the theoretical work, measurements on two different materials: poly(methylmethacrylate) and Stainless Steel A 310, with thermal conductivity of 0.2 and 14 W/mK, respectively, have been performed and analyzed based on the developed theory.
http://dx.doi.org/10.1063/1.1150635
http://scitation.aip.org/content/aip/journal/rsi/71/6/10.1063/1.1150635
The electrical circuit for the recently developed transient plane source (TPS) technique for fast and precise measurements of thermal transport properties of solids has been modified for more convenient and more automated measurements. The technique has been tested for measurements of thermal conductivity and thermal diffusivity for a series of building materials ranging from thermally insulating materials (extruded polystyrene and PMMA) to good thermal conductors (stainless steel and aluminium). The results obtained in this work agree well with other techniques and international standard materials. This agreement indicates that the TPS method is accurate to within ±5% over a thermal conductivity range of four orders of magnitude (0.02 W m−1 K−1 to 200 W m−1 k−1).
The general theory of the transient plane source (TPS) technique is outlined in some details with approximations for the two experimental arrangements that may be referred to as ‘‘hot square’’ and ‘‘hot disk.’’ Experimental arrangements and measurements on two materials, Cecorite 130P and Corning 9606 Pyroceram, using a hot disk configuration, are reported and assessed.
On the use of the Hot Disk sensor for measuring thermal transport properties of materials with direction dependent properties
- S E Gustafsson
- M Gustavsson
- J S Gustavsson
Gustafsson S.E., Gustavsson M. and Gustavsson J.S. 2000. "On the use of the Hot Disk sensor for
measuring thermal transport properties of materials with direction dependent properties," Patent
application PCT/SE00/00868.
Specific heat measurements with the hot disk thermal constants analyser
- M Gustavsson
- N S Saxena
- E Karawacki
- S E Gustafsson
Gustavsson, M., Saxena, N.S., Karawacki, E., and Gustafsson, S.E. 1995. Specific heat
measurements with the hot disk thermal constants analyser, Thermal Conductivity 23 (published
1996), pp. 56-65.