UDC 536.2.083; 536.2.081.7; 536.212.2; 536.24.021 A. V. Luzina, A. V. Rudin
MEASURING THE THERMAL CONDUCTIVITY OF METALLIC SAMPLES BY THE STATIONARY HEAT FLOW METHOD
Annotation. The technique is described and design features installations for measuring the thermal conductivity of metal samples made in the form of a homogeneous cylindrical rod or a thin rectangular plate by the method of stationary heat flow. Heating of the test sample is carried out by means of direct electric heating with a short pulse alternating current, fixed in massive copper current clamps, which simultaneously perform the function of a heat sink.
Keywords: coefficient of thermal conductivity, sample, Fourier's law, stationary heat transfer, measuring device, transformer, multimeter, thermocouple.
Introduction
The transfer of thermal energy from more heated parts of a solid body to less heated ones by means of randomly moving particles (electrons, molecules, atoms, etc.) is called the phenomenon of thermal conductivity. The study of the phenomenon of thermal conductivity is widely used in various industries, such as: oil, aerospace, automotive, metallurgical, mining, etc.
There are three main types of heat transfer: convection, thermal radiation and thermal conductivity. Thermal conductivity depends on the nature of the substance and its physical state. In this case, in liquids and solids (dielectrics), energy transfer is carried out by elastic waves, in gases - by collision and diffusion of atoms (molecules), and in metals - by diffusion of free electrons and with the help of thermal vibrations of the lattice. The transfer of heat in a body depends on whether it is in a gaseous, liquid or solid state.
The mechanism of heat conduction in liquids is different from the mechanism of heat conduction in gases and has much in common with the heat conduction of solids. In areas with elevated temperature, there are vibrations of molecules with a large amplitude. These vibrations are transmitted to adjacent molecules, and thus the energy of thermal motion is transferred gradually from layer to layer. This mechanism provides a relatively small value of the thermal conductivity. With increasing temperature, for most liquids, the thermal conductivity decreases (the exception is water and glycerin, for which the thermal conductivity increases with increasing temperature).
The phenomenon of transfer of kinetic energy by means of molecular motion in ideal gases is due to the transfer of heat through heat conduction. Due to the randomness of molecular motion, molecules move in all directions. Moving from places with a higher temperature to places with a lower temperature, the molecules transfer the kinetic energy of movement due to paired collisions. As a result of molecular motion, there is a gradual equalization of temperature; in an unevenly heated gas, heat transfer is the transfer of a certain amount of kinetic energy during the random (chaotic) movement of molecules. As the temperature decreases, the thermal conductivity of gases decreases.
In metals, the main heat transmitter is free electrons, which can be likened to an ideal monatomic gas. Therefore, with some approximation
The coefficient of thermal conductivity of building and thermal insulation materials increases with temperature, and increases with bulk density. The thermal conductivity coefficient strongly depends on the porosity and moisture content of the material. Thermal conductivity various materials varies in the range: 2-450 W / (m K) .
1. Heat equation
The law of heat conduction is based on the Fourier hypothesis about the proportionality of the heat flow to the temperature difference per unit length of the heat transfer path per unit time. Numerically the coefficient of thermal conductivity equal to the number heat flowing per unit time through a unit surface, with a temperature drop per unit length of the normal equal to one degree.
According to Fourier's law, the surface heat flux density h is proportional to
nal temperature gradient -:
Here the factor X is called the coefficient of thermal conductivity. The minus sign indicates that heat is transferred in the direction of decreasing temperature. The amount of heat that has passed per unit of time through a unit of isothermal surface is called the heat flux density:
The amount of heat passing per unit time through the isothermal surface B is called the heat flux:
O = | chB = -1 -kdP^B. (1.3)
The total amount of heat that has passed through this surface S during the time t is determined from the equation
From=-DL-^t. (1.4)
2. Boundary conditions for thermal conductivity
Exists various conditions uniqueness: geometric - characterizing the shape and dimensions of the body in which the process of heat conduction takes place; physical - characterizing the physical properties of the body; temporary - characterizing the distribution of body temperature at the initial moment of time; boundary - characterizing the interaction of the body with the environment.
Boundary conditions of the first kind. In this case, the temperature distribution on the body surface is set for each moment of time.
Boundary conditions of the second kind. In this case, the value of the heat flux density for each point of the body surface at any time is given:
Yara \u003d I (X, Y, 2.1).
Boundary conditions of the third kind. In this case, the temperature of the medium T0 and the conditions for heat exchange of this medium with the surface of the body are set.
Boundary conditions of the IV kind are formed on the basis of the equality of heat fluxes passing through the contact surface of the bodies.
3. Experimental setup for measuring the thermal conductivity
Modern methods determination of thermal conductivity coefficients can be divided into two groups: methods of stationary heat flow and methods of non-stationary heat flow.
In the first group of methods, the heat flux passing through a body or system of bodies remains constant in magnitude and direction. The temperature field is stationary.
The non-stationary regime methods use a time-varying temperature field.
In this work, one of the methods of stationary heat flow, the Kohlrausch method, is used.
The block diagram of the installation for measuring the thermal conductivity of metal samples is shown in fig. one.
Rice. 1. Block diagram of the measuring setup
The main element of the installation is a power step-down transformer 7, the primary winding of which is connected to an autotransformer of the LATR 10 type, and the secondary winding, made of a rectangular copper bus with six turns, is directly connected to massive copper current clamps 2, which simultaneously perform the function of a heat sink-refrigerator . The test sample 1 is fixed in massive copper current clamps 2 with the help of massive copper bolts (not shown in the figure), which simultaneously perform the function of a heat sink. Temperature control at various points of the test sample is carried out using chromel-copel thermocouples 3 and 5, the working ends of which are directly fixed on the cylindrical surface of the sample 1 - one in the central part of the sample, and the other at the end of the sample. The free ends of thermocouples 3 and 5 are connected to multimeters of the DT-838 4 and 6 type, which allow temperature measurements with an accuracy of 0.5 °C. The sample is heated by direct electrical heating with a short pulse of alternating current from the secondary winding of the power transformer 7. The measurement of the current in the test sample is carried out indirectly - by measuring the voltage on the secondary winding of the ring current transformer 8, the primary winding of which is the power bus of the secondary winding of the power transformer 7 passed through the free gap of the annular magnetic core. The measurement of the voltage of the secondary winding of the current transformer is carried out by a multimeter 9.
The change in the magnitude of the pulsed current in the test sample is carried out using a linear autotransformer 10 (LATR), the primary winding of which is connected to the AC network with a voltage of 220 V through a series-connected mains fuse 13 and a button 12. The voltage drop across the test sample in the mode of direct electric heating is carried out with using a multimeter 14 connected in parallel directly to current clamps 2. The duration of current pulses is measured using an electric stopwatch 11 connected to the primary winding of a linear autotransformer 10. Switching on and off the heating mode of the test sample is provided by button 12.
When carrying out measurements of the thermal conductivity coefficient on the above-described installation, the following conditions must be met:
Homogeneity of the section of the test sample along the entire length;
The diameter of the test specimen must be between 0.5 mm and 3 mm (otherwise the main thermal power will stand out in power transformer, not in the test sample).
A diagram of the dependence of temperature on the length of the sample is shown in fig. 2.
Rice. 2. Dependence of temperature on sample length
As can be seen in the diagram, the dependence of temperature on the length of the sample under study is linear with a pronounced maximum in the central part of the sample, and at the ends it remains minimal (constant) and equal to the temperature environment during the time interval for establishing the equilibrium mode of heat transfer, which for this experimental setup does not exceed 3 minutes, i.e. 180 seconds.
4. Derivation of the working formula for the thermal conductivity coefficient
The amount of heat released in the conductor during the passage electric current, can be determined by the Joule-Lenz law:
Qel = 12-I^ = and I I, (4.1)
where u, I - voltage and current strength in the test sample; I am the sample resistance.
The amount of heat transferred through the cross section of the sample under study for a time interval t, made in the form of a uniform cylindrical rod of length t and cross section 5, can be calculated according to the Fourier law (1.4):
Qs \u003d R-dT- 5-t, (4.2)
where 5 \u003d 2-5 basic, 5 basic \u003d ^ 4-, at \u003d 2-DT \u003d 2- (Gmax -Gtk1); dt = Dt = 1-t.
Here, the coefficients 2 and 1/2 indicate that the heat flux is directed from
from the center of the sample to its ends, i.e. splits into two streams. Then
^^b \u003d S-R-(Gmax -Tm | n) -B^. (4.3)
5. Accounting for heat losses on the side surface
§Ozhr = 2- Bbok -DTha, (5.1)
where Bbok = n-th-1; a is the heat transfer coefficient of the surface of the test sample with the environment, having the dimension
temperature difference
DGx \u003d Tx - T0cr, (5.2)
where Tx is the temperature at a given point on the sample surface; Gocr - ambient temperature, can be calculated from the linear equation of the dependence of the sample temperature on its length:
Tx = T0 + k-x, (5.3)
where the angular coefficient k can be determined through the tangent of the slope of the linear dependence of the sample temperature on its length:
DT T - T T - T
k \u003d f \u003d MT * \u003d Tmax Ttt \u003d 2 "max Vr. (5.4)
Substituting expressions (5.2), (5.3) and (5.4) into equation (5.1), we obtain:
SQaup \u003d 2a-nd■ dx■ (+ kx-T0Kr) dt,
where T0 Tszhr.
8Q0Kp = 2a.nd ■ kx ■ dx ■ dt. (5.5)
After integrating expression (5.5), we obtain:
Q0Kp = 2nd■ dk j jdt■ x■ dx = 2nd-a-k■-I - | ■ t = -4a^nd■ k■ I2 ■ t. (5.6)
Substituting the obtained expressions (4.1), (4.3) and (5.6) into the heat balance equation
UIt = 8 ■X ■ S^ ^^-o ■t + -a^n ■d ■ -(Tmax - To) ■t.
Solving the resulting equation with respect to the thermal conductivity coefficient, we obtain:
u1 a £2 , l
The resulting expression makes it possible to determine the thermal conductivity coefficient of thin metal rods in accordance with the calculations performed for typical samples under study with a relative error
AU f (AI f (L(LH) ^ (At2
not exceeding 1.5%.
Bibliography
1. Sivukhin, D. V. General course of physics / D. V. Sivukhin. - M. : Nauka, 1974. - T. 2. - 551 p.
2. Rudin, A. V. Investigation of structural relaxation processes in glass-forming objects at various modes cooling / A. V. Rudin // News of higher educational institutions. Volga region. Natural Sciences. - 2003. - No. 6. - S. 123-137.
3. Pavlov, P. V. Solid state physics: textbook. manual for students studying in the specialties "Physics" / P. V. Pavlov, A. F. Khokhlov. - M.: Higher. school, 1985. - 384 p.
4. Berman, R. Thermal conductivity of solids / R. Berman. - M., 1979. - 287 p.
5. Livshits, B. G. Physical properties of metals and alloys / B. G. Livshits, V. S. Kraposhin. - M.: Metallurgy, 1980. - 320 p.
Luzina Anna Vyacheslavovna Luzina Anna Vyacheslavovna
undergraduate, master degree student,
Penza State University Penza State University E-mail: [email protected]
Rudin Alexander Vasilievich
Candidate of Physical and Mathematical Sciences, Associate Professor, Deputy Head of the Department of Physics, Penza State University E-mail: [email protected]
Rudin Alexander Vasil"evich
candidate of physical and mathematical sciences, associate professor,
deputy head of sub-department of physics, Penza State University
UDC 536.2.083; 536.2.081.7; 536.212.2; 536.24.021 Luzina, A.V.
Measurement of thermal conductivity of metal samples by the method of stationary heat flow /
A. V. Luzina, A. V. Rudin // Bulletin of the Penza State University. - 2016. - No. 3 (15). -WITH. 76-82.
21 State budgetary educational institution of higher vocational education Moscow Region "International University of Nature, Society and Man "Dubna" (University "Dubna")
2 CJSC Interregional Production Association for Technical Acquisition TECHNOKOMPLEKT (CJSC MPOTK TECHNOKOMPLEKT)
A method for measuring the thermal conductivity of polycrystalline diamond plates has been developed. The method includes the application of two thin-film resistance thermometers, made according to the bridge scheme, on opposite sides of the plate. On the one hand, at the location of one of the resistance thermometers, the plate is heated by contact with a hot copper rod. On the opposite side (at the location of another resistance thermometer), the plate is cooled by contact with a water-cooled copper rod. The heat flux flowing through the plate is measured by thermocouples mounted on a hot copper rod and controlled by an automatic device. Thin-film resistance thermometers deposited by the vacuum deposition method have a thickness of 50 nanometers and are almost integral with the plate surface. Therefore, the measured temperatures correspond exactly to the temperatures on opposite surfaces of the plate. The high sensitivity of thin-film resistance thermometers is ensured by the increased resistance of their resistors, which makes it possible to use a bridge supply voltage of at least 20 V.
thermal conductivity
polycrystalline diamond plates
thin film bridge temperature sensor
1. Bityukov V.K., Petrov V.A., Tereshin V.V. Methodology for determining the coefficient of thermal conductivity of translucent materials // International Thermophysical School, Tambov, 2004. - P. 3-9.
2. Dukhnovsky M.P., Ratnikova A.K. A method for determining the thermophysical characteristics of a material and a device for its implementation//RF Patent No. 2319950 IPC G01N25/00 (2006).
3. Kolpakov A., Kartashev E. Control of thermal regimes of power modules. //Components and technologies. - 2010. - No. 4. - S. 83-86.
4. Determination of the thermal conductivity of diamond polycrystalline films using the photoacoustic effect // ZhTF, 1999. - V. 69. - Issue. 4. - S. 97-101.
5. Installation for measuring the thermal conductivity of powder materials // Abstracts of reports submitted to the Third International Conference and the Third International School for Young Scientists and Specialists "Interaction of Hydrogen Isotopes with Structural Materials" (INISM-07). - Sarov, 2007. - S. 311-312.
6. Tsarkova O.G. Optical and thermophysical properties of metals, ceramics and diamond films during high-temperature laser heating // Proceedings of the Institute of General Physics. A.M. Prokhorova, 2004. - T. 60. - C. 30-82.
7. Minituarized thin film temperature sensor for wide range of measurement // Proc. of 2nd IEEE International workshop on advances in sensors and interfaces, IWASI. - 2007. - P.120-124.
Modern electronic components, especially power electronics, generate a significant amount of heat. To provide reliable operation of these components, heat sink devices are currently being created that use synthetic diamond plates with ultra-high thermal conductivity. Accurate measurement of the thermal conductivity of these materials is of great importance for the creation of modern power electronics devices.
To measure the thermal conductivity with acceptable accuracy in the main heat sink direction (perpendicular to the plate thickness), it is necessary to create a heat flux on the sample surface with a surface density of at least 20 due to the very high thermal conductivity of polycrystalline diamond heat sink plates. The methods described in the literature, using laser systems (see ), provide an insufficient surface heat flux density of 3.2 and, in addition, cause undesirable heating of the measured sample. Methods for measuring thermal conductivity using pulsed heating of a sample with a focused beam, and methods using the photoacoustic effect, are not direct methods, and therefore cannot provide the required level of reliability and accuracy of measurements, and also require complex equipment and cumbersome calculations. The measurement method described in the paper, which is based on the principle of plane thermal waves, is suitable only for materials with a relatively low thermal conductivity. The method of stationary thermal conductivity can only be used to measure thermal conductivity in the direction along the plate, and this direction is not the main direction of heat removal and is not of scientific interest.
Description of the selected measurement method
The required surface density of a stationary heat flux can be provided by contacting a hot copper rod on one side of the diamond plate and contacting a cold copper rod on the opposite side of the diamond plate. The measured temperature difference can then be small, for example only 2 °C. Therefore, it is necessary to accurately measure the temperature on both sides of the plate at the points of contact. This can be done using miniature thin-film resistance thermometers, which can be fabricated by vacuum deposition of a thermometer bridge measuring circuit onto the surface of a plate. The paper describes our previous experience in the design and manufacture of miniature high-precision thin-film resistance thermometers, which confirms the possibility and usefulness of using this technology in our case. Thin-film thermometers have a very small thickness of 50–80 nm, and therefore their temperature does not differ from the temperature of the surface of the plate on which they are deposited. The hot copper rod is heated by an electrically insulated nichrome wire wrapped around the rod for a considerable length to provide the necessary thermal power. The thermal conductivity of the copper rod ensures the transfer of a heat flux with a density of at least 20 in the axial direction of the rod. This heat flux is measured using two thin chromel-alumel thermocouples located at a given distance from each other in two sections along the axis of the rod. The heat flux passing through the plate is removed by means of a water-cooled copper rod. DowCorningTC-5022 silicone grease is used to reduce thermal resistance at the contact points of the copper rods with the plate. Thermal contact resistances do not affect the magnitude of the measured heat flux, they cause a slight increase in the temperature of the plate and heater. Thus, the thermal conductivity of the plate in the main direction of heat removal is determined by direct measurements of the magnitude of the heat flux passing through the plate and the magnitude of the temperature difference on its surfaces. For these measurements, a sample plate with dimensions of approximately 8x8mm can be used.
It should be noted that thin-film resistance thermometers can be used in the future to monitor the operation of power electronics products containing heat-removing diamond plates. The literature also emphasizes the importance of built-in thermal monitoring of power modules.
Description of the design of the stand, its main elements and devices
Thin film bridge temperature sensors
For high-precision temperature measurement, a bridge circuit of a resistance thermometer is deposited on the surface of a plate of polycrystalline artificial diamond by magnetron sputtering. In this circuit, two resistors are made of platinum or titanium, and the other two are made of nichrome. At room temperature, the resistances of all four resistors are the same and equal. Consider the case when two resistors are made of platinum. As the temperature changes, the resistance of the resistors increases:
Resistance sums: . The bridge resistance is . The value of the signal on the measuring diagonal of the bridge is equal to: U m= I 1 R 0 (1+ 3,93.10 -3 Δ T)- I 4 R 0 ( 1+0,4.10 -3 Δ T) .
With a small temperature change of several degrees, it can be assumed that the total bridge resistance is R0, the current through the bridge arm is 0.5.U0/R0, where U0 is the bridge supply voltage. Under these assumptions, we obtain the value of the measuring signal equal to:
U m= 0,5. U 0 . 3,53.10 -3 Δ T= 1,765.10 -3 .U 0 Δ T.
Let's assume that the value Δ T= 2? C, then at a supply voltage of 20 V we will obtain the value of the measuring signal equal to U m\u003d 70 mV. Taking into account that the error of measuring instruments will be no more than 70 μV, we find that the thermal conductivity of the plate can be measured with an error of no worse than 0.1%.
For strain and thermistors, the dissipated power is usually taken to be no more than 200 mW. With a supply voltage of 20 V, this means that the bridge resistance must be at least 2000 ohms. For technological reasons, the thermistor consists of n threads 30 microns wide, spaced 30 microns apart. The thickness of the resistor thread is 50 nm. The length of the resistor thread is 1.5 mm. Then the resistance of one thread of platinum is 106 ohms. 20 platinum threads will make up a resistor with a resistance of 2120 ohms. The width of the resistor will be 1.2 mm. The resistance of one nichrome thread is 1060 ohms. Therefore, a nichrome resistor will have 2 threads and a width of 0.12 mm. When two resistors R 0 , R 3 are made of titanium, the sensitivity of the sensor will decrease by 12%, however, instead of 20 platinum filaments, the resistor can be made of 4 titanium filaments.
Figure 1 shows a diagram of a thin-film bridge temperature sensor.
Fig.1. Thin film bridge temperature sensor
Plate sample 1 has a size of 8x8 mm and a thickness of 0.25 mm. The dimensions correspond to the case when platinum resistors are used, and nichrome resistors. The connections of 2 resistors to each other (shaded), contact pads 3,4,5,6 of the power buses and measurements are made with copper-nickel conductors. The circle of contact with the copper rods of the heater 7, on the one hand, and the cooler, on the other hand, has a diameter of 5 mm. Shown in Figure 1 circuit diagram resistance thermometer is applied on both sides of the sample plate. For electrical insulation, the surface of each resistance thermometer is coated with a thin film of silicon dioxide or silicon oxide using vacuum deposition.
Heating and cooling devices
To create a stationary temperature difference between the two surfaces of the diamond plate, a heater and a cooler are used (Figure 2).
Rice. 2. Stand scheme:
1 - housing, 2 - cooling housing, 3 - diamond plate, 4 - heater rod, 5 - nichrome wire, 6 - glass, 7 - thermal insulation, 8 - micrometric screw, 9 - housing cover, 10 - Belleville spring, 11, 12 - thermocouples, 13 - steel ball,
14 - base plate, 15 - screw.
The heater consists of an electrically insulated nichrome wire 5, which is wound on a copper rod of the heater 4. From the outside, the heater is closed with a copper tube 6 surrounded by thermal insulation 7. In the lower part, the copper rod 4 has a diameter of 5 mm and the end of the rod 4 is in contact with the surface of the diamond plate 3. On the opposite side, the diamond plate is in contact with the upper cylindrical part of the copper body 2 cooled by water (cooling body). 11,12-chromel-alumel thermocouples.
Let us denote the temperature measured by thermocouple 11, - the temperature measured by thermocouple 12, - the temperature on the surface of plate 3 from the heater side, - the temperature on the surface of plate 3 from the cooler side, and - the water temperature. In the described device, heat exchange processes take place, characterized by the following equations:
(1)
( (2)
)
(4)
where: - electric power of the heater,
Heater efficiency,
thermal conductivity of copper,
l is the length of the contact rod,
d- diameter of the contact rod,
Expected thermal conductivity of plate 3,
t-thickness of the plate,
Heat removal coefficient for water velocity,
cooling surface area,
Volumetric heat capacity of water,
D- diameter of the water pipe in the cooling case,
Change in water temperature.
Assume that the temperature difference across the plate is 2°C. Then a heat flux 20 passes through the plate. With a copper rod diameter of 5 mm, this heat flux corresponds to a power of 392.4 W. Taking the efficiency of the heater equal to 0.5, we get the electric power of the heater 684.8 W. From equations (3.4) it follows that the water almost does not change its temperature, and the temperature on the surface of the diamond plate 3 will be 11 is equal to = 248ºC.
To heat the copper rod 4, a nichrome wire 5 is used, insulated. The ends of the heater wires exit through the groove in the parts 4. The heater wires through thicker copper wires are connected to the PR1500 triac electric power amplifier, which is controlled by the TRM148 regulator. The controller program is set according to the temperature measured by thermocouple 11, which is used as a feedback for the controller.
The sample cooling device consists of a copper body 2 with a contact cylinder 5 mm in diameter in the upper part. Case 2 is water cooled.
The heating device is mounted on a Belleville spring 10 and is connected to the head of the fine screw 8 with the help of a ball 13, which is located in the recess of the part 4. The spring 10 allows you to adjust the voltage in the contact of the rod 4 with the sample 3. This is achieved by rotating the upper head of the fine screw 8 with a key. A certain movement of the screw corresponds to the known force of the spring 10. By making the initial calibration of the forces of the spring without a sample at the contact of the rod 4 with the body 2, we can achieve good mechanical contact of the surfaces at allowable stresses. If it is necessary to accurately measure the contact stresses, the design of the stand can be modified by connecting the body 2 with calibrated leaf springs to the lower part of the body of the stand 1.
Thermocouples 11 and 12 are installed, as shown in Figure 2, in narrow cuts in the head of rod 4. Thermocouple wire chromel and alumel with a diameter of 50 microns is welded together and covered with epoxy glue for electrical insulation, then installed in its cut and fixed with glue. It is also possible to caulk the end of each type of thermocouple wire close to each other without forming a junction. At a distance of 10 cm to thin thermocouple wires, you need to solder thicker (0.5 mm) wires of the same name, which will be attached to the regulator and to the multimeter.
Conclusion
Using the method and measuring instruments described in this paper, it is possible to measure the thermal conductivity coefficient of synthetic diamond plates with high accuracy.
The development of a method for measuring thermal conductivity is carried out as part of the work "Development of advanced technologies and designs of products of intelligent power electronics for use in household and industrial equipment, in transport, in the fuel and energy complex and in special systems (power module with a polycrystalline diamond heat sink)" under the financial support of the Ministry of Education and Science Russian Federation under the state contract No. 14.429.12.0001 dated March 05, 2014
Reviewers:
Akishin P.G., Doctor of Physics and Mathematics, Senior Researcher (Associate Professor), Deputy Head of Department, Laboratory information technologies, Joint Institute for Nuclear Research (JINR), Dubna;
Ivanov VV, Doctor of Physics and Mathematics, Senior Researcher (Associate Professor), Chief Researcher, Laboratory of Information Technologies, Joint Institute for Nuclear Research (JINR), Dubna.
Bibliographic link
Miodushevsky P.V., Bakmaev S.M., Tingaev N.V. PRECISE MEASUREMENT OF THE SUPERHIGH THERMAL CONDUCTIVITY OF THE MATERIAL ON THIN PLATES // Modern Problems of Science and Education. - 2014. - No. 5.;URL: http://science-education.ru/ru/article/view?id=15040 (date of access: 02/01/2020). We bring to your attention the journals published by the publishing house "Academy of Natural History"
FEDERAL AGENCY FOR TECHNICAL REGULATION AND METROLOGY
NATIONAL
STANDARD
RUSSIAN
FEDERATION
COMPOSITES
Official edition
Strshdfttftsm
GOST R 57967-2017
Foreword
1 PREPARED BY Federal State unitary enterprise"All-Russian Research Institute of Aviation Materials" together with the Autonomous Non-Profit Organization "Center for Rationing, Standardization and Classification of Composites" with the participation of the Association legal entities"Union of Composites Manufacturers" based on the official translation into Russian of the English version of the standard specified in paragraph 4, which is made by TC 497
2 INTRODUCED by the Technical Committee for Standardization TK 497 "Composites, structures and products from them"
3 APPROVED AND INTRODUCED BY Order federal agency on technical regulation and metrology dated November 21, 2017 No. 1785-st
4 This standard is modified from ASTM E1225-13 Standard Test Method for Thermal Conductivity of Solids Using the Guard ed-Comparative -Longitudinal Heat Flow Technique", MOD) by changing its structure to bring it in line with the rules established in GOST 1.5-2001 (subsections 4.2 and 4.3).
This standard does not include clauses 5. 12. subclauses 1.2, 1.3 of the applied ASTM standard. which it is inappropriate to use in the Russian national standardization due to their redundancy.
The specified clauses and subclauses, not included in the main part of this standard, are given in the additional appendix YES.
The name of this standard has been changed relative to the name of the specified ASTM standard to bring it into line with GOST R 1.5-2012 (subsection 3.5).
A comparison of the structure of this standard with the structure of the specified ASTM standard is given in the additional appendix DB.
Information about the compliance of the reference national standard with the ASTM standard. used as a reference in the applied ASTM standard. are given in the additional appendix DV
5 INTRODUCED FOR THE FIRST TIME
Rules for the application of this standard are set out in clause 26 federal law dated June 29, 2015 N9 162-FZ "On standardization in the Russian Federation". Information about changes to this standard is published in the annual (as of January 1 of the current year) information index "National Standards", and the official text of the changes and half a year - in the monthly information index "National Standards". In case of revision (replacement) or cancellation of this standard, a corresponding notice will be published in the next issue of the monthly information index "National Standards". Relevant information. notification and texts are also placed in information system common use- on the official website of the Federal Agency for Technical Regulation and Metrology on the Internet ()
© Stamdartinform. 2017
This standard cannot be fully or partially reproduced, replicated and distributed as an official publication without the permission of the Federal Agency for Technical Regulation and Metrology
GOST R 57967-2017
1 area of use............................................... ..................one
3 Terms, definitions and designations............................................... .......one
4 Essence of the method.................................................... ...................2
5 Equipment and materials............................................................... .............4
6 Preparing for testing .............................................................. .......eleven
7 Testing .............................................................................. ...............12
8 Processing test results .................................................................. .......thirteen
9 Test report............................................................... ..................thirteen
Annex YES (informative) Original text of structural elements not included
applied ASTM standard .................................................15
Annex DB (informative) Comparison of the structure of this standard with the structure
the ASTM standard applied in it ............................................... 18
Annex DV (informative) Information on the compliance of the reference national standard with the ASTM standard. used as a reference in the applied ASTM standard .................................................................. .............nineteen
GOST R 57967-2017
NATIONAL STANDARD OF THE RUSSIAN FEDERATION
COMPOSITES
Determination of the thermal conductivity of solids by the method of stationary one-dimensional heat flow with a guard heater
Composites. Determination of thermal conductivity of soHds by stationary one-dimensional heat flow
with a guard heater technique
Introduction date - 2018-06-01
1 area of use
1.1 This International Standard specifies the determination of the thermal conductivity of homogeneous opaque solid polymer, ceramic and metal composites by the steady-state one-dimensional heat flow method with a guard heater.
1.2 This International Standard is intended for use in testing materials having an effective thermal conductivity in the range of 0.2 to 200 W/(m-K) in the temperature range of 90 K to 1300 K.
1.3 This standard can also be applied to materials having effective thermal conductivity outside the specified ranges with lower accuracy.
2 Normative references
This standard uses normative references to the following standards:
GOST 2769 Surface roughness. Parameters and characteristics
GOST R 8.585 State system ensuring the uniformity of measurements. Thermocouples. Rated static conversion characteristics
Note - When using this standard, it is advisable to check the validity of reference standards in the public information system - on the official website of the Federal Agency for Technical Regulation and Metrology on the Internet or according to the annual information index "National Standards", which was published as of January 1 of the current year, and on issues of the monthly information index "National Standards" for the current year. If an undated referenced reference standard has been replaced, it is recommended that the current version of that standard be used, taking into account any changes made to that version. If the reference standard to which the dated reference is given is replaced, then it is recommended to use the version of this standard with the year of approval (acceptance) indicated above. If, after the approval of this standard, a change is made to the reference standard to which the dated screed is given, affecting the provision to which the reference is given, then this provision is recommended to be applied without taking into account this change. If the reference standard is canceled without replacement, then the provision in which the reference to it is given is recommended to be applied in the part that does not affect this reference.
3 Terms, definitions and symbols
3.1 The following terms are used in this standard with their respective definitions:
3.1.1 thermal conductivity /.. W / (m K): The ratio of the heat flux density under stationary conditions through a unit area to a unit temperature gradient e direction perpendicular to the surface.
Official edition
GOST R 57967-2017
3.1.2 apparent thermal conductivity represent the apparent or effective thermal conductivity.
3.2 8 of this standard, the following designations are used:
3.2.1 X M (T), W / (m K) - thermal conductivity of reference samples depending on temperature.
3.2.2 Eci, W/(m K) - thermal conductivity of the upper reference sample.
3.2.3 Xjj'. 8t/(m K) - thermal conductivity of the lower reference sample.
3.2.4 edT), W / (m K) - thermal conductivity of the test sample, corrected for heat transfer, if necessary.
3.2.5 X "$ (T), W / (m K) - thermal conductivity of the test sample, calculated without correction for heat transfer.
3.2.6 >y(7), W/(m K) - thermal conductivity of insulation depending on temperature.
3.2.7 T, K - absolute temperature.
3.2.8 Z, m - the distance measured from the top end of the package.
3.2.9 /, m - length of the test sample.
3.2.10 G (, K - temperature at Z r
3.2.11 q", W / m 2 - heat flux per unit area.
3.2.12 ZX LT, etc. - deviations X. G. etc.
3.2.13 g A, m is the radius of the test specimen.
3.2.14 g in, m - the inner radius of the protective shell.
3.2.15 f 9 (Z), K - the temperature of the containment shell depending on the distance Z.
4 Essence of the method
4.1 General scheme method of stationary one-dimensional heat flow using a security heater is shown in Figure 1. Test sample with unknown thermal conductivity X s . having an estimated thermal conductivity X s // s . placed under load between two reference specimens of thermal conductivity X m having the same cross-sectional area and thermal conductivity X^//^. The design is a package consisting of a disk heater with a test sample and reference samples on each side between the heater and the heat sink. A temperature gradient is created in the test package, heat losses are minimized by using a longitudinal guard heater having approximately the same temperature gradient. Approximately half of the energy flows through each sample. In the equilibrium state, the thermal conductivity coefficient is determined from the measured temperature gradients* of the test sample and the corresponding reference samples and the thermal conductivity of the reference materials.
4.2 Apply force to the bag to ensure good contact between the samples. The package is surrounded by an insulating material with thermal conductivity. The insulation is enclosed in a protective shell * with a radius of r 8, located at a temperature T d (2). Establish a temperature gradient in the bag by maintaining the upper part at a temperature of T t and the lower part at a temperature of T in. Temperature T 9 (Z) is usually a linear temperature gradient, approximately corresponding to the gradient set in the test package. An isothermal security heater with temperature T ? (Z). equal to the average temperature of the test sample. It is not recommended to use the design of the instrument's measuring cell without protective heaters due to possible large heat losses, especially at elevated temperatures. At steady state, the temperature gradients along the sections are calculated from the measured temperatures along the two reference samples and the test sample. The value of X "s without taking into account the correction for heat transfer is calculated by the formula ( conventions shown in Figure 2).
T 4 -G 3 2 U 2 -Z, Z e -Z 5
where Г, - temperature at Z,. K T 2 - temperature at Z 2, K G 3 - temperature at Z 3. TO
GOST R 57967-2017
Г 4 - temperature at Z 4 . TO;
Г 5 - temperature at Z s . TO:
Г в - temperature at Z e. TO:
Z, - coordinate of the 1st temperature sensor, m;
Zj - coordinate of the 2nd temperature sensor, m;
Z 3 - coordinate of the 3rd temperature sensor, m;
Z 4 - coordinate of the 4th temperature sensor, m;
Z 5 - coordinate of the 5th temperature sensor, m;
Z e - coordinate of the 6th temperature sensor, m.
Such a scheme is idealized, since it does not take into account the heat transfer between the package and the insulation at each point and the uniform heat transfer at each interface between the reference samples and the test sample. The errors caused by these two assumptions can vary greatly. Because of these two factors, there should be restrictions on this method tests. if you want to achieve the required accuracy.
1 - temperature gradient in the protective shell; 2 - temperature gradient in the package; 3 - thermocouple: 4 - clamp.
S - upper heater. b - upper reference sample: 7 - lower reference sample, c - lower heater: c - refrigerator. 10 - upper security heater: I - security heater
Figure 1 - Diagram of a typical test package and containment, showing the correspondence of temperature gradients
GOST R 57967-2017
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b
Refrigerator
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Insulation; 2 - security heater. E - metal or ceramic protective shell: 4 - heater. S - reference sample, b - test sample, x - approximate location of thermocouples
Figure 2 - Scheme of the method of one-dimensional stationary heat flow using a security heater, indicating possible locations for installing temperature sensors
5 Equipment and materials
5.1 Reference samples
5.1.1 For reference samples, reference materials or reference materials shall be used with known values thermal conductivity. Table 1 lists some of the commonly recognized reference materials. Figure 3 shows an example change in >. m with temperature * tura.
GOST R 57967-2017
Typlofoaodoost, EGL^m-K)
Figure 3 - Reference values of thermal conductivity of reference materials
NOTE The material chosen for the reference specimens should have a thermal conductivity that is closest to that of the material being measured.
5.1.2 Table 1 is not exhaustive and other materials may be used as reference. The reference material and the source of X m values must be specified in the test report.
Table 1 - Reference data for the characteristics of reference materials
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End of table 1
Table 2 - Thermal conductivity of electrolytic iron
|
Temperature. TO |
Thermal conductivity. W/(m K) |
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Table 3 - Thermal conductivity of tungsten
|
Temperature, K |
Thermal conductivity. 6t/(mK) |
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Table 4 - Thermal conductivity of austenitic steel
|
Temperature. TO |
Thermal conductivity, W/(m K) |
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End of table 4
5.1.3 Requirements for any reference materials include stability of properties over the entire operating temperature range, compatibility with other components of the instrument's measuring cell, ease of attachment of the temperature sensor, and accurately known thermal conductivity. Since the errors due to heat loss for a particular increase in k are proportional to the change in k and Jk s , reference material c) should be used for reference samples. m closest to >. s .
5.1.4 If the thermal conductivity of the test specimen k s is between the values of the thermal conductivity coefficient of the two reference materials, a reference material with a higher thermal conductivity k u should be used. to reduce the overall temperature drop along the package.
5.2 Insulating materials
As insulating materials, powder, dispersed and fibrous materials are used to reduce the radial heat flux into the annular space surrounding the package and heat losses along the package. There are several factors to consider when choosing insulation:
The insulation must be stable over the expected temperature range, have a low thermal conductivity k, and be easy to handle;
The insulation must not contaminate instrument measuring cell components such as temperature sensors, it must be of low toxicity and must not conduct electricity.
Powders and solids are usually used as they are easy to compact. Low density fiber mats can be used.
5.3 Temperature sensors
5.3.1 At least two temperature sensors shall be installed on each reference sample and two on the test sample. If possible, the reference samples and the test sample should contain three temperature sensors each. Additional sensors are needed to confirm the linearity of the temperature distribution along the package or to detect an error due to an uncalibrated temperature sensor.
5.3.2 The type of temperature sensor depends on the size of the measuring cell of the instrument, the temperature range and the environment in the measuring cell of the instrument, determined by the insulation, reference samples, test sample and gas. Any sensor with sufficient accuracy can be used to measure the temperature, and the measuring cell of the device must be large enough so that the perturbation of the heat flow from the temperature sensors is negligible. Thermocouples are usually used. Their small size and ease of attachment are clear advantages.
5.3.3 Thermocouples shall be made of wire with a diameter not exceeding 0.1 mm. All cold junctions must be maintained at a constant temperature. This temperature is maintained by a chilled slurry, thermostat or electronic reference point compensation. All thermocouples shall be made from either calibrated wire or wire that has been certified by the supplier to meet the error limits specified in GOST R 8.585.
5.3.4 Thermocouple fastening methods are shown in Figure 4. Internal contacts can be obtained in metals and alloys by welding individual thermoelements to surfaces (Figure 4a). Butt-welded or bead-welded thermocouple junctions can be rigidly attached by hammering, cementing, or welding into narrow grooves or small holes (Figures 4b, 4c and 4 5.3.5 In Figure 46 the thermocouple is in a radial slot, while in Figure 4c the thermocouple is pulled through a radial hole in the material. 8 case of using a thermocouple in a protective sheath or a thermocouple, both thermocouples of which are in an electrical insulator with two GOST R 57967-2017 holes, the thermocouple mount shown in Figure 4d can be used. In the last three cases, the thermocouple must be thermally bonded to the solid surface with a suitable adhesive or high temperature adhesive. All four procedures shown in Figure 4 should include tempering wires on surfaces, wrapping wires in isothermal areas, thermally grounding wires on a guard, or a combination of all three. 5.3.6 Since the inaccuracy of the location of the temperature sensor leads to large errors. special attention must be paid to determining the correct distance between the sensors and calculating the possible error resulting from any inaccuracy. c - internal cheese shoye with separated thermoelements welded to the test specimen or reference specimens in such a way that the signal passes through the material. 6 - a radial groove on a flat surface for attaching a bare wire or a ceramic-insulated thermocouple sensor; c a small radial hole drilled through the test piece or reference pieces and an uninsulated (allowed if the material is an electrical insulator) or insulated thermocouple threaded through the hole: d a small radial hole drilled through the test piece or reference pieces and the thermocouple , placed about the hole Figure 4 - Mounting of thermocouples NOTE In all cases, thermocouples should be thermally hardened or thermally grounded to the containment to minimize measurement error due to heat flow to or from the hot junction. 5.4 Loading system 5.4.1 The test method requires uniform heat transfer across the interface between the reference specimens and the test specimen when the temperature sensors are within rk of the interface. To do this, it is necessary to ensure uniform contact resistance. GOST R 57967-2017 The variation in the adjacent areas of the reference specimens and the test specimen, which can be created by applying an axial load in combination with a conductive medium at the interfaces. It is not recommended to carry out measurements in a vacuum, unless it is required for protective purposes. 5.4.2 When testing materials with low thermal conductivity, thin test specimens are used, so temperature sensors should be installed close to the surface. In such cases, a very thin layer of a highly thermally conductive liquid, paste, soft metal foil or screen must be introduced at the interfaces. 5.4.3 The design of the measuring instrument shall provide means for imposing a reproducible and constant load along the package in order to minimize interfacial resistances at the interfaces between the reference samples and the test sample. The load may be applied pneumatically, hydraulically, by spring action, or by positioning a load. The above load application mechanisms are constant as the package temperature changes. In some cases, the compressive strength of the test specimen may be so low that the applied force must be limited by the weight of the upper reference specimen. In this case, special attention must be paid to errors that can be caused by poor contact, for which the temperature sensors must be located away from any disturbance in the heat flow at the interfaces. 5.5 Protective shell 5.5.1 The package consisting of the test sample and reference samples shall be enclosed in a protective sheath with correct circular symmetry. The protective sheath may be metal or ceramic, and its inner radius must be such that the ratio r^r A is in the range from 2.0 to 3.5. The guard shell must contain at least one guard heater to control the temperature profile along the shell. 5.5.2 The containment shall be designed and operated in such a way that its surface temperature is either isothermal and approximately equal to the average temperature of the test sample, or has an approximate linear profile matched at the top and bottom ends of the containment with the corresponding positions along the package. In each case, at least three temperature sensors must be installed on the containment at pre-coordinated points (see Figure 2) to measure the temperature profile. 5.6 Measuring equipment 5.6.1 The combination of the temperature sensor and the measuring instrument used to measure the output of the sensor shall be adequate to provide a temperature measurement accuracy of ± 0.04 K and an absolute error of less than ± 0.5 %. 5.6.2 The measuring equipment for this method shall maintain the required temperature and measure all relevant output voltages with an accuracy commensurate with the accuracy of the temperature measurement. temperature sensors. 6.1 Requirements for test specimens 6.1.1 The test pieces tested by this method are not limited to candy geometry. Most preferably, the use of cylindrical or prismatic specimens. The conduction regions of the test specimen and the reference specimens shall be the same to within 1 % and any difference in area shall be taken into account in the calculation of the result. For a cylindrical configuration, the radii of the test specimen and reference specimens shall agree to within ± 1 %. and the radius of the specimen to be tested, r A, shall be such that r B fr A is between 2.0 and 3.5. Each flat surface of the test and reference samples must be flat with a surface roughness of not more than R a 32 in accordance with GOST 2789. and the normals to each surface must be parallel to the axis of the sample with an accuracy of ± 10 min. NOTE In some cases this requirement is not necessary. For example, some instruments may consist of reference samples and test samples with high values of >. m and >. s . where errors due to heat loss are negligible for long sections. Such sections may be of sufficient length to allow GOST R 57967-2017 which should be used to mount the temperature sensors at a sufficient distance from the points of contact, thereby ensuring the uniformity of the heat flow. The length of the specimen to be tested shall be selected based on knowledge of radius and thermal conductivity. When). and higher than the thermal conductivity of stainless steel, long test specimens with a length of 0g A » 1 can be used. Such long test specimens allow the use of large distances between temperature sensors, and this reduces the error due to inaccuracy in the location of the sensor. When). m lower than the thermal conductivity of stainless steel, the length of the test specimen must be reduced, as the measurement error due to heat loss becomes too large. 6.1.2 Unless otherwise provided in normative document or technical documentation for the material. one test specimen is used for testing. 6.2 Hardware setup 6.2.1 Calibration and verification of equipment is performed in the following cases: After hardware assembly: If the ratio of X m to X s is less than 0.3. or more than 3. and it is not possible to select the values of thermal conductivities; If the shape of the test piece is complex or the test piece is small: If changes have been made to geometric parameters measuring cell of the device; If it has been decided to use other reference materials or insulation than those given in sections 6.3 and 6.4: If the equipment has previously operated to a temperature high enough that the properties of the components may change, such as. for example, the sensitivity of a thermocouple. 6.2.2 These checks shall be carried out by comparing at least two reference materials as follows: Select a reference material whose thermal conductivity is closest to the expected thermal conductivity of the test sample: The thermal conductivity X of a test specimen made from a reference material is measured using reference specimens made from another reference material which has an X value closest to that of the test specimen. For example, the test can be carried out on a sample of glass-ceramic. using reference samples made of stainless steel. If the measured thermal conductivity of the sample does not agree with the value in Table 1 after applying a heat transfer correction, the sources of error must be determined. 7.1 Select reference samples so that their thermal conductivity is of the same order of magnitude as expected for the test sample. After equipping the required reference samples with temperature sensors and placing them in the measuring cell, the test sample is equipped with similar means. The test specimen is inserted into the bag so that it is placed between the reference specimens and is in contact with adjacent reference specimens for at least 99% of each surface area. Soft foil or other contact media can be used to reduce surface resistance. If the measuring cell must be protected from oxidation during the test, or if the measurement requires a specific gas or gas pressure to control X /t, then the measuring cell is filled and purged with the working gas at the set pressure. To load the package, the force necessary to reduce the effects of uneven thermal resistance at the interface should be applied. 7.2 Turn on the top and bottom heaters at both ends of the bag and adjust until. while the temperature difference between points 2, and Zj. Z3 and Z4. and Z s and 2^ shall not be greater than 200 times the error of the temperature sensor, but not greater than 30 K. and the test specimen shall not be at the mean temperature required for the measurement. Despite. that an accurate temperature profile along the sheath is not required for 3. the power of the sheath heaters is controlled until the temperature profile along the sheath is T g )
6 Preparation for testing
7 Testing
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