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Dynamic plane-source technique for the study of the thermal transport properties of solids
Abstract
A transient technique has been developed for simultaneous determination of specific heat, thermal conductivity, and thermal diffusivity of solid samples from one thermogram. The basic principles of the method are discussed and the practical realization of the experiment is described. The results of the test of the method for different materials at room temperature and below are presented.
... There are situations in which heat flow is essentially 1-dimensional, flowing essentially in the normal direction to the sensor plane: either for very short experimental times (as discussed in [11]), oralternativelywhen the sample geometry is limited to only allow heat flux in the normal direction, for instance when the sample is in the shape of a rod (with diameter or cross-section area similar to the sensor diameter or cross-section area) [15], [16]. ...
... This approach was utilized in testing rod-shaped samples in [16], and disc-shaped samples in [18]. Primarily, one would perform a test with long-enough test time to come beyond a temperature increase with time variation which is not linear, and reach a set of experimental times where the temperature increase versus time appears to increase equally among all spatial points within the sample (at any instance in time). ...
... In [16] efforts were made to propose a stricter analysis time window for a rod-shaped sample and it was argued that the optimal time window for a computation of the specific heat that should be selected is Θ < t < 2Θ, where the characteristic length in Eq. (3a) should be selected equal to the length of the rod being tested. ...
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.
... where a is thermal diffusivity. For values of the function argument u<0,1 we can approximate exponential integral by a formula: (4)(5) Where A, B are regression line coefficients obtained from function: ...
... ideal thermal source ideal contact between the source and the measured sample zero thermal resistance between the surface of the measured sample and the contact material zero thermal losses from the flank of the sample The thermal source is located between two identical samples with thickness L. In time t=0 s, the thermal source starts affecting a unit area with constant thermal power q, then the relation of the temperature to the time can be express by the following equation (Karawacki at al., 2001): Θ-is characteristic time, a -is thermal diffusivity of the measured sample, a M -is thermal conductivity of the metal blocks, β -is a parameter which describes the heat sink imperfection, ierfc -is the error function integral,for short time t < 0,3 Θequation (7) has a simplified form: ...
... This assumption can be reasonable when the surrounding medium has a much lower thermal conductivity than the system being studied. This results is one-dimensional heat flow, where the temperature changes on the sensor can be simplified to [11]: ...
... ( 3) where: a -thermal diffusivity λ -thermal conductivity of the sample ierf -error function We consider the PS sensor placed between two identical samples having the same cross section as the sensor in the plate x = 0. Temperature increase in the sample as a function of time conforms to: ( , ) T t q a t 0 λ π = (4) which corresponds to linear heat flow into an infinite medium (Karawacki et al., 2001). Measured samples were placed in laboratory storage boxes at temperature 5 o C and 90 % air moisture content during 24 hours before measurement, and relations of thermal conductivity to temperature were measured during the temperature stabilization of samples. ...
This article deals with thermophysical properties of red and white bricks. If we want to protect the high standard of quality building materials, we need to know the physical parameters which can evaluate the quality. The most important for building materials are mainly thermophysical, mechanical parameters and parameters which can determine the structure of materials. The article presents results of thermophysical parameters measurements of red and white bricks during the temperature stabilization for different values of moisture content. For our measurements, we have chosen a hot wire method and a dynamic plane source method. Both methods are classified as transient methods and they are very convenient for measurements of thermophysical parameters of materials with a compact structure. The results of measurements show that temperature and moisture content have a significant effect on thermophysical parameters of bricks.
... which corresponds to the linear heat flow into an infinite medium (Karawacki and Suleiman, 2001). The sensor is made of a Ni-foil, 23 µm thick protected from both sides by an insulating layer made of kapton of 25 µm thick made on SAS. ...
The thermophysical parameters of selected cheeses (processed cheese and half hard cheese) are presented in the article. Cheese is a generic term for a diverse group of milk-based food products. Cheese is produced throughout the world in wide-ranging flavors, textures, and forms. Cheese goes during processing through the thermal and mechanical manipulation, so thermal properties are one of the most important. Knowledge about thermal parameters of cheeses could be used in the process of quality evaluation. Based on the presented facts thermal properties of selected cheeses which are produced by Slovak producers were measured. Theoretical part of article contains description of cheese and description of plane source method which was used for thermal parameters detection. Thermophysical parameters as thermal conductivity, thermal diffusivity and volume specific heat were measured during the temperature stabilisation. The results are presented as relations of thermophysical parameters to the temperature in temperature range from 13.5°C to 24°C. Every point of graphic relation was obtained as arithmetic average from measured values for the same temperature. Obtained results were statistically processed. Presented graphical relations were chosen according to the results of statistical evaluation and also according to the coefficients of determination for every relation. The results of thermal parameters are in good agreement with values measured by other authors for similar types of cheeses.
... (5) which corresponds to linear heat flow into an infinite medium (Karawacki and Suleiman, 2001). Thermal conductivity can be determined from the time-temperature relation. ...
This article focuses on temperature relations of selected thermophysical parameters for soft wheat flour. The main aim of experiment was to determine the thermal conductivity, thermal diffusivity and volume specific heat of soft wheat flour in Slovakia marked as Špeciál 00 Extra. Measurements were performed in laboratory settings. Thermal parameters were measured using the thermal analyser Isomet 2104 with two types of probes - a linear probe and plane probe. Measurement by the linear probe is based on a hot wire method, and measurement by the plane probe is based on a simplified plane source method. Both methods are described in the text. Two types of measurement method were used because of the non-homogenous structure of measured material. All thermophysical parameters were measured during the temperature stabilisation in the temperature interval 5-24 °C. Obtained graphical relations had linear increasing progresses with high values of determination coefficients in all cases. Measurement results showed that measurement method has no significant influence on thermophysical parameters values.
Transient measurements of thermal conductivity, thermal diffusivity, and specific heat capacity have been performed with hot disk sensors in thin samples of metallic materials. With this new variation of the hot disk method the sample size can be reduced to a volume less than ten cubic centimeters for copper at room temperature. It is also shown that the specific heat capacity can be conveniently measured in transient recordings of slightly longer duration. On comparing with standard values the accuracy turns out to be better than 1% while the precision (standard deviation of the mean from six measurements) on the average is about 0.5% for all values recorded. © 1994 American Institute of Physics.
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