RU2601234C1 - Method of measuring thermophysical properties of heat-insulating materials by flat pulse heat source - Google Patents

Abstract

FIELD: measurement technology.

SUBSTANCE: invention relates to researches of thermophysical properties of heat-insulating materials. Proposed method of measuring thermophysical properties of heat-insulating materials by flat pulse heat source involves, that the sample of analyzed material is made in the form of three plates, the thin plate is placed between two massive ones. Between the lower massive and thin plates the flat electric heater is placed, and thermoelectric converter is located between the upper massive and thin plates. Obtained system is preliminarily held at specified initial temperature, then electric pulse is made on the electric heater duration of which is in the range of 18≤τ_p≤24 sec. During the active stage of the experiment, measurement and record of temperature with constant spacing in time are performed, maximum value of temperature is determined, temperature value T′ and time interval τ′ are measured. Then the values of coefficients of thermal conductivity a _op and heat conductivity λ_op of tested material at the specified indicative value of parameter γ_op= 0.5 are measured, optimum values of parameter γ_opt, structural dimensions

,

and optimum heat pulse duration

are found. Thickness of the middle plate is calculated as

, and then the measurements are performed, and subsequent treatment of the obtained data is made by a series of experiments, and as a result, the values of the thermal conductivity coefficients a and heat conductivity λ of the analyzed material are obtained.

EFFECT: high measurement accuracy.

1 cl, 4 dwg

Description

The invention relates to the field of research of thermophysical characteristics of insulating materials.

A known method for determining the complex of thermophysical properties of solid materials [RF Patent No. 2125258, class. G01N 25/18, 1999], including exposure to thermal pulses from a linear source on a flat surface of the test and reference samples, measurement of excess temperatures at the moments of heat pulses at points located at fixed distances from the heating line on the surface of the samples. The measured temperatures are approximated with a minimum error to the calculated temperatures formed by software control of the parameters of thermophysical characteristics. The identified parameters of the samples and the actual values of the characteristics of the standard determine the desired characteristics.

The disadvantages of this method are the long duration and complexity of the experiment, as well as the need to use a reference sample.

A known method of measuring the thermophysical properties of solid materials by the method of a plane instantaneous heat source [Ponomarev S.V. Theoretical and practical foundations of thermophysical measurements: monograph / ed. S.V. Ponomareva. - M .: FIZMATLIT, 2008. -. 408], which consists in that the test material is made from three plates, one with a thin thickness x ₀ is placed between two bulk thickness which is ten to twenty times greater than x _0. A flat electric heater made of thin nichrome (manganin) wire is placed between the lower massive and thin plates, and a temperature sensor made of copper wire is placed at a distance x = x ₀ from the heater. The resulting system is pre-maintained at a given initial temperature T _{0 for} at least two hours. The active part of the experiment begins at that moment in time when a short electric pulse is supplied to the electric heater. During the action of this pulse in the unit area of a flat heater, the amount of heat Q _{n is released} . During the active stage of the experiment, the temperature is measured and recorded at x = x ₀ , and the maximum temperature T _{max is} determined. The active stage of the experiment is completed at τ> τ _max , where τ _max is the time instant corresponding to the achievement of the maximum temperature T _max . According to the obtained data (x ₀ , Q _n , T _max , τ _max ), the desired thermophysical properties of the material under study are calculated.

The disadvantage of this method is that the value of the time instant τ = τ _max according to experimental data is determined with a high relative error, often reaching a value of (15 ... 20)%.

The closest technical solution is a method of measuring the thermophysical properties of solid materials by the method of a plane instantaneous heat source [RF Patent No. 2534429, class. G01N 25/18, 2014], which consists in the fact that the sample of the test material is made in the form of three plates, and a thin plate with a thickness of x _{0 is} placed between two massive, whose thickness is ten to twenty times greater than x ₀ . A flat electric heater made of permalloy foil is placed in the x = 0 plane between the lower massive and thin plates, and the thermoelectric transducer is placed in another plane at a distance x = x ₀ from the heater between the upper massive and thin plates. The resulting system is pre-maintained at a given initial temperature T ₀ , then a short electrical pulse is applied to the electric heater. During the active stage of the experiment, the temperature is measured and recorded at x = x ₀ with a constant step in time, and the maximum temperature T _{max is} determined. After reaching the maximum temperature T _{max, the} active stage of the experiment is terminated when the temperature difference (T _i -T ₀ ) becomes less than α (T _max -T ₀ ). Then calculate the temperature value T ′ = β (T _max -T ₀ ) + T ₀ corresponding to the given value of the parameter β, determine the four values closest to T ′ T _j-1 <T _j , T _j ≤T ′, T _{j + 1} > T ′, T _{j + 2} > T _{j + 1} , calculate the parameters b ₀ , b _{1 of the} dependence T = b ₀ + b ₁ τ by the least squares method over four pairs of values (τ _j-1 , T _j-1 ), ( τ _j , T _j ), (τ _{j + 1} , T _{j + 1} ), (τ _{j + 2} , T _{j + 2} ), determine the instant of time τ ′ as the root of the equation T ′ = b ₀ + b ₁ τ, and the desired thermophysical properties are calculated by the formulas:

;

;

;

;

λ = a cρ,

; значение параметра α выбирают из диапазона 0,95…0,98; значение параметра β выбирают из диапазона 0,3…0,6, причем оптимальным является значение β_опт=0,498.where a is the thermal diffusivity of the investigated material; cρ is the volumetric heat capacity of the studied material; λ is the thermal conductivity of the investigated material; Q _n is the amount of heat instantly released in a unit area of a flat heater at the time the active stage of the experiment begins; z ′ is the larger root of the equation

; the value of the parameter α is selected from the range of 0.95 ... 0.98; the value of the parameter β is selected from the range 0.3 ... 0.6, and the optimum value is β _opt = 0.498.

The disadvantage of this method is that in the mathematical model of the temperature field, the internal heat source is set in the form of a flat instantaneous pulse, although in reality the heat is supplied to the heater over a period of time 0 <τ <τ _u , where τ _u is the duration of the real (not instantaneous) heat pulse supplied to the heater. Until now, questions have not been considered about choosing the optimal value of the thermal pulse duration τ _u and the rational structural size x _{0 of the} thin middle plate of the sample of the material under study.

The technical task of the invention is to increase the accuracy of measuring the thermophysical properties of insulating materials by selecting the optimal operating parameters of the thermophysical experiment and the rational structural size of the measuring device.

The technical problem is achieved by the fact that in the method of measuring the thermophysical properties of insulating materials by the method of a flat pulsed heat source, which consists in the fact that the sample of the studied material is made in the form of three plates, and a thin middle plate with a thickness of x _{0 is} placed between two massive, whose thickness is ten twenty times greater than x ₀ , in the x = 0 plane a flat electric heater is placed between the lower massive and thin middle plates, and the thermoelectric converter is placed in of a different plane at a distance x = x ₀ from the heater between the upper massive and thin middle plates, the resulting system is preliminarily held at a given initial temperature T ₀ , then an electric impulse is applied to the electric heater, during the active stage of the experiment, temperature is measured and recorded at x = x ₀ with a constant step in time, determine the maximum temperature T _max , after reaching the maximum temperature T _{max, the} active stage of the experiment is completed when the separation temperature (T _i -T ₀ ) becomes less than α (T _max -T ₀ ) at 0.95≤α≤0.98, calculate the temperature value T ′ = γ (T _max -T ₀ ) + T ₀ corresponding to the given value of the parameter γ, determine the four values closest to T ′ T _j-1 <T _j , T _j ≤T ′, T _{j + 1} > T ′, T _{j + 2} > T _{j + 1} , calculate the parameters b ₀ , b ₁ dependences T = b ₀ + b ₁ τ by the least squares method over four pairs of values (τ _j-1 , T _j-1 ), (τ _j , T _j ), (τ _{j + 1} , T _{j + 1} ), ( τ _{j + 2} , T _{j + 2} ), determine the time instant τ ′ as the root of the equation T ′ = b ₀ + b ₁ τ, according to the invention a heat pulse is supplied to the electric heater, the duration of which finds approximately in the range 18≤τ _u ≤24 sec, determine the approximate values of the coefficients of thermal diffusivity a _op and thermal conductivity λ _{op of the} investigated material to the formulas:

;

;

,

,

,Where

,

q _c is the heat flux supplied to the sample through the surface x = 0 for a period of time 0 <τ≤τ _u ; U (τ ') - dimensionless function defined for a given value of the parameter indicative γ _op = 0,5 of the equation

,

,

after which from addiction

и значение толщины

, а из зависимости

find

and thickness value

, and from the dependence

и оптимальную длительность теплового импульса

, толщину средней пластины рассчитывают как

, а затем путем проведения серии экспериментов осуществляют измерения и последующую обработку полученных данных при найденных значениях x_опт, γ_опт и

и в результате получают значения искомых коэффициентов температуропроводности a и теплопроводности λ исследуемого материала по формуламdetermine the thickness value

and optimal heat pulse duration

, the thickness of the middle plate is calculated as

and then, through a series of experiments, the measurements and subsequent processing of the obtained data are carried out at the found values of x _opt , γ _opt and

and as a result, the values of the required coefficients of thermal diffusivity a and thermal conductivity λ of the material under study are obtained by the formulas

,

,

.

.

The physical model of the measuring device is a cell in which a sample is placed, consisting of three plates: lower, middle and upper. The highest requirements are imposed on the accuracy of manufacturing the middle plate of a given thickness x ₀ = x _opt , the edges of which must be made strictly parallel to each other. A low-inertia flat heater is placed between the lower and middle plates, and a primary temperature measuring transducer, for example, a thermocouple, is installed between the middle and upper plates.

The mathematical model of the temperature field T (x, τ) in a flat sample (in the case of using a pulsed flat heat source) can be written in the form:

- коэффициент температуропроводности; q(τ, τ_u) - импульсный плоский источник теплоты; q_c - тепловой поток, подводимый к образцу через поверхность x=0 в течение промежутка времени 0<τ≤τ_u; h(τ), h(τ-τ_u) - единичные асимметричные ступенчатые функции, задаваемые соотношениями:Where

- coefficient of thermal diffusivity; q (τ, τ _u ) is a pulsed plane heat source; q _c is the heat flux supplied to the sample through the surface x = 0 for a period of time 0 <τ≤τ _u ; h (τ), h (τ-τ _u ) are unit asymmetric step functions defined by the relations:

τ _u is the duration of the heat pulse q (τ, τ _u ).

The relation (3) used in the mathematical model (1) to (4) is graphically illustrated in FIG. one.

Based on the use of the superposition principle, the solution of the boundary-value problem (1) - (4) taking into account (5) takes

Where

- специальная функция, представляющая собой интеграл от функции

;

- функция ошибок Гаусса.

- a special function representing the integral of the function

;

- Gaussian error function.

For time τ≥τ _u, solution (6), taking into account (7), takes the form

,

- безразмерные функции, зависящие от x, τ, τ_u, a, причем

.Where

,

are dimensionless functions depending on x, τ, τ _u , a , and

.

A plot of dependence (8) is also shown in FIG. one.

.From FIG. 1 it can be seen that the change in temperature difference [T (x, τ) -T ₀ ] calculated by formula (8) at the time instant τ = τ _max reaches the maximum value [T _max -T ₀ ] = [T (x, τ _max ) -T ₀ ], and this time instant τ = τ _max corresponds to a certain value of the dimensionless function

.

The developed experimental data processing technique is based on the fact that a dimensionless parameter is introduced into consideration

representing the ratio of the current value of the temperature difference [T (x, τ) -T ₀ ] taking place at the time instant τ to the maximum value [T _max -T ₀ ] = [T (x, τ _max ) -T ₀ ] of the difference temperature at time τ = τ _max .

.From FIG. 1 it can be seen that for each value of the temperature difference γ · [T _max -T ₀ ] = [T (x, τ ′) - T ₀ ], that is, each value of the dimensionless parameter γ corresponds to a specific value of the time instant τ ′ and, therefore, dimensionless function

.

When numerically simulating the measurement process on a computer, first, using the formula (8), the temperature difference T (x, τ) -T _{0 was} calculated, and then the maximum value of this temperature difference T _max -T ₀ , which is analytically written as

Dividing (8) by (10), we obtain the equation

,

,

which can easily be converted to

where it is taken into account that

.

.

If the value of [T _max -T ₀ ] is determined during the experiment, then (for a predetermined value of the dimensionless parameter γ), by solving equation (11), the value of the dimensionless function

.

.

From the last relation we obtain the formula for calculating the desired value of the thermal diffusivity

and taking into account relation (8), we obtain the formula for calculating the thermal conductivity

.Where

.

After obtaining formulas (12), (13), we determine at what values of the dimensionless parameter γ there will be minimal measurement errors for the sought values of a and λ of the thermal diffusivity and thermal conductivity coefficients.

In accordance with the recommendations of the theory of errors, after the logarithm of dependence (12) and the subsequent determination of the differential from the left and right sides, we obtain:

Having made the accepted in the theory of errors:

- replacement of the differentials d a ≈Δ a , dx≈Δx, dτ′≈Δτ ′, dU (τ ′) ≈ΔU (τ ′) by the absolute errors Δ a , Δx, Δτ ′, ΔU (τ ′);

- taking into account that the differential of the constant is d4 = 0;

или (δa)_пр=2δx+δτ′+2δU(τ′), где

,

,

,

- относительные погрешности определения соответствующих физических величин a, x, τ′, U(τ′).- replacing the signs “-” with the signs “+” in (14), we obtain an expression for calculating the so-called limiting estimate of the relative error in measuring the thermal diffusivity

or (δ a ) _pr = 2δx + δτ ′ + 2δU (τ ′), where

,

,

,

- relative errors in determining the corresponding physical quantities a , x, τ ′, U (τ ′).

After the transition from the limiting (δ a ) _pr to the root mean square estimate (δ a ) _{ck of the} error in determining the thermal diffusivity coefficient, we obtain

Let us consider in more detail the procedure for determining the errors included in the last expression (15). Taking into account that the value of the time instant τ ′ depends on the dimensionless parameter γ, i.e., τ ′ = τ ′ (γ), we obtain

To determine the absolute error Δγ, we perform (by analogy with the above) transformations of formula (9) and obtain

или

or

where ΔT is the absolute error of measuring the temperature difference; δ (T _max -T ₀ ) is the relative error of measuring the maximum value of the temperature difference (T _max -T ₀ ); Δγ, (δγ) _ck is the absolute and mean square relative errors in determining the dimensionless parameter γ from the experimentally measured values of the temperature differences [T (x, τ ′) - T ₀ ] and [T _max -T ₀ ].

получаемIncluded in (15), the relative error δτ ′ of determining the instant of time τ ′ is also associated with errors in measuring temperature differences [T (x, τ ′) - T ₀ ]. From the relation

we get

where Δτ ′, δτ ′ are the absolute and relative errors in determining the instant of time τ ′ corresponding to a given value of the dimensionless parameter γ.

Substituting (16), (17) into formula (15), we obtain the relation

used in further calculations to determine the optimal value of the dimensionless parameter γ (when measuring the thermal diffusivity a ).

When performing work (in order to obtain a ratio for calculating the mean-square estimate of the relative error (δλ) _{ck of} measuring the thermal conductivity λ), taking into account that for each value of the duration of the thermal pulse τ _{u, the} values are: 1) time instant τ ′ = τ ′ (γ); 2) the dimensionless functions U (τ ′ (γ)) = U ′ (γ) depend on the dimensionless parameter γ, formula (13) for calculating the thermal conductivity λ was presented in the form

where F (γ) ≡ Ф [U (τ (γ)), U (τ (γ) -τ _u )].

As a result of the transformations performed on the basis of the theory of errors by analogy with the actions with the formulas set forth above (12) - (18) based on the formula (19) was obtained dependence for calculating mean square estimation of relative errors (δλ) _ck thermal conductivity measurement, having the form:

In the process of calculations, it became apparent that the relative root mean square errors (δλ) _{ck of} measuring the thermal conductivity λ additionally depend on the duration τ _{u of the} heat pulse.

When making measurements, it is desirable to ensure that the requirement for supplying a heater with a power value P at which the maximum temperature difference reached at a time instant τ = τ _max during each experiment is [T (x, τ _max ) -T ₀ ] = [T _max - T ₀ ] at a distance x ₀ from the heater remains approximately the same and is within certain limits, which is necessary for the following reasons:

- if this maximum difference [T _max -T ₀ ] is small, then the relative errors in the measurement of temperature differences [T (x, τ) -T ₀ ] will be too large, which can lead to an increase in the relative errors (δ a ) _ck , ( δλ) _{ck of the} measurement of the desired thermophysical properties (TFS);

- if this maximum difference [T _max -T ₀ ] is too large, then the assumption that the heat transfer processes in the sample are described by the linear mathematical model (1) - (4) will not be fulfilled, which again will lead to an increase in the resulting the errors (δ a ) _ck , (δλ) _{ck of the} measurement sought. TFS due to nonlinearities not taken into account by the linear boundary value problem (1) - (4).

, при котором к единице поверхности внутри образца в каждом эксперименте подводится постоянное количество теплотыTo fulfill this requirement (that [T _max -T ₀ ] ≈const) for each value of the duration of the thermal pulse τ _{u the} flat heater must ensure the creation of a heat flow

in which a constant amount of heat is applied to the surface unit inside the sample in each experiment

- тепловой поток, подводимый нагревателем мощности P и площадью S к нижней стороне средней пластины образца в течение промежутка времени 0≤τ≤τ_u.The above notation is used:

- heat flow supplied by the heater with power P and area S to the lower side of the middle plate of the sample for a period of time 0≤τ≤τ _u .

.Numerical calculations and experimental studies showed that when studying samples of heat-insulating materials with an average plate thickness of 2.5≤x≤5 mm to obtain a temperature difference [T _max -T ₀ ] = 3 ... 7 ° C, the total amount of heat Q _n should be kept within

.

Let us consider in more detail the calculation of the error component δq _c , which is part of formula (20). From the above it follows

. При этом электрическую мощность P, подведенную к плоскому нагревателю, следует выбирать из соотношенияthose.

. In this case, the electric power P supplied to the flat heater should be selected from the relation

To ensure the requirement that [T (x, τ _max ) -T ₀ ] = [T _max -T ₀ ] ≈const, for Q _n = const and S = const, the amount of electric power supplied to the heater should be selected by the formula (23).

Taking into account that the most accurately measured physical quantity today is time τ, we assume that the duration τ _{u of the} heat pulse is set with high accuracy, and the relative error of a given time interval 0 <τ≤τ _u tends to zero, i.e. . δτ _u ≈0%. Then, to calculate the relative error δq _c , which is part of formula (20), we use the relation (22).

After logarithm (22), determination of the differentials from the left and right sides, and other recommendations of the theory of errors, we obtain

in which the value of P (τ _u ) was calculated by the formula (23).

After substituting (24) into (20) we obtain

In the calculations according to formula (25), ΔP = 0.5 W was taken, and the error in measuring the area S of the heater was considered equal to δS = 0.5%.

,

, ΔP=0,25 Вт; Δx=0,1 мм; ΔT=0,05 K, δS=0,5%.Using the obtained formulas (18) and (25), the dependences of the mean square relative errors (δ a ) _ck , (δλ) _cc were calculated for a heat pulse duration of τ _u = 10 s. In this case, the following initial data were used in the calculations: P = 55 W,

,

, ΔP = 0.25 W; Δx = 0.1 mm; ΔT = 0.05 K, δS = 0.5%.

In FIG. Figure 2 shows the dependences of the mean square relative errors (δ a ) _ck and (δλ) _ck on the dimensionless parameter γ for various values of the distance x ₀ from the place of action of the plane pulsed heat source to the plane in which the thermocouple measuring the temperature difference is located [T (x, τ ′) -T ₀ ].

In the course of the studies, it turned out that the minimum values of the relative errors (δ a ) _ck , (δλ) _ck depend not only on the dimensionless parameter γ, but also on the value of the distance x ₀ from the plane of the heater to the plane of the thermocouple measuring the temperature difference [ T (x, τ ′) - T ₀ ]. In this regard, lines of equal error levels were plotted on the plane with coordinates γ and x ₀ for several values of the thermal pulse duration τ _u shown in FIG. 3 (at τ _u = 20 s) and FIG. 4 (at τ _u = 5 s).

Presented in FIG. 3 and FIG. 4, the calculation results show that (with the initial data used in the calculations), the minimum values of the mean square relative errors (δ a ) _{ck of} measuring the thermal diffusivity a are achieved with dimensionless parameters in the range 0.45 <γ≤0.47 and with the values of the main structural size measuring device within 4.0 mm <x ₀ ≤4.5 mm.

At the same time, the minimum values of the mean square relative errors (δλ) _{ck for} measuring the thermal conductivity λ take place at 0.95 <γ≤1.0 and 2.8 mm <x ₀ ≤3.0 mm.

In this way:

1) to achieve the minimum values of the error (δ a ) _ck when measuring the thermal diffusivity a , a sample of the studied material with a plate thickness of 4.2 mm <x ₀ ≤4.5 mm should be used;

2) to ensure the minimum values of the error (δλ) _ck when measuring the thermal conductivity λ, it is necessary to use a sample with a thickness of the middle plate of 2.8 mm <x ₀ ≤3.0 mm.

If it is necessary to simultaneously measure the coefficient of thermal diffusivity a and thermal conductivity λ in one experiment, then the thickness x _{0 of the} middle plate of the sample from the studied material should be selected from the range of 3.5 mm <x ₀ ≤3.8 mm, which ensures relative measurement errors of the order of ( δ a ) _ck ≈ (6.0 ... 7.1)% and (δλ) _ck ≈ (5.2 ... 6.4)%.

измерения ТФС a и λ, были выполнены расчеты по формулам (18) и (25), в результате которых можно сделать вывод, что при увеличении длительности τ_u теплового импульса: 1) погрешность (δλ)_ск монотонно возрастает; 2) погрешность (δa)_ск убывает; 3) однако среднеарифметическое значение этих погрешностей

принимает минимальные значения при 18<τ_u<24.To determine the values of the duration of the _u thermal pulse, ensuring the achievement of the minimum values of the relative errors (δ a ) _ck , (δλ) _ck and the arithmetic mean of the errors

measurements of the TPS a and λ, calculations were performed according to formulas (18) and (25), as a result of which we can conclude that with an increase in the duration of the thermal pulse τ _u : 1) the error (δλ) _c monotonically increases; 2) the error (δ a ) _ck decreases; 3) however, the arithmetic mean value of these errors

takes minimum values at 18 <τ _u <24.

Thus, when measuring the thermophysical properties of the investigated thermal insulation material, one should do the following:

- by conducting preliminary measurements, it is necessary to determine the approximate values of the coefficient of thermal diffusivity a _op and thermal conductivity λ _{op of the} investigated material;

и

средней пластины, применяемой для измерения коэффициента температуропроводности a и теплопроводности λ;- to carry out calculations (at the found values of a _op and λ _op ) in order to determine (clarify) the optimal values of the parameter γ _opt and structural dimensions

and

the middle plate used to measure the coefficient of thermal diffusivity a and thermal conductivity λ;

, и рассчитать значение длительности τ_u теплового импульса, обеспечивающего достижение δ_ср=min;- accept the thickness of the middle plate

, and calculate the value of the duration τ _{u of the} heat pulse, ensuring the achievement of δ _sr = min;

;- make a sample with one middle plate thickness

;

) и в результате получить значения искомых коэффициента температуропроводности a и теплопроводности λ исследуемого материала.- by conducting a series of experiments (with the fabricated sample), carry out measurements and subsequent processing of the obtained data (at the found values γ = γ _opt and

) and as a result, obtain the values of the required coefficient of thermal diffusivity a and thermal conductivity λ of the material under study.

Claims (1)

A method of measuring the thermophysical properties of heat-insulating materials by the method of a flat pulsed heat source, which consists in the fact that the sample of the studied material is made in the form of three plates, and a thin middle plate with a thickness of x _{0 is} placed between two massive, whose thickness is ten to twenty times greater than x ₀ , a plane x = 0 between the lower massive and thin middle plates place a flat electric heater, and the thermoelectric converter is placed in another plane at a distance x = x ₀ from the heat between the upper massive and thin middle plates, the resulting system is preliminarily held at a given initial temperature T ₀ , then an electric pulse is supplied to the electric heater, during the active stage of the experiment, the temperature is measured and recorded at x = x ₀ with a constant time step, determine maximum temperature value T _max, after achieving the maximum temperature T _max active step experiment terminated when the temperature difference (T _i -T ₀₎ becomes smaller in masks α (T _max -T ₀₎ for 0,95≤α≤0,98, calculated temperature value T '= γ (T _max -T ₀₎ + T ₀ corresponding to the specified value of the parameter γ, determined by four closest to T' values of T _j-1 <T _j , T _j ≤T ′, T _{j + 1} > T ′, T _{j + 2} > T _{j + 1} , calculate the parameters b ₀ , b _{1 of the} dependence T = b ₀ + b ₁ τ by the method least squares over four pairs of values (τ _j-1 , T _j-1 ), (τ _j , T _j ), (τ _{j + 1} , T _{j + 1} ), (τ _{j + 2} , T _{j + 2} ), determined at time τ 'as a root of the equation T' = b ₀ + b ₁ τ, characterized in that the electric heater is supplied to the thermal pulse, the duration of which is in the range 18≤τ _u ≤24 sec, determined on ientirovochnye values of the coefficients of thermal diffusivity and thermal conductivity of a _{op op} λ of the material by the formulas:

Where

q _c is the heat flux supplied to the sample through the surface x = 0 for a period of time 0 <τ≤τ _u ; U (τ ′) is a dimensionless function determined for a given approximate value of the parameter γ _op = 0.5 from the equation

,
after which from addiction

find

and thickness value

, and from the dependence

determine the thickness value

and optimal heat pulse duration

, the thickness of the middle plate is calculated as

and then, through a series of experiments, the measurements and subsequent processing of the obtained data are carried out at the found values of x _opt , γ _opt and

and as a result, the values of the required coefficients of thermal diffusivity a and thermal conductivity λ of the material under study are obtained by the formulas

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