Measuring the thermal conductivity of a material at home. Basic Research

Goal of the work: study of the methodology for experimental determination of the coefficient

thermal conductivity of solid materials by the plate method.

Exercise:1. Determine the thermal conductivity coefficient of the material under study.

2. Determine the dependence of the thermal conductivity coefficient on temperature

the material being studied.

BASIC PROVISIONS.

Heat exchange is a spontaneous irreversible process of heat transfer in space in the presence of a temperature difference. There are three main methods of heat transfer, which differ significantly in their physical nature:

thermal conductivity;

convection;

thermal radiation.

In practice, heat, as a rule, is transferred simultaneously in several ways, but knowledge of these processes is impossible without studying the elementary processes of heat transfer.

Thermal conductivity is the process of heat transfer caused by the thermal movement of microparticles. In gases and liquids, heat transfer by thermal conductivity occurs through the diffusion of atoms and molecules. IN solids However, the free movement of atoms and molecules throughout the entire volume of a substance is impossible and is reduced only to their vibrational motion relative to certain equilibrium positions. Therefore, the process of thermal conductivity in solids is caused by an increase in the amplitude of these oscillations, propagated throughout the volume of the body due to the disturbance of force fields between the oscillating particles. In metals, heat transfer by thermal conductivity occurs not only due to vibrations of ions and atoms located at the nodes of the crystal lattice, but also due to the movement of free electrons, forming the so-called “electron gas”. Due to the presence in metals of additional thermal energy carriers in the form of free electrons, the thermal conductivity of metals is significantly higher than that of solid dielectrics.

When studying the process of thermal conductivity, the following basic concepts are used:

Quantity of heat (Q  ) – thermal energy passing during the entire processthrough a surface of arbitrary area F. In the SI system it is measured in joules (J).

Heat flow (thermal power) (Q) – the amount of heat passing per unit time through a surface of arbitrary area F.

In the SI system, heat flow is measured in watts (W).

Heat flux density (q) – the amount of heat passing per unit time through a unit surface.

In the SI system it is measured in W/m2.

Temperature field– a set of temperature values at a given moment in time at all points of space occupied by a body. If the temperature at all points of the temperature field does not change over time, then such a field is called stationary, if it changes, then – non-stationary.

Surfaces formed by points having the same temperature are called isothermal.

Temperature gradient (gradT) – a vector directed along the normal to the isothermal surface in the direction of increasing temperature and numerically defined as the limit of the ratio of the temperature change between two isothermal surfaces to the distance between them along the normal when this distance tends to zero. Or in other words, the temperature gradient is the derivative of temperature in this direction.

The temperature gradient characterizes the rate of temperature change in the direction normal to the isothermal surface.

The process of thermal conductivity is characterized by the basic law of thermal conductivity - Fourier's law(1822). According to this law, the heat flux density transmitted through thermal conductivity is directly proportional to the temperature gradient:

where  is the thermal conductivity coefficient of the substance, W/(mdeg).

The (-) sign indicates that the heat flow and temperature gradient are opposite in direction.

Coefficient of thermal conductivity shows how much heat is transferred per unit time through a unit surface with a temperature gradient equal to unity.

The thermal conductivity coefficient is an important thermophysical characteristic of a material and knowledge of it is necessary when performing thermal calculations related to determining heat losses through the enclosing structures of buildings and structures, walls of machines and apparatus, calculating thermal insulation, as well as when solving many other engineering problems.

Another important law of thermal conductivity is Fourier-Kirchhoff law, which determines the nature of temperature changes in space and time during thermal conductivity. Its other name is differential heat equation, because it was obtained by methods of the theory of mathematical analysis based on Fourier’s law. For a 3-dimensional non-stationary temperature field, the differential equation of thermal conductivity has the following form:

Where
- thermal diffusivity coefficient, characterizing the thermal inertia properties of the material,

,C p , - respectively, the coefficient of thermal conductivity, isobaric heat capacity and density of the substance;

- Laplace operator.

For a one-dimensional stationary temperature field (
) the differential equation of thermal conductivity takes on a simple form

By integrating equations (1) and (2), it is possible to determine the heat flux density through the body and the law of temperature change inside the body during heat transfer by conduction. To obtain a solution, a task is required conditions of unambiguity.

Uniqueness conditions– this is additional private data characterizing the problem under consideration. These include:

Geometric conditions characterizing the shape and size of the body;

Physical conditions characterizing the physical properties of the body;

temporary (initial) conditions characterizing the temperature distribution at the initial moment of time;

boundary conditions characterizing the features of heat exchange at the boundaries of the body. There are boundary conditions of the 1st, 2nd and 3rd kind.

At boundary conditions of the 1st kind the distribution of temperatures on the surface of the body is specified. In this case, it is necessary to determine the heat flux density through the body.

At boundary conditions of the 2nd kind the heat flux density and the temperature of one of the surfaces of the body are specified. It is necessary to determine the temperature of another surface.

Under boundary conditions of the 3rd kind the conditions of heat transfer between the surfaces of the body and the media washing them from the outside must be known. From these data the heat flux density is determined. This case refers to the combined process of heat transfer by conduction and convection, called heat transfer.

Let's consider the simplest example for the case of heat conduction through a flat wall. Flat called a wall whose thickness is significantly less than its other two dimensions - length and width. In this case, the uniqueness conditions can be specified as follows:

geometric: wall thickness is known. The temperature field is one-dimensional, therefore the temperature changes only in the direction of the X axis and the heat flow is directed normal to the wall surfaces;.

physical: the wall material and its thermal conductivity coefficient are known, and for the whole body=const;

temporary: the temperature field does not change over time, i.e. is stationary;

border conditions: 1st kind, the wall temperatures are T 1 and T 2.

It is required to determine the law of temperature change along the wall thickness T=f(X) and the heat flux density through the wallq.

To solve the problem we use equations (1) and (3). Taking into account the accepted boundary conditions (at x=0T=T 1; at x=T=T 2) after double integration of equation (3) we obtain the law of temperature change along the wall thickness

The temperature distribution in a flat wall is shown in Fig. 1.

Fig.1. Temperature distribution in a flat wall.

The heat flux density is then determined according to the expression

Determining the thermal conductivity coefficient theoretically cannot give the accuracy of the result necessary for modern engineering practice, therefore the only reliable way remains its experimental determination.

One of the well-known experimental methods for determining is flat layer method. According to this method, the thermal conductivity coefficient of a flat wall material can be determined based on equation (5)

;

In this case, the obtained value of the thermal conductivity coefficient refers to the average temperature T m = 0.5 (T 1 + T 2).

Despite its physical simplicity, the practical implementation of this method has its own difficulties associated with the difficulty of creating a one-dimensional stationary temperature field in the samples under study and taking into account heat losses.

DESCRIPTION OF THE LABORATORY STAND.

Determination of the thermal conductivity coefficient is carried out on a laboratory installation based on the method of simulation of real physical processes. The installation consists of a PC connected to a layout of the work area, which is displayed on the monitor screen. The working area was created by analogy with the real one and its diagram is presented in Fig. 2.

Fig.2. Diagram of the installation working area

The working section consists of 2 fluoroplastic samples 12, made in the form of disks with a thickness of  = 5 mm and a diameter of d = 140 mm. The samples are placed between a heater 10 with a height h = 12 mm and a diameter d n = 146 mm and a refrigerator 11 cooled with water. The creation of heat flow is carried out by a heating element with electrical resistance R= 41 Ohm and refrigerator 11 with spiral grooves for directed circulation of cooling water. Thus, the heat flow passing through the fluoroplastic samples under study is carried away by the water flowing through the refrigerator. Part of the heat from the heater escapes through the end surfaces into the environment, therefore, to reduce these radial losses, a thermal insulating casing 13 made of asbestos cement is provided (k = 0.08 W/(mdeg)). The casing with a height of h k = 22 mm is made in the form of a hollow cylinder with an internal diameter d h = 146 mm and an outer diameter d k = 190 mm. The temperature is measured using seven Chromel-Copel thermocouples (type XK) pos. 1…7, installed at various points of the working area. Temperature sensor switch 15 allows you to sequentially measure the thermo-EMF of all seven temperature sensors. Thermocouple 7 is installed on the outer surface of the heat-insulating casing to determine heat leaks through it.

ORDER OF WORK.

3.1. The temperature mode of operation of the installation is selected by setting the temperature of the hot surface of the plates T g in the range from 35°C to 120°C.

3.2. On the installation console, the power switches for the indicator devices that record the voltage on the electric heater U, the thermo-EMF of the temperature sensors E and the heating switch are turned on in sequence.

3.3. By smoothly rotating the rheostat knob, the desired voltage is set on the heater. The rheostat is made in a step version, so the voltage changes in steps. Voltage U and temperature T g must be in accordance with each other according to the dependence presented in Fig. 3.

Fig.3. Working heating zone.

3.4. By sequentially interrogating temperature sensors using switch 15, the thermo-EMF values of seven thermocouples are determined, which, together with the value U, are entered into the experiment protocol (see Table 1). Registration of readings is carried out using indicator devices on the control panel, the readings of which are duplicated on the PC monitor.

3.5. At the end of the experiment, all regulatory bodies of the installation are transferred to their original position.

3.6. Repeated experiments are carried out (their total number must be at least 3) and at other values of Tg in the manner prescribed in paragraphs. 3.1…3.5.

PROCESSING OF MEASUREMENT RESULTS.

4.1. According to the calibration characteristic of a Chromel-Copel thermocouple, the readings of temperature sensors are converted to degrees on the Kelvin scale. .

4.2. The average temperatures of the internal hot and external cold surfaces of the samples are determined

where i is the thermocouple number.

4.3. The total heat flux created is determined electric heater

, W

where U is the electric current voltage, V;

R= 41 Ohm – resistance of the electric heater.

4.4. The heat flux lost as a result of heat transfer through the casing is determined

where k is a coefficient characterizing the process of heat transfer through the casing.

, W/(m 2 deg)

where  k = 0.08 W/(mdeg) – thermal conductivity coefficient of the casing material;

dn = 0.146 m – outside diameter heater;

dк = 0.190 m – outer diameter of the casing;

h n = 0.012 m – heater height;

h k = 0.022 m – casing height.

T t – temperature of the outer surface of the casing, determined by the 7th thermocouple

4.5. The heat flow passing through the samples under study is determined by thermal conductivity

, W

4.6. The thermal conductivity coefficient of the material under study is determined

, W/(mdeg)

where Q  is the heat flow passing through the test sample through thermal conductivity, W;

 = 0.005 m – sample thickness;

- surface area of one sample, m2;

d= 0.140 m – sample diameter;

T g, T x – temperatures of the hot and cold surfaces of the sample, respectively, K.

4.7. The thermal conductivity coefficient depends on temperature, therefore the obtained values  refer to the average temperature of the sample

The results of processing the experimental data are entered in Table 1.

Table 1

Results of measurements and processing of experimental data

Thermocouple readings, mV/K

E 1

4.8. Using the graphic-analytical method of processing the obtained results, we obtain the dependence of the thermal conductivity coefficient of the material under study on the average temperature of the sample T m in the form

where  0 and b- are determined graphically based on analysis of the dependence graph =f(T m).

CONTROL QUESTIONS

What are the main methods of heat transfer?

What is thermal conductivity?

What are the features of the mechanism of thermal conductivity in conductors and solid dielectrics?

What laws describe the process of heat conduction?

What is a flat wall?

What are boundary conditions?

What is the nature of the temperature change in a flat wall?

What is the physical meaning of the thermal conductivity coefficient?

Why do you need to know the thermal conductivity coefficient? various materials and how is its value determined?

What are the methodological features of the flat layer method?

STUDY OF HEAT TRANSFER DURING FREE CONVECTION

Goal of the work: study the patterns of convective heat transfer using the example of heat transfer during free convection for cases of transverse and longitudinal flow around a heated surface. Acquire skills in processing experimental results and presenting them in a generalized form.

Exercise:

1. Determine the experimental values of the heat transfer coefficients from a horizontal cylinder and a vertical cylinder to the medium during free convection.

2. By processing experimental data, obtain the parameters of the criterion equations characterizing the process of free convection relative to the horizontal and vertical surface.

BASIC THEORETICAL PROVISIONS.

There are three main methods of heat transfer, which differ significantly from each other in their physical nature:

thermal conductivity;

convection;

thermal radiation.

With thermal conductivity, the carriers of thermal energy are microparticles of matter - atoms and molecules, with thermal radiation - electromagnetic waves.

Convection is a way of transferring heat by moving macroscopic amounts of matter from one point in space to another.

Thus, convection is possible only in media that have the property of fluidity - gases and liquids. In heat transfer theory they are generally designated by the term "liquid", without making a distinction, unless specifically stated, between droplet liquids and gases. The process of heat transfer by convection is usually accompanied by thermal conductivity. This process is called convective heat exchange.

Convective heat transfer is a combined process of heat transfer by convection and conduction.

In engineering practice, they most often deal with the process of convective heat exchange between the surface of a solid body (for example, the surface of the wall of a furnace, heating device, etc.) and a fluid surrounding this surface. This process is called heat transfer.

Heat dissipation– a special case of convective heat exchange between the surface of a solid body (wall) and the fluid surrounding it.

Distinguish forced and free (natural) convection.

Forced convection occurs under the influence of pressure forces that are created forcibly, for example by a pump, fan, etc.

Free or natural convection occurs under the influence of mass forces of different nature: gravitational, centrifugal, electromagnetic, etc.

On Earth, free convection occurs under the influence of gravity, which is why it is called thermal gravitational convection. The driving force of the process in this case is the lifting force, which arises in the medium in the presence of heterogeneity in the density distribution inside the volume under consideration. During heat transfer, such heterogeneity arises due to the fact that individual elements of the medium can be at different temperatures. In this case, the more heated, and therefore less dense, elements of the medium will move upward under the action of the lifting force, transferring heat with them, and the colder, and therefore, more dense elements of the medium will flow to the vacant space, as shown in Fig. 1.

Rice. 1. The nature of the movement of flows in a liquid during free convection

If a constant source of heat is located in this place, then when heated, the density of the heated elements of the medium will decrease, and they will also begin to float upward. So, as long as there is a difference in the densities of individual elements of the environment, their circulation will continue, i.e. free convection will continue. Free convection occurring in large volumes of the medium, where nothing prevents the development of convective flows, is called free convection in unlimited space. Free convection in an unlimited space, for example, occurs in space heating, heating water in hot water boilers, and many other cases. If the development of convective flows is prevented by the walls of channels or layers that are filled with a fluid medium, then the process in this case is called free convection in a limited space. This process occurs, for example, during heat exchange inside the air gaps between window frames.

The basic law describing the process of convective heat transfer is Newton-Richmann law. In analytical form for a stationary temperature regime of heat transfer, it has the following form:

Where
- the elementary amount of heat given off in an elementary period of time
from an elementary surface area
;

- wall temperature;

- liquid temperature;

- heat transfer coefficient.

Heat transfer coefficient shows how much heat is given off per unit time from a unit surface when the temperature difference between the wall and the liquid is one degree. The unit of measurement of the heat transfer coefficient in the SI system is W/m 2 ∙deg. In a steady stationary process, the heat transfer coefficient can be determined from the expression:

, W/m 2 ∙deg

Where - heat flow, W;

- heat exchange surface area, m2;

- temperature difference between the surface and the liquid, degrees.

The heat transfer coefficient characterizes the intensity of heat exchange between the wall and the liquid washing it. By its physical nature, convective heat transfer is a very complex process. The heat transfer coefficient depends on a very large number of different parameters - the physical properties of the liquid, the nature of the liquid flow, the speed of the liquid flow, the size and shape of the channel, as well as many other factors. In this regard, it is impossible to give a general dependence for finding the heat transfer coefficient theoretically

The heat transfer coefficient can most accurately and reliably be determined experimentally based on equation (2). However, in engineering practice, when calculating heat transfer processes in various technical devices, as a rule, it is not possible to experimentally determine the value of the heat transfer coefficient under the conditions of a real full-scale object due to the complexity and high cost of setting up such an experiment. In this case, to solve the problem of determining , it comes to the rescue similarity theory.

The main practical significance of the theory of similarity is that it allows one to generalize the results of a single experiment conducted on a model in laboratory conditions to the entire class of real processes and objects similar to the process studied on the model. The concept of similarity, well known in relation to geometric shapes, can be extended to any physical processes and phenomena.

Class of physical phenomena is a set of phenomena that can be described by one common system equations and having the same physical nature.

Single occurrence– this is part of a class of physical phenomena that are distinguished by certain conditions of uniqueness (geometric, physical, initial, boundary).

Similar phenomena– a group of phenomena of the same class with the same conditions of unambiguity, except for the numerical values of quantities contained in these conditions.

The theory of similarity is based on the fact that dimensional physical quantities characterizing a phenomenon can be combined into dimensionless complexes, and in such a way that the number of these complexes will be less than the number of dimensional quantities. The resulting dimensionless complexes are called similarity criteria. Similarity criteria have a certain physical meaning and reflect the influence not of one physical quantity, but of their entire set included in the criterion, which significantly simplifies the analysis of the process under study. The process itself in this case can be represented in the form of an analytical relationship
between similarity criteria
, characterizing its individual aspects. Such dependencies are called criterion equations. The similarity criteria were named after the names of scientists who made a significant contribution to the development of hydrodynamics and heat transfer theory - Nusselt, Prandtl, Grashof, Reynolds, Kirpichev and others.

Similarity theory is based on 3 similarity theorems.

1st theorem:

Phenomena similar to each other have the same similarity criteria.

This theorem shows that in experiments it is necessary to measure only those physical quantities that are contained in the similarity criteria.

2nd theorem:

The original mathematical equations characterizing a given physical phenomenon can always be presented in the form of a relationship between similarity criteria characterizing this phenomenon.

These equations are called criterial. This theorem shows that the results of experiments should be presented in the form of criterion equations.

3rd theorem.

Similar are those phenomena for which the criteria of similarity, composed of conditions of uniqueness, are equal.

This theorem defines the condition necessary to establish physical similarity. Similarity criteria made up of unambiguity conditions are called defining. They determine the equality of all others or determined similarity criteria, which is actually the subject of the 1st similarity theorem. Thus, the 3rd similarity theorem develops and deepens the 1st theorem.

When studying convective heat transfer, the following similarity criteria are most often used.

Reynolds criterion (Re) – characterizes the relationship between the forces of inertia and the forces of viscous friction acting in the fluid. The Reynolds criterion value characterizes the fluid flow regime during forced convection.

Where - speed of fluid movement;

- coefficient of kinematic viscosity of the liquid;

- determining size.

Grashof criterion (Gr) – characterizes the relationship between the forces of viscous friction and the lifting force acting in a fluid during free convection. The value of the Grashof criterion characterizes the fluid flow regime during free convection.

Where - acceleration of gravity;

- determining size;

- temperature coefficient of volumetric expansion of liquid (for gases
, Where - determining temperature on the Kelvin scale);

- temperature difference between the wall and the liquid;

- wall and liquid temperatures, respectively;

- coefficient of kinematic viscosity of the liquid.

Nusselt criterion (Nu) – characterizes the relationship between the amount of heat transferred through thermal conductivity and the amount of heat transferred through convection during convective heat exchange between the surface of a solid (wall) and a liquid, i.e. during heat transfer.

Where - heat transfer coefficient;

- determining size;

- coefficient of thermal conductivity of the liquid at the boundary of the wall and liquid.

Peclet criterion (Pe) – characterizes the relationship between the amount of heat received (given) by the fluid flow and the amount of heat transmitted (given) through convective heat exchange.

Where - fluid flow speed;

- determining size;

- thermal diffusivity coefficient;

- respectively, the coefficient of thermal conductivity, isobaric heat capacity, and density of the liquid.

Prandtl criterion (Pr) – characterizes the physical properties of a liquid.

Where - coefficient of kinematic viscosity;

- coefficient of thermal diffusivity of the liquid.

From the considered similarity criteria it is clear that the most important parameter in calculating convective heat transfer processes, characterizing the intensity of the process, namely, the heat transfer coefficient , is included in the expression for the Nusselt criterion. This determined that for solving problems of convective heat transfer using engineering methods based on the use of similarity theory, this criterion is the most important of the criteria determined. The value of the heat transfer coefficient in this case is determined according to the following expression

In this regard, criterion equations are usually written in the form of a solution with respect to the Nusselt criterion and have the form of a power function

Where
- values of similarity criteria characterizing different aspects of the process under consideration;

- numerical constants determined on the basis of experimental data obtained by studying a class of similar phenomena using models experimentally.

Depending on the type of convection and the specific conditions of the process, the set of similarity criteria included in the criterion equation, the values of constants and correction factors may be different.

At practical application criterion equations, the important issue is the correct choice of the determining size and determining temperature. The determining temperature is necessary for the correct determination of the values of the physical properties of the liquid used in calculating the values of the similarity criteria. The choice of determining size depends on relative position the flow of liquid and the surface being washed, i.e., on the nature of its flow. In this case, you should be guided by the existing recommendations for the following typical cases.

Forced convection when fluid moves inside a round pipe.

- internal diameter of the pipe.

Forced convection during fluid movement in channels of arbitrary cross-section.

- equivalent diameter,

Where - cross-sectional area of the channel;

- section perimeter.

Transverse flow around a round pipe with free convection (horizontal pipe (see Fig. 2) with thermal gravitational convection)

- outer diameter of the pipe.

Fig.2. The nature of the flow around a horizontal pipe during thermal gravitational convection

Longitudinal flow around a flat wall (pipe) (see Fig. 3) during thermal gravitational convection.

- wall height (pipe length).

Rice. 3. The nature of the flow around a vertical wall (pipe) during thermal gravitational convection.

Defining temperature necessary for the correct determination of the thermophysical properties of the medium, the values of which vary depending on temperature.

When heat transfer occurs, the arithmetic mean between the wall and liquid temperatures is taken as the determining temperature

In case of convective heat exchange between individual elements of the medium inside the volume under consideration, the arithmetic mean between the temperatures of the elements of the medium participating in the heat exchange is taken as the determining temperature.

IN this work The procedure for conducting a laboratory experiment and the methodology for obtaining criterion equations for 2 characteristic cases of flow around a heated surface (transverse and longitudinal) with free convection of various gases relative to horizontal and vertical cylinders are considered.

EXPERIMENTAL PART.

To study the thermal conductivity of a substance, two groups of methods are used: stationary and non-stationary.

The theory of stationary methods is simpler and more fully developed. But non-stationary methods, in principle, in addition to the thermal conductivity coefficient, make it possible to obtain information about the thermal diffusivity coefficient and heat capacity. Therefore, recently much attention has been paid to the development of non-stationary methods for determining the thermophysical properties of substances.

Some stationary methods for determining the thermal conductivity of substances are discussed here.

A) Flat layer method. For a one-dimensional heat flow through a flat layer, the thermal conductivity coefficient is determined by the formula

Where d- thickness, T 1 and T 2 - temperatures of the “hot” and “cold” surface of the sample.

To study thermal conductivity using this method, it is necessary to create a heat flow close to one-dimensional.

Typically, temperatures are measured not on the surface of the sample, but at some distance from them (see Fig. 2), therefore it is necessary to introduce corrections into the measured temperature difference for the temperature difference in the heater and cooler layer, to minimize the thermal resistance of the contacts.

When studying liquids, to eliminate the phenomenon of convection, the temperature gradient must be directed along the gravitational field (down).

Rice. 2. Diagram of flat layer methods for measuring thermal conductivity.

1 – sample under study; 2 – heater; 3 – refrigerator; 4, 5 – insulating rings; 6 – security heaters; 7 – thermocouples; 8, 9 – differential thermocouples.

b) Jaeger method. The method is based on solving a one-dimensional heat equation that describes the propagation of heat along a rod heated by an electric current. The difficulty in using this method is the impossibility of creating strict adiabatic conditions on the outer surface of the sample, which violates the one-dimensionality of the heat flow.

The calculation formula looks like:

(14)

Where s- electrical conductivity of the test sample, U– voltage drop between the extreme points at the ends of the rod, D.T.– temperature difference between the middle of the rod and the point at the end of the rod.

Rice. 3. Scheme of the Jaeger method.

1 – electric furnace; 2 – sample; 3 – trunnions for fastening the sample; T 1 ¸ T 6 – places where thermocouples are sealed.

This method is used in the study of electrically conductive materials.

V) Cylindrical layer method. The liquid under study (bulk material) fills a cylindrical layer formed by two coaxially located cylinders. One of the cylinders, most often the internal one, is a heater (Fig. 4).

Fig. 4. Scheme of the cylindrical layer method

1 - inner cylinder; 2 - main heater; 3 - layer of the test substance; 4 – outer cylinder; 5 - thermocouples; 6 – security cylinders; 7 - additional heaters; 8 - body.

Let us consider in more detail the stationary process of heat conduction in a cylindrical wall, the temperature of the outer and internal surfaces which is maintained constant and equal to T 1 and T 2 (in our case, this is the layer of the test substance 5). Let us determine the heat flow through the wall provided that the inner diameter of the cylindrical wall is d 1 = 2r 1, and the outer diameter is d 2 = 2r 2, l = const and heat propagates only in the radial direction.

To solve the problem, we use equation (12). In cylindrical coordinates, when ; equation (12), according to (1O), takes the form:

. (15)

Let us introduce the notation dT/dr= 0, we get

After integrating and potentiating this expression, moving to the original variables, we obtain:

. (16)

As can be seen from this equation, the dependence T=f(r) is logarithmic.

The integration constants C 1 and C 2 can be determined if boundary conditions are substituted into this equation:

at r=r 1 T = T 1 And T 1 =C 1 ln r 1 +C 2,

at r=r 2 T=T 2 And T 2 =C 1 ln r 2 +C 2.

The solution to these equations is relative to WITH 1 and C 2 gives:

;

Substituting these expressions instead C 1 And C 2 into equation (1b), we get

(17)

heat flow through the area of a cylindrical surface of radius r and the length is determined using Fourier’s law (5)

After substitution we get

. (18)

Thermal conductivity coefficient l for known values Q, T 1 , T 2 , d 1 , d 2, calculated by the formula

. (19)

To suppress convection (in the case of liquid), the cylindrical layer must have a small thickness, usually a fraction of a millimeter.

Reducing end losses in the cylindrical layer method is achieved by increasing the ratio / d and security heaters.

G) Hot wire method. In this method the relation / d increases due to decrease d. The inner cylinder is replaced with a thin wire, which is both a heater and a resistance thermometer (Fig. 5). As a result of the relative simplicity of the design and detailed development of the theory, the heated wire method has become one of the most advanced and accurate. In the practice of experimental studies of the thermal conductivity of liquids and gases, it occupies a leading place.

Rice. 5. Diagram of a measuring cell made using the heated wire method. 1 – measuring wire, 2 – tube, 3 – test substance, 4 – current leads, 5 – potential leads, 6 – external thermometer.

Under the condition that the entire heat flow from section AB extends radially and the temperature difference T 1 – T 2 is not large, so that within these limits we can consider l = const, the thermal conductivity coefficient of the substance is determined by the formula

, (20)

Where Q AB = T×U AB is the power released on the wire.

d) Ball method. Finds application in the practice of studying the thermal conductivity of liquids and bulk materials. The substance under study is given the shape of a spherical layer, which allows, in principle, to eliminate uncontrolled heat loss. Technically, this method is quite complicated.

Many methods have been used in the past to measure thermal conductivity. Currently, some of them are outdated, but their theory is still of interest, since they are based on solutions to the heat conduction equations for simple systems, which are often encountered in practice.

First of all, it should be noted that the thermal properties of any material appear in various combinations; however, if considered as material characteristics, they can be determined from various experiments. Let us list the main thermal characteristics of bodies and the experiments from which they are determined: a) thermal conductivity coefficient measured in a stationary experimental mode; b) heat capacity per unit volume, which is measured by calorimetric methods; c) the quantity measured in periodic stationary mode of experiments; d) thermal diffusivity x, measured in unsteady experimental conditions. In fact, most experiments carried out in a non-stationary mode, in principle, allow both determination and determination

We will briefly describe the most common methods here and indicate the sections that cover them. Essentially, these methods are divided into those in which measurements are carried out in a stationary mode (steady mode methods), with periodic heating and in a non-stationary mode (non-stationary mode methods); They are further divided into methods used in the study of poor conductors and in the study of metals.

1. Stationary mode methods; bad conductors. In this method, the conditions of the main experiment set out in § 1 of this chapter must be strictly fulfilled, and the material under study must have the shape of a plate. In other versions of the method, you can study material in the form of a hollow cylinder (see § 2, Chapter VII) or a hollow sphere (see § 2, Chapter IX). Sometimes the material being tested, through which heat passes, has the shape of a thick rod, but in in this case the theory turns out to be more complex (see §§ 1, 2 of Chapter VI and § 3 of Chapter VIII).

2. Thermal methods stationary mode; metals. In this case, a metal sample in the form of a rod is usually used, the ends of which are maintained at different temperatures. A semi-bounded rod is considered in § 3 of Chapter. IV, and a rod of finite length - in § 5 of Ch. IV.

3. Stationary electrical methods, metals. In this case, a metal sample in the form of a wire is heated by passing an electric current through it, and its ends are maintained at given temperatures (see § 11, Chapter IV and example IX, § 3, Chapter VIII). You can also use the case of radial heat flow in a wire heated by electric current (see example V, § 2, Chapter VII).

4. Stationary mode methods for moving fluids. In this case, the temperature of the liquid moving between two reservoirs is measured, in which different temperatures are maintained (see § 9, Chapter IV).

5. Periodic heating methods. In these cases, the conditions at the ends of the rod or plate change with a period of time; after reaching a steady state, temperatures are measured at certain points of the sample. The case of a semi-bounded rod is considered in § 4 of Chapter. IV, and a rod of finite length - in § 8 of the same chapter. A similar method is used to determine the thermal diffusivity of soil during temperature fluctuations caused by solar heating (see, § 12, Chapter II).

Recently, these methods have begun to play an important role in measurements low temperatures; they also have the advantage that, in theory, relatively complex systems you can use methods developed for studying electrical waveguides (see § 6, Chapter I).

6. Non-stationary mode methods. In the past, transient methods have been used somewhat less than steady-state methods. Their disadvantage is the difficulty of establishing how the actual boundary conditions in the experiment are consistent with the conditions postulated by the theory. It is very difficult to take into account such a discrepancy (for example, when it comes to contact resistance at the boundary), and this is more important for these methods than for stationary mode methods (see § 10, Chapter II). At the same time, non-stationary mode methods themselves have well-known advantages. Thus, some of these methods are suitable for making very fast measurements and for taking into account small changes in temperature; In addition, a number of methods can be used “in situ”, without transporting the sample to the laboratory, which is highly desirable, especially when studying materials such as soils and rocks. Most older methods use only the last portion of the temperature versus time graph; in this case, the solution to the corresponding equation is expressed by one exponential term. In § 7 ch. IV, § 5 ch. VI, § 5 ch. VIII and § 5 ch. IX the case of simple body cooling is considered geometric shape with linear heat transfer from its surface. In § 14 ch. IV, the case of non-stationary temperature in a wire heated by electric current is considered. In some cases, the entire graph of temperature changes at a point is used (see § 10, Chapter II and § 3, Chapter III).

Physical methods of analysis are based on the use of any specific physical effect or a certain physical property of a substance. For gas analysis use density, viscosity, thermal conductivity, refractive index, magnetic susceptibility, diffusion, absorption, emission, absorption electromagnetic radiation, as well as selective absorption, speed of sound, thermal effect of reaction, electrical conductivity, etc. Some of these physical properties and phenomena make continuous gas analysis possible and allow high sensitivity and accuracy of measurements to be achieved. The choice of physical quantity or phenomenon is very important to exclude the influence of unmeasured components contained in the mixture being analyzed. The use of specific properties or effects makes it possible to determine the concentration of the desired component in a multicomponent gas mixture. Nonspecific physical properties can be used, strictly speaking, only for the analysis of binary gas mixtures. Viscosity, refractive index and diffusion in gas analysis practical significance Dont Have.

Transfer of heat between two points with different temperatures occurs in three ways: convection, radiation and thermal conduction. At convection heat transfer is associated with matter transfer (mass transfer); heat transfer radiation occurs without the participation of matter. Heat Transfer thermal conductivity occurs with the participation of matter, but without mass transfer. Energy transfer occurs due to the collision of molecules. Coefficient of thermal conductivity ( X) depends only on the type of substance transferring heat. It is a specific characteristic of a substance.

The dimension of thermal conductivity in the CGS system cal/(s cm K), in technical units - kcalDmch-K), in the international SI system - WtDm-K). The ratio of these units is as follows: 1 cal/(cm s K) = 360 kcalDm h K) = 418.68 WDm-K).

Absolute thermal conductivity during the transition from solid to liquid and gaseous substances varies from X = 418.68 WDm-K)] (thermal conductivity of the best heat conductor - silver) up to X about 10_6 (thermal conductivity of the least conductive gases).

The thermal conductivity of gases increases greatly with increasing temperature. For some gases (GH 4: NH 3), the relative thermal conductivity increases sharply with increasing temperature, and for some (Ne) it decreases. According to kinetic theory, the thermal conductivity of gases should not depend on pressure. However, various reasons lead to the fact that with increasing pressure the thermal conductivity increases slightly. In the pressure range from atmospheric to several millibars, thermal conductivity does not depend on pressure, since the average free path of molecules increases with a decrease in the number of molecules per unit volume. At a pressure of -20 mbar, the mean free path of the molecules corresponds to the size of the measuring chamber.

Thermal conductivity measurement is the oldest physical method of gas analysis. It was described in 1840, in particular, in the works of A. Schleiermacher (1888-1889) and has been used in industry since 1928. In 1913, Siemens developed a hydrogen concentration meter for airships. Thereafter, for many decades, instruments based on thermal conductivity measurements were developed and widely used in the rapidly growing chemical industry with great success. Naturally, at first only binary gas mixtures were analyzed. top scores obtained when there is a large difference in the thermal conductivity of gases. Among gases, hydrogen has the greatest thermal conductivity. In practice, it has also been justified to measure the concentration of CO s in flue gases, since the thermal conductivities of oxygen, nitrogen and carbon monoxide are very close to each other, which allows the mixture of these four components to be considered as quasi-binary.

The temperature coefficients of thermal conductivity of different gases are not the same, so you can find the temperature at which the thermal conductivities of different gases are the same (for example, 490 ° C - for carbon dioxide and oxygen, 70 ° C - for ammonia and air, 75 ° C - for carbon dioxide and argon) . When solving a certain analytical problem, these coincidences can be used by taking the ternary gas mixture as a quasi-binary one.

In gas analysis it can be assumed that thermal conductivity is an additive property. By measuring the thermal conductivity of the mixture and knowing the thermal conductivity of the pure components of the binary mixture, their concentrations can be calculated. However, this simple relationship cannot be applied to any binary mixture. For example, mixtures of air - water vapor, air - ammonia, carbon monoxide - ammonia and air - acetylene at a certain ratio of components have maximum thermal conductivity. Therefore, the applicability of the thermal conductivity method is limited to a certain concentration range. For many mixtures there is a nonlinear relationship between thermal conductivity and composition. Therefore, it is necessary to remove the calibration curve, according to which the scale of the recording device should be made.

Thermal conductivity sensors(thermoconductometric sensors) consist of four small gas-filled chambers of small volume with thin platinum conductors of the same size and with the same electrical resistance placed in them, isolated from the body. The same constant current of a stable value flows through the conductors and heats them. The conductors - heating elements - are surrounded by gas. Two chambers contain the gas to be measured, the other two contain the reference gas. All heating elements are included in a Wytheton bridge, with which measuring a temperature difference of about 0.01°C is not difficult. Such high sensitivity requires exact equality of the temperatures of the measuring chambers, so the entire measuring system is placed in a thermostat or in the measuring diagonal of the bridge, and a resistance is included for temperature compensation. As long as heat removal from heating elements in the measuring and comparison chambers is the same, the bridge is in equilibrium. When gas with a different thermal conductivity is supplied to the measuring chambers, this equilibrium is disrupted and the temperature changes sensitive elements and with it their resistance. The resulting current in the measuring diagonal is proportional to the concentration of the measured gas. To increase sensitivity operating temperature sensitive elements should be increased, but care must be taken to maintain a sufficiently large difference in the thermal conductivity of the gas. Thus, for various gas mixtures there is an optimal temperature for thermal conductivity and sensitivity. Often the difference between the temperature of the sensitive elements and the temperature of the chamber walls is selected from 100 to 150°C.

Measuring cells of industrial thermal conductometric analyzers consist, as a rule, of a massive metal case in which measuring chambers are drilled. This ensures uniform temperature distribution and good calibration stability. Since the readings of the thermal conductivity meter are affected by the gas flow rate, gas is introduced into the measuring chambers through a bypass channel. Solutions various designers to ensure the required exchange of gases are given below. In principle, it is assumed that the main gas flow is connected by connecting channels to measuring chambers through which the gas flows at a slight difference. In this case, diffusion and thermal convection have a decisive influence on the renewal of gas in the measuring chambers. The volume of the measuring chambers can be very small (several cubic millimeters), which ensures a small influence of convective heat transfer on the measurement result. To reduce the catalytic effect of platinum conductors, they different ways melted into thin-walled glass capillaries. To ensure the resistance of the measuring chamber to corrosion, all gas pipeline parts are covered with glass. This allows you to measure the thermal conductivity of mixtures containing chlorine, hydrogen chloride and other aggressive gases. Thermal conductometric analyzers with closed comparative chambers are common mainly in the chemical industry. Selecting the appropriate reference gas simplifies instrument calibration. In addition, it is possible to obtain a scale with a suppressed zero. To reduce zero point drift, the comparison chambers must be well sealed. IN special cases, for example, when there are strong fluctuations in the composition of the gas mixture, you can work with flow-through comparative chambers. In this case, using a special reagent, one of the components is removed from the measured gas mixture (for example, CO and a solution of caustic potassium), and then the gas mixture is sent to comparative chambers. The measuring and comparative branches differ in this case only by the absence of one of the components. This method often makes it possible to analyze complex gas mixtures.

Recently, instead of metal conductors, semiconductor thermistors are sometimes used as sensitive elements. The advantage of thermistors is the temperature coefficient of resistance is 10 times higher compared to metal thermal resistances. This achieves a sharp increase in sensitivity. However, at the same time, much higher demands are placed on stabilizing the bridge current and the temperature of the chamber walls.

Earlier than others and most widely, thermal conductometric instruments began to be used for the analysis of exhaust gases from combustion furnaces. Due to their high sensitivity, high speed, ease of maintenance and reliable design, as well as their low cost, analyzers of this type were subsequently quickly introduced into industry.

Thermal conductivity analyzers are best suited for measuring the concentration of hydrogen in mixtures. When selecting reference gases, mixtures of different gases should also be considered. The following data (Table 6.1) can be used as an example of minimum measurement ranges for various gases.

Table 6.1

Minimum measuring ranges for various gases,

% to volume

The maximum measurement range is most often 0-100%, with 90 or even 99% being suppressed. In special cases, a thermal conductivity analyzer makes it possible to have several different measurement ranges on one device. This is used, for example, to control the filling and emptying processes of hydrogen-cooled turbogenerators in thermal power plants. Due to the danger of explosions, the generator housing is not filled with air, but carbon dioxide is first introduced as a purge gas, and then hydrogen. Gas is released from the generator in the same way. The following measurement ranges can be obtained with fairly high reproducibility on a single analyzer: 0-100% (vol/vol) CO (in air for CO purge), 100-0% H 2 in CO (for filling with hydrogen) and 100-80% H 2 (in the air to control the purity of hydrogen during generator operation). This cheap way measurements.

To determine the hydrogen content in the chlorine released during the electrolysis of potassium chloride using a thermal conductometric analyzer, you can work with both a sealed reference gas (S0 2, Ar) and a flowing reference gas. In the latter case, a mixture of hydrogen and chlorine is first sent to the measuring chamber and then to an afterburning furnace with a temperature of > 200°C. Hydrogen burns with excess chlorine to form hydrogen chloride. The resulting mixture of HC and C1 2 is fed into the comparative chamber. In this case, the hydrogen concentration is determined from the difference in thermal conductivity. This method significantly reduces the influence of small amounts of air.

To reduce the error that occurs when analyzing wet gas, the gas must be dried, which is done either using a moisture absorber or lowering the gas temperature below the dew point. There is another possibility to compensate for the influence of humidity, which is only applicable when measuring using a flowing reference gas scheme.

To work with explosive gases, a number of companies manufacture explosion-proof devices. In this case, thermal conductivity measuring chambers are designed to high pressure, fire arresters are installed at the entrance and exit of the chambers, and the output signal is limited to an intrinsically safe level. However, such devices cannot be used to analyze mixtures of explosive gases with oxygen or hydrogen with chlorine.

Centimeter-gram-second is a system of units that was widely used before the adoption of the International System of Units (SI).

FEDERAL AGENCY FOR TECHNICAL REGULATION AND METROLOGY

NATIONAL

STANDARD

RUSSIAN

FEDERATION

COMPOSITES

Official publication

Stshdfttftsm

GOST R 57967-2017

Preface

1 PREPARED BY Federal State unitary enterprise"All-Russian Research Institute of Aviation Materials" together with the Autonomous non-profit organization "Center for Standardization, Standardization and Classification of Composites" with the participation of the Association legal entities“Union of Composite Manufacturers” based on the official translation into Russian of the English version of the standard specified in paragraph 4, which was carried out by TC 497

2 INTRODUCED by the Technical Committee for Standardization TC 497 “Composites, structures and products made from them”

3 APPROVED AND ENTERED INTO EFFECT by Order of the Federal Agency for Technical Regulation and Metrology dated November 21, 2017 No. 1785-st

4 This standard is modified from ASTM E1225-13 Standard Test Method for Determining Thermal Conductivity solids method of comparative longitudinal-enclosed heat flow" (ASTM E122S-13 "Standard Test Method for Thermal Conductivity of Solids Using the Guard ed-Comparative-Longitudinal Heat Flow Technique", MOD) by changing its structure to comply 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 are inappropriate to use in Russian national standardization due to their redundancy.

The specified paragraphs and subparagraphs not included in the main part of this standard are given in Additional Appendix YES.

The name of this standard has been changed relative to the name of the specified ASTM standard to bring it into compliance 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 on the compliance of the reference national standard with the ASTM standard. used as a reference in the applied ASTM standard. are given in additional appendix DV

5 INTRODUCED FOR THE FIRST TIME

The rules for applying this standard are established in Article 26 of the Federal Law of June 29, 2015 N9 162-FZ “On standardization in 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 instructions is published in the monthly information index “National Standards”. In case of revision (replacement) or cancellation of this standard, the corresponding notice will be published in the next issue of the monthly information index “National Standards”. Relevant information. notification and texts are also posted in information system for general use - on the official website of the Federal Agency for Technical Regulation and Metrology on the Internet ()

This standard cannot be fully or partially reproduced, replicated or distributed as an official publication without permission from the Federal Agency for Technical Regulation and Metrology

GOST R 57967-2017

1 area of use............................................... ..................1

3 Terms, definitions and designations................................................... .......1

4 Essence of the method................................................... ....................2

5 Equipment and materials.................................................... .............4

6 Preparation for testing.................................................... .......eleven

7 Carrying out tests................................................... ...............12

8 Processing of test results................................................................. .......13

9 Test report................................................................... ..................13

Appendix YES (reference) Original text unincluded structural elements

applied ASTM standard...................................................15

Appendix DB (informative) Comparison of the structure of this standard with the structure

ASTM standard applied in it....................................................18

Appendix DV (reference) Information on the compliance of the reference national standard with the ASTM standard. used as a reference in the applied ASTM standard.................................................... .............19

GOST R 57967-2017

NATIONAL STANDARD OF THE RUSSIAN FEDERATION

COMPOSITES

Determination of thermal conductivity of solids using the method of stationary one-dimensional heat flow with a protective heater

Composites. Determination of thermal conductivity of soHds by stationary one-dimensional heat flow

with a guard heater technique

Date of introduction - 2018-06-01

1 area of use

1.1 This standard specifies the determination of thermal conductivity of homogeneous opaque solid polymer, ceramic and metal composites using a steady-state one-dimensional heat flow method with a guard heater.

1.2 This standard is intended for use when testing materials having an effective thermal conductivity in the range from 0.2 to 200 W/(m-K) in the temperature range from 90 K to 1300 K.

1.3 This standard may also be used when testing 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 uniformity of measurements. Thermocouples. Nominal static conversion characteristics

Note - When using this standard, it is advisable to check the validity of the reference standards in the public information system - on the official website of the Federal Agency for Technical Regulation and Metrology on the Internet or using 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 reference standard is replaced, it is recommended that the current version of that standard be used, taking into account any changes made to that version. If a dated reference standard is replaced, it is recommended to use the version of that standard with the year of approval (adoption) indicated above. If, after the approval of this standard, a change is made to the referenced standard to which the dated scree is given, affecting the provision to which the reference is given, then it is recommended that this provision be applied without taking into account this change. If the reference standard is canceled without replacement, then the provision in which a reference to it is given is recommended to be applied in the part that does not affect this reference.

3 Terms, definitions and designations

3.1 The following terms with corresponding definitions are used in this standard:

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 in a direction perpendicular to the surface.

Official publication

GOST R 57967-2017

3.1.2 apparent thermal conductivity: When there are methods of heat transfer through a material other than thermal conductivity, the results of measurements made using this test method. represent the apparent or effective thermal conductivity.

3.2 8 of this standard the following symbols are used:

3.2.1 X M (T), W/(m K) - thermal conductivity of reference samples depending on temperature.

3.2.2 Oetzi, 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, adjusted for heat transfer if necessary.

3.2.5 X"$(T), W/(m K) - thermal conductivity of the test sample, calculated without taking into account the correction for heat transfer.

3.2.6 >у(7), W/(m K) - thermal conductivity of insulation depending on temperature.

3.2.7 G, K - absolute temperature.

3.2.8 Z, m - distance measured from the upper 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 flow per unit area.

3.2.12 ZH LT, etc. - deviations X. G. etc.

3.2.13 g A, m - radius of the test sample.

3.2.14 g in, m - internal radius of the security shell.

3.2.15 f 9 (Z), K - temperature of the protective 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 . installed under load between two reference samples with thermal conductivity X m, having the same cross-sectional area and specific 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 package under study; heat losses are minimized through the use of a longitudinal security heater, which has approximately the same temperature gradient. About half the energy flows through each sample. In the equilibrium state, the thermal conductivity coefficient is determined based on 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 samples. The package is surrounded by an insulating material with thermal conductivity. The insulation is enclosed in a protective shell with a radius r 8, located at a temperature T d (2). A temperature gradient is established in the bag by maintaining the upper part at temperature Tm and the lower part at temperature Tb. Temperature T 9 (Z) is usually a linear temperature gradient approximately corresponding to the gradient established in the package under test. An isothermal security heater with a temperature T ? (Z). equal to the average temperature of the test sample. It is not recommended to use the design of the measuring cell of the device without safety heaters due to possible large heat losses, especially at elevated temperatures. In the steady state, temperature gradients along sections are calculated based on the measured temperatures along two reference samples and the test sample. The value of X" s without taking into account the correction for heat transfer is calculated using the formula (symbols are shown in Figure 2).

T 4 -G 3 2 U 2 -Z, Z e -Z 5

where Г, is the temperature at Z,. K T 2 - temperature at Z 2, K G 3 - temperature at Z 3. TO

GOST R 57967-2017

G 4 - temperature at Z 4. TO;

Г 5 - temperature at Z s. TO:

Гв - 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.

This scheme is idealized, since it does not take into account the heat exchange 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 must be restrictions on this method tests. if you need to achieve the required accuracy.

1 - temperature gradient in the protective shell: 2 - temperature gradient in the package; 3 - thermocouple: 4 - clamp.

S - top 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 shell showing the correspondence of temperature gradients

GOST R 57967-2017

7 b

Refrigerated

Oai oimshprmi

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 one-dimensional stationary heat flow method using a security heater with indication possible places installation of temperature sensors

5 Equipment and materials

5.1 Reference samples

5.1.1 For reference samples, reference materials or standard materials with known values thermal conductivity. Table 1 shows some of the generally accepted reference materials. Figure 3 shows the approximate change >. m with temperature.

GOST R 57967-2017

Typlofoaodoost, EGL^m-K)

Figure 3 - Reference values of thermal conductivity of reference materials

Note - The material selected for reference samples should have a thermal conductivity that is closest to the thermal conductivity of the material being measured.

5.1.2 Table 1 is not exhaustive and other materials may be used as reference materials. The reference material and source of X m values must be specified in the test report.

Table 1 - Reference data for the characteristics of reference materials

GOST R 57967-2017

End of table 1

Table 2 - Thermal conductivity of electrolytic iron

Temperature. TO	Thermal conductivity. W/(m K)

GOST R 57967-2017

Table 3 - Thermal conductivity of tungsten

Temperature, K	Thermal conductivity. 6t/(mK)

GOST R 57967-2017

Table 4 - Thermal conductivity of austenitic steel

Temperature. TO	Thermal conductivity, W/(m K)

GOST R 57967-2017

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 mounting the temperature sensor, and accurately known thermal conductivity. Since 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 sample k s is between the thermal conductivity values of two reference materials, the 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

Powder, dispersed and fibrous materials are used as insulating materials to reduce the radial heat flow into the annular space surrounding the package and heat loss 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 value, and be easy to handle;

The insulation must not contaminate instrument cell components such as temperature sensors, it must have low toxicity, and it must not conduct electrical current.

Powders and solids are commonly 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 must be installed on each reference sample and two on the test sample. If possible, the reference samples and the test sample should each contain three temperature sensors. Additional sensors are required 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 device, the temperature range and environment in the measuring cell of the device, determined by insulation, reference samples, test sample and gas. Any sensor with sufficient accuracy can be used to measure temperature, and the measuring cell of the device must be large enough so that the disturbance of the heat flow from the temperature sensors is insignificant. Typically thermocouples are used. Their small size and ease of fastening are clear advantages.

5.3.3 Thermocouples must be made of wire with a diameter of no more than 0.1 mm. All cold junctions must be maintained at a constant temperature. This temperature is maintained by a cooled suspension, a thermostat or electronic reference point compensation. All thermocouples must be manufactured from either calibrated wire or wire that has been certified by the supplier to ensure the error limits specified in GOST R 8.585.

5.3.4 Methods for attaching thermocouples are shown in Figure 4. Internal contacts can be obtained in metals and alloys by welding individual thermoelements to surfaces (Figure 4a). Thermocouple junctions, either butt or socket welded, can be rigidly attached by forging, cementing or welding into narrow grooves or small holes (Figures 4b, 4c and 4

5.3.5 In Figure 46, the thermocouple is located in a radial slot, and in Figure 4c, the thermocouple is pulled through a radial hole in the material. 8 in the case of using a thermocouple in a protective shell or a thermocouple, both thermoelements of which are located 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 cement. All four procedures shown in Figure 4 should include hardening wires on surfaces, wrapping wires in isothermal zones, thermally grounding wires on the guard, or a combination of all three.

5.3.6 Because inaccuracy in the location of the temperature sensor leads to large errors. Particular care must be taken to determine the correct distance between sensors and to calculate the possible error resulting from any inaccuracy.

c - internal cheese shoye with separated thermocouples welded to the test sample or reference samples so that the signal passes through the material. 6 - radial groove on the flat surface of the fastening of a bare wire or thermocouple sensor with ceramic insulation; c - a small radial hole drilled through the test piece or reference samples, and a bare (permissible if the material is an electrical insulator) or insulated thermocouple pulled through the hole: d - a small radial hole drilled through the test piece or reference samples, and a thermocouple , placed on the hole

Figure 4 - Mounting thermocouples

NOTE In all cases, thermoelements 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 located within r k of the interface. To do this, it is necessary to ensure uniform contact resistance

GOST R 57967-2017

melting of 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 must be installed close to the surface. In such cases, a very thin layer of 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 repeatable and constant load along the stack in order to minimize interfacial resistances at the interfaces between the reference samples and the test sample. The load can be applied pneumatically, hydraulically, by spring action, or by the placement of a load. The above load application mechanisms are constant as the temperature of the package 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 may be caused by poor contact, for which the temperature sensors must be located away from any disturbance to the heat flow at the interfaces.

5.5 Security cover

5.5.1 The package consisting of the test sample and reference samples must be enclosed in a protective shell with correct circular symmetry. The containment shell may be metal or ceramic, and its inner radius should be such that the r^r A ratio is in the range of 2.0 to 3.5. The containment shell must contain at least one safety heater to regulate the temperature profile along the shell.

5.5.2 The containment shall be designed and operated such that its surface temperature is either isothermal and approximately equal to the average temperature of the test sample, or has an approximate linear profile consistent at the top and bottom ends of the containment with the corresponding positions along the side of the package. In each case, at least three temperature sensors must be installed on the containment shell at pre-coordinated points (see Figure 2) to measure the temperature profile.

5.6 Measuring equipment

5.6.1 The combination of temperature sensor and measuring instrument used to measure the sensor output 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 must maintain the required temperature and measure all associated output voltages with an accuracy commensurate with the accuracy of the temperature measurement. temperature sensors.

6 Preparation for testing

6.1 Requirements for test samples

6.1.1 Test samples examined using this method are not limited to candy geometry. It is most preferable to use cylindrical or prismatic samples. The conductivity areas of the test sample and the reference samples must be identical to within 1% and any difference in area must be taken into account when calculating the result. For a cylindrical configuration, the radii of the test specimen and reference specimens shall be consistent to within ± 1%. and the radius of the test sample r A should be such that r B fr A is from 2.0 to 3.5. Each flat surface of the test and reference samples must be flat with a surface roughness of no 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. 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 mounts temperature sensors at a sufficient distance from the contact points, thereby ensuring uniform heat flow. The length of the test piece should be selected based on radius and thermal conductivity information. When). and higher than thermal conductivity of stainless steel, long test pieces with a length of 0g A » 1 can be used. Such long test pieces allow the use of large distances between temperature sensors, and this reduces the error resulting from inaccuracy in the location of the sensor. When). m lower than the thermal conductivity of stainless steel, the length of the test piece must be reduced since the measurement error due to heat loss becomes too large.

6.1.2 Unless otherwise stated in regulatory document or technical documentation on the material. One test sample is used for testing.

6.2 Equipment setup

6.2.1 Calibration and verification of equipment is performed in the following cases:

After assembling the equipment:

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 thermal conductivity values;

If the shape of the test sample is complex or the test sample is small:

If changes have been made to the geometric parameters of the measuring cell of the device;

If it has been decided to use reference materials or insulation materials other than those given in sections 6.3 and 6.4:

If the equipment has previously functioned sufficiently high temperature, which may change the properties of components, such as. for example, the sensitivity of a thermocouple.

6.2.2 These checks must 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 piece made from a reference material is measured using reference pieces made from another reference material that has an X value closest to that of the test piece. For example, the test can be carried out on a glass glass sample. using reference samples made of stainless steel. If the measured thermal conductivity of a sample does not agree with the value in Table 1 after applying a heat transfer correction, the sources of error must be identified.

7 Testing

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 necessary reference samples with temperature sensors and installing them in the measuring cell, the test sample is equipped with similar means. The test sample is inserted into the bag so that it fits between the reference samples and is in contact with adjacent reference samples for at least 99% of each surface area. To reduce surface resistance, soft foil or other contact media can be used. If the measuring cell must be protected from oxidation during testing, or if the measurement requires a specific gas or gas pressure to control X/t, then the measuring cell is filled and purged with working gas with set pressure. To load the stack, the force necessary to reduce the effects of non-uniform thermal resistance at the interface should be applied.

7.2 Turn on the upper and lower heaters at both ends of the package and adjust until. while the temperature difference between points 2 and Zj. Z3 and Z4. and Z s and 2^ will not be more than 200 times the temperature sensor error, but not more than 30 K. and the test sample will not be at the average temperature required for the measurement. Despite. that the exact temperature profile along the protective shell is not required for 3. The power of the security heaters is adjusted until the temperature profile along the shell T g)