JP2920510B2 - A method for measuring the thermal constant of a substance by heating the inner surface of a cylindrical partition - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention mainly relates to a physical property value defined by a thermal constant (thermal conductivity λ, thermal diffusivity κ, and a combination thereof) of a substance to be measured (hereinafter, referred to as a measuring substance) of a fluid. The method relates to a method for easily measuring the thermal permeability (λ ² / κ) ^1/2 ) by heating the inner surface of a cylindrical partition wall.

[0002]

2. Description of the Related Art Unsteady thin wire heating method, which has been conventionally used as a method for measuring the thermal constant of a fluid substance, conducts heat energy generated in a thin wire that looks like a cylinder to a measuring substance in contact with the thin wire. This is to measure the temperature rise of the fine wire by diffusion. In this measurement method, the measurement condition is a dimensionless number based on the radius a of the fine wire, that is, the Fourier number κt / a ² that defines the speed of heat conduction is sufficiently larger than 1 (that is, the radius of the fine wire). Is sufficiently small). In this measurement method, the logarithm of time (lnκt / a ² ) is included as a central term in the regression function used for measurement, and data near the reference point (time t = 0) at the start of measurement becomes invalid. Further, the equilibrium point of the initial condition (time t = 0) must be obtained from the equilibrium condition using a resistor bridge or the like.

[0003]

The technical problem of the present invention is that it can be applied to the measurement of the thermal constant of an electrically conductive substance and the measurement in the range where the Fourier number is smaller than 1, and the above initial condition (initial equilibrium point) Is included in the regression function as an unknown, thereby providing a means for measuring a thermal constant that does not require a special determination of an initial equilibrium point immediately before the start of measurement.

[0004]

According to the present invention, there is provided a method for measuring a thermal constant according to the present invention, which comprises a cylindrical partition wall made of an electrical insulator having a known thermal constant, and a substance to be measured on the outside and a heat generation on the inside. and partitions the use heater temperature sensing element, the measurement substance, cylindrical partition wall and the heat generating heater temperature sensing element is in thermal equilibrium
From the point in time, through the cylindrical partition wall, heat energy is applied to the substance to be measured outside the partition wall by unsteady heating by the internal heating heater so that the partition wall has a uniform distribution, breaking the thermal equilibrium, Immediately after that,
The Fourier number that defines the speed of heat conduction is 1
Is measured as a response function with respect to time t in a region smaller than 1 and a region larger than 1 and the temperature is regressed to a function relating to a known temperature including the thermal constant of the substance to be measured as an unknown regression coefficient. It is characterized by measuring the thermal constant of a substance.

In the measurement method of the present invention, the substance to be measured, the cylindrical partition wall, and the heating heater / thermometer are placed on the partition wall by the non-stationary heating by the heating heater from a thermal equilibrium state at a uniform temperature. Inject thermal energy in a uniform distribution, measure the temperature during this period as a function of time in a thermometer,
The thermal constant of the substance to be measured is obtained by regression analysis of the measured data of the temperature of the heating heater / temperature measuring body and the heat flux corresponding to the time from the beginning of the measurement. In such a measurement, the measurement substance and the heating heater / thermometer are separated by a cylindrical partition wall made of an electrical insulator, so that the measurement substance can be applied to the measurement of the thermal constant of an electrically conductive substance. As described in detail below, the present invention can be applied to the measurement in a range where the Fourier number is smaller than 1. Furthermore, since the above-mentioned initial equilibrium point can be included in the regression function as an unknown, it is possible to provide an advantageous measuring means in that it is not necessary to specifically determine the initial equilibrium point immediately before the start of measurement.

[0006]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The measuring method according to the present invention will be described in detail. First, the measuring principle is as follows. A heating heater / thermometer is housed inside a cylindrical partition wall having a known heat constant, Inserted into the measurement substance, from the time when they are in thermal equilibrium state, input thermal energy to the outer measurement substance through the partition wall by unsteady heating by the internal heating heater,
It is intended to measure the thermal constant of a substance to be measured by measuring the temperature response of a temperature measuring element.

More specifically, it is appropriate to set the temperature response measurement time to about several seconds.
For example, the diameter is 0.2 mm to 1 mm and the thickness of the wall is 0.1 to
Materials such as 0.3 mm quartz glass or hard glass tubes are suitable. Inside the cylindrical partition wall, an exothermic heater and a temperature measuring element for emitting uniform thermal energy to the periphery are accommodated. In this case, depending on the conditions, by introducing a liquid metal such as mercury or gallium into the inside of the partition wall, the heating element and the temperature measuring element can be used together. Similarly, when a thin metal wire is used as both a heating heater and a temperature measuring element, the condition can be satisfied by bringing an electrical insulating film into close contact with the thin wire surface by an appropriate method.

In the measurement of the thermal constant, the inside of the cylindrical partition wall is started from the time when the substance to be measured, the cylindrical partition wall and the heating heater / thermometer are in a thermal equilibrium state (time t = 0) in a thermostat or the like. Unsteady heating by the heater for heating
Through the partition wall, thermal energy Q (s) is applied to the measurement substance outside the partition wall so as to have a uniform heat distribution on the partition wall. , The temperature during that time is measured as a function of time F (t). The temperature is regressed to a function related to a known temperature, which includes the thermal constant of the test substance as an unknown regression coefficient. From the regression coefficient, the heat constant (thermal conductivity λ, thermal diffusivity κ, and a combination thereof) of the test substance is obtained. The thermal permeability (λ ² / κ) ^{1/2 of the} defined physical property value is measured.

Next, the measurement principle will be described mathematically.
As shown in FIG. 1, the above-described measurement principle is based on the thermal impedance Z _x (s) [which is expressed in the form of Laplace transform, which includes the thermal constant of the measured substance as a parameter when the measured substance side is viewed from the outer surface of the cylindrical partition wall. This impedance is defined by the ratio of the temperature T (s) obtained and the thermal energy function Q (s) of the same type. That is, Z (s) = T (s) / Q (s) (s is a differential parameter with respect to time). ] Through a four-terminal equivalent circuit representing the thermal properties of the cylindrical partition wall cascaded to it.
It is determined from the inside of the cylindrical partition wall. That is, the thermal impedance Z _in (s) as viewed from the heating heater / thermometer side to the measurement substance is given by the following equation.

[0010]

(Equation 1) Here, Z _a (s) is thermally image impedance including the thermal constant of the cylindrical partition wall viewed outward from the inner surface side of the cylindrical partition wall, Z _b (s) the inner from the outer surface side of the cylindrical partition wall Is the thermal image impedance of the cylindrical partition wall, and θ (s) is the thermal image propagation constant depending on the thickness and thermal constant of the cylindrical partition wall.

Developing equation (1) to find the thermal impedance Z _in (s) used for measurement,

(Equation 2) It can be expressed by an approximate expression.

Here, Z _x (s) is theoretically defined by the following equation.

(Equation 3)

However, K ₀ (q _x b) and K ₁ (q _x b) are
Modified Bessel function of the second kind of the 0th and 1st order, q _x = (s
/ Κ _x ) ^1/2 , κ _x = λ _x / C _x , Λ _x = q _x λ _x (κ
_x is the thermal diffusivity of the test substance, λ _x is the thermal conductivity of the test substance,
C _x is the heat capacity per unit volume of the substance to be measured, and b is the outer radius of the cylindrical partition wall.

The thermal impedance Z _x (s) differs in the expansion approximation formula as follows between a small Fourier number region and a large Fourier number region characterizing the problem of heat conduction and diffusion in the target system.

[0015]

(Equation 4) Further, the coefficients A and B (n) in the equations (4) and (5) are mathematically obtained up to the order of terms in a range effective for measurement in consideration of a measurement error.

The temperature response equation can be expressed as T (s) = Z _in (s) · Q (s) (6) using equations (4) and (5) instead of equation (3). it can. The inverse Laplace transform of the equation (6) is performed, a response function relating to time t is obtained, and used as a regression function for measurement.

The input heat flow function Q (s) can be selected as an arbitrary time function. As typical examples, 1) In the case of step heating, Q (s) = Q ₀ / s (7) Here, Q ₀ is a heat flux applied per unit length of the heating heater inside the cylindrical partition wall. 2) In the case of pulse heating, Q (s) = Q _T (8). However, Q _T is the total amount of heat applied to per unit length of the heating heater inside the cylindrical partition wall.

Which of equations (4) and (5) is effective in an actual measuring system depends on the dimensions of the measuring device and the range of the measuring time. In the present invention, the characteristic time t
Is used as valid measurement data, that is, from the measurement data in the range where Expression (4) is valid,
Using a computer algorithm that validates data up to the region where the expression (5) is valid, (4) and (5)
It bridges the formula and uses it as one valid regression function.

[0019]

According to the method for measuring the thermal constant of the present invention described in detail above, the method can be applied to the measurement of the thermal constant of an electrically conductive substance and the measurement in the range where the Fourier number is smaller than 1. Can be included as an unknown in the regression function, so that it is not necessary to specifically determine the initial equilibrium point immediately before the start of measurement.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram of a method for measuring a thermal constant according to the present invention.

Claims (1)

(57) [Claims] In 1. A thermal constant is known an electrical insulator made of cylindrical partition wall, and partitions the outside of the analyte and an inner heat generating heater temperature sensing element, the measurement substance, cylindrical partition wall and heating From the point in time when the heater / thermometer in thermal equilibrium is in a state of equilibrium, the material inside the cylindrical partition wall is subjected to unsteady heating by the internal heating heater so that the material to be measured outside the partition wall is uniformly distributed on the partition wall. Heat energy is applied to break the thermal equilibrium, and the temperature in the
A range in which the Fourier number defining the speed of conduction is smaller than 1;
The temperature is measured as a function of time t in a range greater than 1 , and the temperature is regressed to a function relating to a known temperature including the thermal constant of the substance to be measured as an unknown regression coefficient, and the thermal constant of the substance to be measured is calculated from the regression coefficient. A method for measuring the thermal constant of a substance by heating the inner surface of a cylindrical partition wall, which is characterized by measuring.