SU1721491A1 - Method of measuring thermal and physical characteristics of materials - Google Patents

Abstract

The invention relates to thermophysical instrumentation and is intended to study the thermophysical characteristics. The method consists in simultaneously heating the sample according to a linear law with periodic pulses and measuring its temperature increment over time. In order to increase the productivity and informativeness of the process of measuring the thermophysical characteristics of materials, predominantly with significant heat losses, heats the front surface of the flat sample. The temperature increments of the back surface of the sample are measured in time, the value of the Biot criterion characterizing the heat loss from the sample surface is determined by it, and the thermal diffusivity, thermal conductivity and heat capacity are determined by mathematical dependencies using the Biot criterion. 3 il. with

Description

The invention relates to thermophysical instrument making and is intended to investigate the thermophysical characteristics (TFC) of materials.

A known method for measuring TFH is that an instantaneous thermal impulse of known energy G is supplied to the front surface of a flat adiabatic sample in which a one-dimensional heat flux propagates as a result, and a change in the temperature of its back surface on the oscilloscope screen is recorded. Thermal diffusivity

the heat capacity and thermal conductivity of the sample is calculated by the formulas

a 0.139 2 / ti / 2

Wed G /)

(ITm).

(1) (2) (3)

h

GO

Ј o

where a, Cp, A is the thermal diffusivity, specific heat capacity and thermal conductivity of the sample, respectively, m2 / s, J / (kg K), W / (m-K);

p, I - density and thickness of the sample, respectively, kg / m3, m;

ti / 2 is the time to reach a change in the temperature of the back surface of a sample of half its maximum value, s;

G is the energy of the heat pulse absorbed by the front surface of the sample, J / m;

Tm is the value of the maximum change in the temperature of the back surface of the sample, K;

The disadvantages of this method are the low productivity of the measurements, the limitation on the duration of the heat pulse, and the absence of heat losses from the surface4 of the sample.

Closest to the proposed method is a method consisting in periodic pulsed heating with a known power of the sample, which is inside a massive metal shell, the temperature of which together with the sample monotonously changes. In this case, the temperature increment is measured, and from the consideration of the heat balance equation with and without a heat pulse, only the heat capacity is determined according to the expression

dT

dT

t () p + () o

dt

dt

 (1 + camp-o + o),

(four)

where m is the sample mass, kg;

P is the heat pulse power, W;

(-j-) p, (-t-) o - the rate of temperature change in the straight-line sections of the temperature dependence under the action of a thermal impulse on the sample and without it, respectively, K / s;

  amendment to changes in heat transfer conditions;

Oc Correction for the temperature dependence of the sample heat capacity;

ob is the correction for the change in the linear rate of growth of the shell temperature during the measurement at the transition from the linear portion of the temperature dependence under the action of a heat pulse on the sample and without it.

The disadvantages of this method are low productivity and low information content of the process of measuring the heat capacity of materials.

One of the factors of low productivity is to measure only the heat capacity of the sample, and the thermal conductivity and thermal diffusivity must be measured by other methods.

In addition, this method almost completely excludes the possibility of a reliable measurement of the heat capacity of a thermal destructive material due to the deposition of thermal decomposition products on the inner surface of the shell and a sharp change

herewith, the heat transfer coefficient and, consequently, the corrections (fa. The change for the same reason of the thermal resistance between the low-inertia pulsed heater and the sample also leads to

large unpredictable errors in determining the magnitude of the pulse power and the parasitic heat capacity of the heater and thermocouple.

The aim of the invention is to increase the productivity and informativeness of the process of measuring the thermal characteristics of materials, especially at significant heat losses, for example, their thermal destruction.

The goal is achieved by those. according to a method involving simultaneous heating of the sample according to a linear law and periodic pulses and measuring its increment

temperature in time, heat the front surface of a flat sample of a simple form, exciting in it the spread of a one-dimensional heat flux. By changing the temperature increment of its back surface over time, the value of the Biot criterion characterizing the heat loss from the sample surface, and thermal diffusivity, thermal conductivity and heat capacity is determined.

is calculated according to the expressions:

G Vi -V21 3 -y

five

 Vi -v2i

3L

in, (2 + in,) (T, -T0) -AT ,, - ifAll-uT

oh kl

(five)

(6)

a v 2Bi

-)

On

paN 10Bi (6 + B |) B + 10Bi + 30

-S (3dj-c) - V25 (2d + c) -i; 0d (d-l-cl 2 (d + c)

(7) (8)

Biot criterion:

d AiN / 22 + AaVai;

(A2-Ai); Ai T21 -To;

(YU)

A2 T22 -To - AT T22;

.- (11) -CKOPost linear heating of the sample, K / s;

Tl c; T2i, t2i; t2i; T22, t22 is the temperature and the corresponding time of the time-temperature dependence of the temperature increment of the back surface of the sample for the area of action of the pulsed thermal effect (index 1) and its absence at 2 points (indexes 21, 22), respectively, K, s;

3Ti

ati

at21

3t21

Vi

V21

111

at2 a2T2i

aT22 at22

i - P T22

V22

at22

- first

and the second time temperature derivatives for the area of action of the pulsed heat effect (index 1) and its absence at 2 points (indices 21, 22), respectively, K / s, K / s2;

T0 is the initial temperature of the sample, K;

g is the power density of the thermal pulse action absorbed by the front surface of the sample, W / m2.

The formulas for calculating a, A of the sample are obtained from expressions describing the temperature distribution in an infinite plate of thickness I for the case of boundary conditions of the 3rd kind with monotonic heating of both its surfaces and periodic pulsed thermal effects on one of them. In this case, the differential equation of the plate thermal conductivity is:

ACh EH2

at at

(12)

-a (T-Y (t)) + g (t) ;. (13)

-HS-L -a (T-Y (t)):

, Ј in initial conditions

T (x, o) T0

s

or in relative coordinates

O2T

aj ago

(1.6)

-V | t

at

5G

 - (Bi Y + Rg) Yi (F0)

 Bi Y Y2 (Fo),

(17)

where Ј X / l is the relative coordinate, on the front surface 0, on the rear tubule Ј 1;

X is the current coordinate over the sample thickness, m;

R I / A — thermal resistance of the sample, m2K / W;

about. - heat loss from the sample surface, W / m2K,

Fo at / I2 - Fourier criterion;

Y (t) is the value of linear heating. TO; eM power of step thermal effect, W / m.

Differential equation (16) with boundary conditions (17). It was solved using two modern applied mathematics devices — the Laplace integral transforms and variational methods, which made it possible to obtain a solution of a rather simple form of sufficient accuracy convenient for use in engineering practice of designing thermophysical devices.

The value of g, taking into account the absorption coefficient of the sample material, can be determined before the measurement process using a highly stable source of heat power or directly, for example, using one or another heat radiation power meter (while the error of the earth may be quite small, about ± 0 , 5%) or using an additional reference sample.

The dimensions of the sample under investigation, which has a simple cylindrical shape without the need for additional processing, can be quite small and are determined by the need for a one-dimensional thermal stream to pass through the sample, which is accepted as such if the ratio of sample diameter to thickness is not less than 5, and the speed of the transient registration system that is can be tens of microseconds. In this case, a high rate of linear heating and a short measurement time are achieved. For example, the linear heating rate for a molybdenum sample with a diameter of 5 mm and a thickness of 1 mm is 63 K / min, which is 10 times faster than the linear heating rate by a known method.

The measurement process consists in recording the temperature at three points of the temperature-time dependence of the temperature excess of the back surface of the sample — one for the area of pulsed heat and two for its absence, to determine the Biot criterion.

The Bio criterion is determined by experimental dependence. In the area without pulsed heat exposure, the nature of the temperature change of the back surface of the sample, its rate of change, is proportional to the amount of heat loss, which is characterized by the Biot criterion. Therefore, two operating points are taken on the rear slope of the transient curve, and the Biot criterion is determined from them.

Fig. 1 shows a functional diagram of a measurement device for TFH; FIG. 2 shows the dependences of a change in temperature excess of 6 T (T-T0), the first

V at / ЗРо and the second # Т / ЗРЈ its derivative of the Fourier criterion; Fig. 3 shows a fragment of a change in the temperature excess of the back surface of a molybdenum sample in the process of measuring its thermal characteristics in the temperature range from 300 to SHO.

This method can be implemented using a device (FIG. 1) containing a laser T, a pulse shaper based on a solenoid with a valve 2 and a setting device 3. duration, sample 4, located in the measuring cell 5, heated by an electric resistance furnace 6 linearly using a thermocouple 7 and temperature setting device 8, a thermocouple 9 measuring the temperature excess change on the rear surface of the sample 4. The device also contains an operational amplifier 10, the amplified signal from which is supplied to the microcomputer 11, coupled with the display 12 and the digital print 13, the mirror 14 and the pulse energy meter 15.

The method is carried out as follows.

When the unit 3 is turned on, the valve 2 is triggered, a pulsed thermal effect of a given duration is applied to the front surface of the sample 4 and the temperature setter 8 is simultaneously started heating the measuring cell 5 according to a linear law, and the microelectromagnetic module 11 starts counting the time and recording the back surface temperature of the sample 4 s

its linearization using a thermocouple 9 and the amplifier 10 from the moment of applying a pulsed thermal effect on its front surface. After the cessation of the effect of the pulsed heat effect, after a certain time in sample 4, a regular thermal regime of the 2nd kind is established, the beginning of which is determined by the constant value of the first derivative, and the zero derivative of the second derivative

temperature changes with time (Fig. 2). When these requirements are met with some accuracy, microcomputer 11 outputs a start signal to setpoint 3 and the process repeats again. In this case, the microcomputer 11 registers in its memory not the entire set of values of the temperature-time dependence of the temperature excess, but only three values of the temperatures, the first and second derivatives of them with the corresponding times. Temperature points are chosen rather arbitrarily, although for definiteness they can be defined for the impulse thermal effect region as the temperature corresponding to half

the maximum value of the temperature excess, and for the region of no pulse as temperature, corresponding to 1/3 and 2/3 of the duration of this excess with a negative value of the first derivative of the temperature over time, i.e. in the drop-down area, the magnitude of the pulsed thermal effect power is measured before and after the entire measurement cycle in a given temperature range with the help of a mirror 14, set for the measurement time of this energy on the optical axis of the device and the heat power meter 15 connected to the microcomputer 11, which determines its averaged value over several dimensions.

Claims (1)

The invention The method of measuring the thermophysical characteristics of materials, consisting in simultaneously heating the sample according to a linear law and periodic pulses, measuring its temperature increment over time, characterized in that, in order to increase the productivity and informativeness of the process of measuring the thermophysical characteristics of materials, especially with significant heat losses, the front surface of the sample and when measuring the temperature increment of its back surface over time, the value of the Biot criterion is determined; the working points on the transition curve are chosen ECCA arbitrary manner, and the thermal diffusivity, thermal conductivity and specific heat are determined by the mathematical relationship m and I2 Vi -V21. N Vi -V21 d AiV22 - A2V2i; AI T2i -To (A2-Ai); A2 T22 - To - DT t22; AT ViV21-ViV2i AT fri -V21: SPEED linear temperature rise (K / s); Ti, ti, T21, t2i, T22, 122 - temperature and the corresponding time for the time-time dependence of the temperature rise of the back surface of the sample for the area of action of the thermal pulse effect (index 1) and its absence in two points (indices 21, 22), respectively (K. s). BUT . I2, DT Vi-DTT Ch1 Bi (2 + Bi) (T, -T „) - DT H + - (l-i; N CD. pa where a, i Cp, I, p - thermal diffusivity, thermal conductivity, specific heat, sample thickness and density, respectively, m / s w / mK; j / kgk: m; kg / m; N 10Bi (6 + Bi) in -MOBi + zo: at. 5JLg +) - and (“+ s TYT ™ (a + s), Bio sequence. 25 / -. Lt ti. 0 V21  ET21 3t21 v-4tV21 L; 3t2i d & 2 the first and the second time temperature derivatives for the area of action of the pulsed heat effect (index 1) and its absence at 2 points (indices 21.22), respectively, K / s, K / s2; That is the initial temperature of the sample, K; e is the power density of the pulsed thermal effect absorbed by the front surface of the sample, W / m2. Xg w xi w -x-iS 16NS 3 g ST, K 50 (OS iso fr