=Paper=
{{Paper
|id=Vol-3039/paper15
|storemode=property
|title=Hardware-Software System for Measuring Thermophysical Characteristics of the Materials and Products
|pdfUrl=https://ceur-ws.org/Vol-3039/paper15.pdf
|volume=Vol-3039
|authors=Vitalii Babak,Oleg Dekusha,Zinaida Burova
|dblpUrl=https://dblp.org/rec/conf/ittap/BabakDB21
}}
==Hardware-Software System for Measuring Thermophysical Characteristics of the Materials and Products==
https://ceur-ws.org/Vol-3039/paper15.pdf
Hardware-Software System for Measuring Thermophysical
Characteristics of the Materials and Products
Vitalii Babak a, Oleg Dekushaa and Zinaida Burova b
a
Monitoring and Optimization of Thermal Processes Dept., Institute of Engineering Thermophysics NAS of
Ukraine, 2a, Mary Kapnist str., 03057 Kyiv, Ukraine
b
National University of Life and Environmental Sciences of Ukraine, 15, Heroyiv Oborony str., 03041, Kyiv,
Ukraine
Abstract
Accurate measurements the thermophysical characteristics of materials and products required
in almost all modern fields of technology. The presented in article methods for measuring the
thermophysical and thermal radiation characteristics can be applied not only for materials but
for energy-efficient glasses and thin coatings, as well as methods for determining the
thermophysical parameters of concrete mixtures over a long period of time and a wide range
of temperatures. Proposed unified hardware-software measuring system that combine
described methods for measuring thermophysical characteristics. The main characteristics
which are necessary for carrying out measurements and metrological support are defined.
Methods of analysis of metrological characteristics using working standards as well as indirect
method are proposed for implementation in the system. An algorithm for determining the
metrological characteristics of the measuring system is proposed. Presented the metrological
studies results of the measuring system.
Keywords 1
thermophysical characteristics, measuring system, thermal conductivity, emissivity, heat flux
1. Introduction
Accurate measurements of the thermophysical characteristics of materials and products required in
almost all modern fields of technology. Measuring information can be used in the priority areas of
science and technology development such as: construction and energy, metallurgy and materials
science, aviation and astronautics, electronics and mechanical engineering.
The main thermophysical characteristics are thermal conductivity, specific heat, thermal resistance.
Various methods for measuring these characteristics have been developed, which can be classified
according to the following general features:
• by the thermal state of the sample (or stage of the thermal process): stationary, which provide
for the establishment of thermodynamic equilibrium in the system [1-4], and dynamic, which study
the temperature-time dependence of the thermophysical properties of the sample material [5-7];
• by the method of finding the desired value: absolute (for example, by measuring the electric
power consumed by the heater) [2,4] and differential (comparative);
• by the nature of measurements: direct, based on the measurement of heat flux, while for the
calculation it is necessary to know only the geometric parameters of the sample, and indirect, based
on the measurement of temperature [1,3,5];
• according to the shape of the sample (or its isothermal surfaces): flat, cylindrical and spherical.
The basic differential equations describe thermal phenomena only in the most general form, since
they are derived taking into account the general laws of physics. In order to distinguish from the
innumerable number of thermal processes the considered one and to give its full mathematical
ITTAP’2021: 1nd International Workshop on Information Technologies: Theoretical and Applied Problems, November 16–18, 2021,
Ternopil, Ukraine
EMAIL: vdoe@ukr.net (A. 1); ODekusha@nas.gov.ua (A. 2); zinaburova@nubip.edu.ua (A. 3)
ORCID: 0000-0002-9066-4307 (A. 1); 0000-0003-3836-0485 (A. 2); 0000-0002-4712-6298 (A. 3)
©️ 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
description, the conditions of unambiguity (boundary conditions) are formulated, which reflect the
partial features of a concrete process. Conditions of unambiguity include:
• geometric conditions that characterize the shape and linear dimensions of the body in which
the process takes place;
• physical conditions that characterize the properties of the environment and the body and the
law of distribution of internal heat sources [8,9];
• initial (or temporal) conditions that formulate when considering non-stationary processes and
characterize the distribution of temperatures in the body at the initial time;
• boundary conditions characterizing the interaction of the considered body with the
environment.
A wide range of new materials, different in shape and structure, requiring comprehensive studies of
their thermal characteristics in accordance with the above classification and variation of boundary
conditions, requires the creation of various instruments and measuring systems [10]. Measuring
instruments, in turn, require the development of specific methods of calibration and verification of
research results. Construction of multi-stage calibration schemes is not always technically and
economically viable. This is especially true in the field of non-destructive testing, when the decisive
factor is not the measured thermophysical value, but its relationship with the characteristics that reflect
the quality of the material or product.
Unification of measurements the ability to determine several defining thermal characteristics using
a single intelligent information-measurement system, is a promising area of development.
Considering written above the next research tasks was formulated:
• Propose the methods for measuring thermophysical characteristics that can be unified in one
measuring system;
• Define the main characteristics which are necessary for carrying out measurements and
metrological support;
• Implement hardware-software unified system;
• Propose the methods for metrological support of the system.
2. System for measuring the thermophysical characteristics
One of the main thermophysical characteristics of modern materials is thermal conductivity or
thermal resistance. The methods of thermal conductivity measuring for the particular group of materials
should be chosen depending from the following criteria:
• a suitable range of values of the coefficient of thermal conductivity, as for low- and high-
conductivity materials require different measurement methods;
• range of operating temperature values;
• the corresponding standard size and shape of the sample.
As a result of the analysis of schemes of measurement of thermal conductivity of the materials in
the form of a plate [1,3,11], in the developed complex information-measuring system the thermometric
method with use of two identical heat flux sensors. In order to ensure a uniform thermal field in the
sample in the measuring cell of the system, thermal stabilization of the heater edge zones and the cooler
with the help of protective peripheral heaters is applied. It is this design and thermophysical solution of
the measuring cell allows not only to minimize heat loss, but also provides the fastest access to a
stationary mode of measurement [11].
Based on the measurements results of the heat flux passed through the sample and the temperature
difference on its working surfaces, the thermal resistance is calculated 𝑅, m2·K/W, and thermal
conductivity𝜆 (W/(m∙K)) based on dependences presented in Table 1. The measurement range of the
thermal conductivity from 0,02 up to 3 W/(m∙K) in the temperature range from 240 up to 400 K, sample
sizes from 100 × 100 to 300 × 300 mm with thickness up to 120 mm.
The Heat module of the measuring system during installing the sample for thermal conductivity
measurements is shown in Fig. 1.
A special place among modern thermal insulators is occupied by thin-layer coatings, such as paints
and mastics based on acrylic binders containing hollow ceramic or glass microspheres. Determination
of their thermal resistance is usually carried out by the calculation method, based on data for ordinary
paints, which is incorrect for complex inhomogeneous compositions. To objectively assess the
effectiveness of such thermal insulation materials, a method for measuring the thermal resistance and
thermal conductivity of thin coatings has been developed. A uniform layer of the studied paint is
thickness ℎcoat = 1. . .2 mm applied to a substrate of rigid sheet dielectric material (for example glass),
whose thermal resistance 𝑅gl (m2·K/W) determined in advance. The coated sample is placed in the
measuring cell of the system, and in the centers of the working surfaces of the sample are placed the
joints of the tape differential thermocouple thickness 0,05 ... 0,07 mm and provide their pressing to the
surface of the sample with thin elastic silicone gaskets, which eliminates possible micro-irregularities
of the coating surface. Based on measurements of the heat flux and temperature the calculation of the
thermal conductivity value for the investigated coating performed.
Figure 1: Heat module of the system during sample installation
Heat-protective properties of thin coatings are characterized not only by the thermal conductivity,
but also the thermal radiation characteristics. The emissivity which is determined using a specialized
expensive device - Fourier spectrophotometer [13]. For unify the measurements, an experimental and
computational method for measuring the emissivity of energy-saving glass and other coatings proposed
calorimetric method. This method requires two identical samples of glass or coated material are
collected in a package having a layer of air of known thickness between the two test surfaces. This
package is placed in the measuring cell of the system and determine its thermal resistance, which
depends on the conductive-convective and radiative heat transfer in the package. Based on the obtained
results the emission of the coatings is determined by calculation (see Table 1) [11, 14].
The scheme of the study and calculation formulas presented in Table 1.
Table 1
Measurement schemes and main data for determining thermal properties
Sought quantity, Design equation Data characteristics
measurement scheme
Thermal conductivity λ, 𝑞̅ = (𝑞1 + 𝑞2 )/2
thermal resistance R of material 𝜆 = ℎ ∙ 𝑞̅⁄𝛥𝑇 – average heat flux
recorded by HFM1, 2
𝑅 = 𝛥𝑇⁄𝑞̅
𝛥𝑇 = 𝑇1 − 𝑇2
– temperature
difference on the
sample surfaces
ℎ – sample thickness
Thermal conductivity λ, ℎcoat
𝜆c𝑜𝑎𝑡 =
thermal resistance R of a thin coating 𝑅coat − 𝑅gl ℎ𝑐𝑜𝑎𝑡 – coating
thickness
𝑅coat = 𝛥𝑇⁄𝑞̅
𝑅coat , 𝑅gl , 𝑅𝑎𝑖𝑟 –
thermal resistance
of coating, glass and
air layer
Emissivity 𝜀sp of thin coating 𝜀sp = 𝑅𝑟𝑎𝑑 ⁄4𝜎𝑇̅ 3 𝑇̅ – average sample
temperature
1
𝑅𝑟𝑎𝑑 = − 𝑅𝑎𝑖𝑟 𝜎 – Stefan-
𝑅 − 2𝑅gl
Boltzmann constant
𝑅 = 𝛥𝑇⁄𝑞̅
Volumetric 𝑞𝑣 and integral 𝑄𝜏 heat release of 𝑞𝑣 = 𝛥𝑞⁄ℎ 𝛥𝑞 = |𝑞1 + 𝑞2 |
thermolabile materials – heat flux recorded
𝜏
by HFM1, 2
𝑄𝜏 = ∫ 𝑞𝑣 𝑑𝜏
𝜏0
Particular interest for modern technologies of monolithic frame construction is the study of the
process of hydration of concrete mixtures and forecasting the strength and durability of building
structures. Design of the information-measuring system, as well as technical characteristics allows to
study the thermophysical parameters of thermolabile substances during long-time range (up to several
days). In one experiment, it is possible to measure the current values of heat output during hydration of
binders or concrete and their thermal conductivity for 72 hours, as required by the relevant standards,
in the range of temperature values, which is of greatest interest in these studies. A special cuvette with
a prepared sample of concrete mixture is inserted into the measuring cell of the system and the intensity
of its heat release during hydration is recorded according to the signals of heat flux sensors (see Table
1) [11]. The result of calorimetric analysis is to obtain thermokinetic information, which allows to give
recommendations on the composition of concrete and conclude the need to adjust the composition in a
certain direction, the favorable modes of hardening of concrete, taking into account the influence of
technological factors. From the analysis Table. 1, the main information parameters when measuring
several thermophysical characteristics are the values of heat flux and temperature, as well as the
geometric parameters of the sample.
3. Hardware-software modules of the system
The hardware part of the system consists from modules for setting and maintaining measurement
modes and modules for recording primary data [14].
The module for setting and maintaining measurement mode consists from four units that perform
the functions of setting and monitoring the thermal modes of the system.
The unit for setting and maintaining the reference temperature is implemented using a temperature
regulator of the reference junctions of thermocouples, which controls the thermostat device of the
reference junctions to set a stable value of the temperature of the thermocouples of the reference
junctions of all measuring thermocouples.
The unit for setting and maintaining the temperature of the heater is implemented using a
temperature regulator that controls the electric heater for setting the temperature depending on the
operating mode.
The units for setting and maintaining the temperature of the cooler and the side insulation have
separate temperature regulator, which respectively controls the mode of operation of the cooler and the
side insulation.
The module of registration of primary data consists of units for registration temperature and heat
fluxes. These units receive signals from analog temperature sensors and heat flux sensors, which are
built into the heat and cooler units. ADC modules with a bit rate of 16 bits and a conversion frequency
of 10 Hz were used for these tasks.
The software part of the system can be divided into a module for control system of the system and
a module for processing measuring information [15,16].
The Module for control system of the system operation provides system settings, general control of
operating modes, system settings also it responds for displaying measurement information using 2D
graphs and tables. Also, the unit for control of the system operation connected with pre-censorship unit
in receiving and processing measurement information. In the case of an error, the control module
decides to send an additional request to the ADC modules or stop the measurement process and provides
the relevant information to the operator.
The module of processing of the measuring information consists of units for pre-censorship,
processing of the measured data, and data storage. This module also includes a unit for analysis of
metrological characteristics that can be used for calibration and recalibration of the system according
to the main indicators.
The pre-censorship unit of measurement data is designed to avoid cases of storage of data with
errors, such as those arising from the transmission of information and the exclusion of measurement
data with excessive errors.
The measured data processing unit converts the signals received from the ADC using polynomials
into temperature (K) and heat fluxes (W / m2). A separate polynomial is defined for each channel. In
the future, data processing is carried out in accordance with the formulas given in Table 1.
The data storage unit stores the processed thermophysical characteristics and the values of the
signals used for processing. This allows if necessary to conduct post signal processing after recalibration
of the system.
Hardware-software modules of the system
Module for setting and Module for control
Module for recording system of the Module for processing
maintaining
primary data system measuring information
measurement mode
Unit for setting
and maintaining Pre-censorship
the temperature unit
Unit for
of the heater registration System settings
unit for setting temperature unit Measured data
and maintaining processing unit
the temperature
of the cooler Unit for general
control of Unit for analysis
Unit for setting and Unit for operating modes
maintaining the registration heat of metrological
side insulation fluxes characteristics
temperature
Unit for setting and Unit for for
maintaining the displaying
reference Data storage unit
measurement
temperature information
Figure 2: The structure of Hardware- software system modules
The metrological characteristics analysis unit can be used for verification of the calibration. For this
task unit able work with methods based on using reference materials and working standards as well as
an indirect method.
4. Determination the metrological characteristics of the system
4.1. Technique for determining metrological characteristics using
reference materials and working standards
In practice, working standards act as a means of maintaining the uniformity of measurements of
product properties. One of the most important advantages of their use is the ability to calibrate the
working device in conditions close to operational ones, and to verify it directly at the operation site [3].
The working standard acts as a material carrier of the corresponding units, its main metrological
characteristics are the values of the physical quantity and its error.
According to a standardized technique [1-3], the process is carried out by comparing the thermal
conductivity measured value of the reference standard with the value indicated in its certificate or
corresponding regulatory document. As thermal conductivity reference materials Polymethyl
methacrylate, optical glasses LK5 and KV6, High Density Expanded Polystyrene are used. Error of the
thermal conductivity working standard have to be no more than ± 3%, which must be confirmed by the
appropriate certificate.
Thermal conductivity measurement range of the system is determined in experimental studies of the
basic relative error at one fixed sample temperature from the values range close to room temperature
using standard thermal conductivity measures and a control sample from granite.
To determine the basic relative error of the thermal conductivity measuring and establish its
boundaries, experiments are performed at three temperature points of the working temperature range
corresponding to its beginning, middle and end using one thermal conductivity working standard –
optical glass LK5, because its thermal conductivity lies in the middle part measuring range. The list of
materials – working standards of thermal conductivity and their characteristics at certain points of the
temperature range are given in Table 2.
Table 2
Reference standards characteristics at fixed temperature points for metrological certification
Reference standard Sample temperature Thermal conductivity
𝑇, K 𝜆𝑅 , W/(m·K)
Polystyrene EPS HD 290 ± 3 0,047 ± 0,0014
Polymethyl methacrylate 290 ± 3 0,195 ± 0,0059
Optical glass LK5 290 ± 3 1,165 ± 0,0350
Optical glass KV6 290 ± 3 1,350 ± 0,0405
Granite 290 ± 3 2,907 ± 0,0872
Optical glass LK5 250 ± 5 1,094 ± 0,0328
Optical glass LK5 320 ± 5 1,214 ± 0,0364
Optical glass LK5 390 ± 5 1,317 ± 0,0395
In the process of the metrological characteristics studying the reference or control sample is placed
in the system thermal block measuring cell. After establishing a stationary temperature regime, a series
of measurements the sample's thermal conductivity values is carried out. As a result of measurement
data processing in each temperature mode the basic relative measurement error limit is ± 6%, since it
includes the thermal conductivity working standards error ± 3% [11].
So, the metrological characteristics of the system evaluation by the comparison method need to have
several working standards, their characteristics have to cover the range of the desired thermophysical
quantity and be confirmed by studies on the standard device. In this case, the error value of the working
measuring instruments certified with their help includes the error of the working standard and, based
on the example of the thermal conductivity study devices, it is twice the normalized in [1, 3]. To
eliminate these inconsistencies and simplify research, a technique for determining the metrological
characteristics of a measuring system by an indirect method has been developed.
4.2. Technique for determining metrological characteristics by indirect
method
The measurement system calibration is carried out according to the technique [20]. The individual
static transfer functions each of two HFM are determined by the method of two measurements using a
special certification electric heater. Individual calibration of primary thermocouples is carried out using
a reference resistive temperature transducer Pt100 – a 3rd category working standard in the temperature
range from 220 K to 430 K.
The information-measuring system metrological characteristics determination is reduced to the
evaluation the range and the main relative measurement error of the desired value and the range of the
operating temperature. Taking into account that 𝜆 = 𝑓 (𝑇, 𝑞), 𝑅 = 𝑓 (𝑇, 𝑞, 𝐺1 … 𝐺𝑛 ),
𝜀 = 𝑓 (𝑇, 𝑞, 𝐺1 … 𝐺𝑛 ), where 𝐺1 … 𝐺𝑛 are geometric parameters of the sample, this procedure can be
implemented according to the indirect measurements method by evaluating the measurement error
components of the parameters used in determining the thermophysical characteristics: heat flux density
𝑞, temperature values T, as well as geometric parameters of the sample 𝐺1 … 𝐺𝑛 .
As a basis the definition of thermal conductivity metrological characteristics can be accepted [18,
19]. In this case, according to ISO [1, 3], are determined:
• the standard deviation of the measurement result error (RMSD);
• non-excluded systematic error (NSE);
• standard measurement uncertainties.
The total error of measuring the thermal conductivity in the developed system characterized by the
RMSD and NSE was determined by the computational and experimental method for studying individual
errors in measuring basic physical quantities. Components of the error in measuring the heat flux density
and the temperature values difference were determined experimentally using a special certification
electric heater and a reference resistive temperature transducer, respectively [20]. Standard measuring
instruments, such as digital multimeters Picotest M3500A and Fluke 8845A, reference electrical
resistance coil, DC voltage regulator and a digital caliper, are also used [22–25].
The measuring system metrological characteristics determination is carried out according to the
developed algorithm (Figure 3).
The experiments are performed in 10 consecutive thermal regimes in the process of investigating
the components of the error in measuring the heat flux density. The first five modes are carried out at
one constant temperature value, but at different total heat flux values set by the calibration heater, which
correspond to 5%, 25%, 50%, 75% and 95% of the heat flux density measurement range. The following
five modes are carried out at five points of the measuring system operating temperature range
corresponding to 5%, 25%, 50%, 75% and 95% of its value, but at one constant heat flux density value
equal to the middle of its operating range. In each mode, the temperature of the heater, cooler and lateral
isolation is set identical by the appropriate regulators.
Figure 3: Algorithm for determining the metrological characteristics of a measuring system
In each n-mode after reaching a thermal steady state the system software records and averages data
from the heat flux sensors and the electric heater during 20 minutes minimum. The NSE component of
the heat flux density measurement 𝜃𝑞 is taken equal to the value of the series of measurements relative
error 𝛿𝑞 :
𝜃𝑞 = 𝛿𝑞 , (1)
were 𝛿𝑞 − the relative error of the series of measurements in 10 modes, calculated by formula:
𝑁 (2)
1
𝛿𝑞 = ∑ 𝛿𝑞𝑛 , 𝑁 = 10
𝑁
𝑛=1
The root-mean-square deviation (RMSD) of the heat flux density measuring results 𝑆𝑞 is estimated
according to the measurement data in 10 modes by formula:
𝑁
(3)
1 2
𝑆𝑞 = √ ∑(𝛿𝑞𝑛 − 𝛿𝑞 )
𝑁−1
𝑛=1
The components of the temperature difference measurement error are investigated in seven
consecutive temperature modes of the operating temperature range. In each m-mode, the heater, cooler
and lateral isolation regulators are simultaneously set to the same beginning and ending temperatures,
wherein ∆𝑇 = 10 ± 2 К.
In each m-mode, the stationary state is monitored according to HFM data, the parameters for
regulating the heat flux density are not more than 2 W/m2, the set temperature values permissible
fluctuations have to be no more than ±0,5 К.
After reaching a thermal steady state the system software records and averages data from the
temperature sensors and reference resistive temperature transducer during 20 minutes minimum. The
NSE component of the temperature difference measurement 𝜃𝛥𝑇 is taken equal to the value of the series
of measurements relative error 𝛿𝛥𝑇 :
𝜃𝛥𝑇 = 𝛿𝛥𝑇 , (4)
were 𝛿𝛥𝑇 − the relative error of the series of measurements in 7 modes, calculated by formula:
𝑀 (5)
1
𝛿𝛥𝑇 = ∑ 𝛿𝛥𝑇𝑚 , 𝑀 = 7 .
𝑀
𝑚=1
RMSD of the temperature difference measuring results 𝑆𝛥𝑇 is estimated according to the
measurement data in 7 modes by formula:
𝑀
(6)
1 2
𝑆𝛥𝑇 = √ ∑ (𝛿𝛥𝑇𝑛 − 𝛿𝛥𝑇 )
𝑀−1
𝑚=1
NSE boundaries of the thermal conductivity measurement result 𝛩𝜆 are determined as a positive
square root of the sum of squares of all components of the systematic error, in measuring the heat flux
density and temperature difference, as well as the errors of all measuring devices calculated based on
data taken from manufacturer's specifications and calibration certificates, by formula:
2 (7)
𝛩𝜆 = 𝑘√∑ 𝛿𝑖
were k =1,96 − а coverage factor, which is chosen depending on the effective degrees of freedom at the
level of confidence р = 0,95 (see Table G.1 in Annex G [17]).
RMSD of the thermal conductivity measuring 𝑆𝜆 is estimated based on the results obtained as the
square root:
2 (8)
𝑆𝜆 = √𝑆𝑞2 + 𝑆𝛥𝑇 .
Assessment of measurement uncertainties (type A, B, total and extended) is carried out according to
the standard technique [17]. The results are presented in Table 3.
Table 3
Metrological characteristics
Components Designation Value, %
Non-excluded systematic error:
• heat flux density measurement 𝜃𝑞 0,32
• temperature difference measurement 𝜃∆𝑇 0,06
• thermal conductivity measurement 𝛩𝜆 1,25
RMSD:
• heat flux density measurement 𝑆𝑞 0,72
• temperature difference measurement 𝑆𝛥𝑇 0,63
• thermal conductivity measurement 𝑆𝜆 0,96
Type A evaluation of standard uncertainty 𝑢̂𝐴 0,96
Type B evaluation of standard uncertainty 𝑢̂В 0,72
Combined standard uncertainty 𝑢̂С 1,20
Expanded uncertainty (k = 1,96) 𝑈̂𝑃 2,35
These results demonstrate the validity of the developed technique with the requirements of modern
standards [1, 3]. This technique allows to pass the measurements range of the desired value with the
appropriate step in a wide range of temperatures. The software allows to set the required temperature
parameters, assess the stationarity of a stable thermal regime, record the readings of all measuring
sensors in a series of measurements, form a data bank, process information and switch to the next
temperature regime.
5. Conclusions
Analyzed methods for measuring thermophysical and thermal radiation characteristics of materials,
energy-efficient glass and thin coatings. Proposed method for measuring thermophysical characteristics
of concrete mixtures in a long-time interval and a wide temperature range. The main characteristics
which are necessary for carrying out measurements and metrological support are defined.
The hardware-software module of unified system for research of thermophysical characteristics
based on proposed methods is suggested and implemented. The proposed software allows to set the
required temperature parameters, assess the thermal regime, record the readings of all measuring
sensors in a series of measurements, form a data bank, process information. Also, the proposed
construction of heat module system meets requirements of the standard ISO 8301 [1].
Methods of analysis the metrological characteristics using working standards as well as indirect
method are implemented in system. An algorithm for determining the metrological characteristics of a
measuring system is proposed. Presented the metrological studies results of the measuring system.
The results of this study can be used to simplification measurements of thermal characteristics using
a single intelligent information- measurement system. Also, the results of this study improve the data
processing and exclude subjective factor during measurements.
6. Acknowledgements
These researches have been performed within the project № 19 1.7.1.902 «Information-measuring
system for thermophysical characteristics of materials and products studying».
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