A dynamic thermal conductivity measurement method

Abstract

Thermal conductivity measurement methods can generally be categorized as "steady-state" and "dynamic," but both require demanding experimental conditions, hindering widespread application in industrial and production practices. This paper discloses a dynamic thermal conductivity measurement method. By placing a temperature-varying heat source in a high-temperature zone and measuring the temperature curves of multiple equally spaced temperature sensors, this method enables thermal conductivity measurement under non-steady-state conditions. This method is suitable for industrial production applications where the measured object is immovable or inconvenient to disassemble.

Description

Technical Field

[0001] The invention relates to a dynamic thermal conductivity measurement method and belongs to the field of instrument measurement. Background Art

[0002] Thermal conduction relies on the movement of electrons, atoms, molecules, and lattice heat in the material to transfer heat. Thermal conductivity K is an inherent performance parameter of the material itself, which is used to describe the thermal conductivity of the material. It is also called thermal conductivity (thermal conductivity coefficient) and its unit is W / (m·K). The magnitude of thermal conductivity is related to the type of substance. Different material properties have different thermal conductivities. Generally speaking, the thermal conductivity of metals is greater than that of non-metals, and the thermal conductivity of pure metals is greater than that of alloys. Accurate measurement of thermal conductivity has always been a difficult problem. Generally speaking, the smaller the thermal conductivity of a material, the more difficult it is to accurately measure its thermal conductivity. At present, even for metals with relatively high thermal conductivity (for example, at 20°C, the thermal conductivity of copper is 397W / (m·K)), accurate measurement of thermal conductivity is still a problem. According to Fourier's law of heat conduction, the macroscopic expression of heat conduction can be written as:

[0003]

[0004] Where ΔQ is the amount of heat that passes through the heat transfer interface within Δt time, S is the cross-sectional area of ​​the heat transfer channel, is the temperature gradient near the heat transfer surface, that is, the change in temperature T per unit length along the direction of heat conduction X, while κ is the thermal conductivity, with a negative sign indicating that heat flows in the direction of decreasing temperature. Therefore, to obtain the thermal conductivity κ through macroscopic measurements, when the heat conduction cross-sectional area S is known, it is only necessary to measure the time Δt required for the heat ΔQ to be transferred through the conductor and the temperature gradient near the heat conduction surface. That's it.

[0005] Currently, a wide variety of experimental instruments are used to measure the thermal conductivity of metals. While these instruments vary in structure and measurement methods, they can generally be categorized into two main methods: the steady-state method (also known as the steady-flow method) and the dynamic method. The steady-state method involves allowing heat to flow steadily from a high-temperature heat source through the metal conductor being measured to a low-temperature heat source. Currently, the vast majority of thermal conductivity measuring instruments employ this method. A common feature of the steady-state method is that the instrument's temperature measurement points are located at the ends of the object being measured, with no measurement point located in the center. These steady-state thermal conductivity measuring instruments are based on the physical theory of Fourier's law of heat conduction. While simple to operate and highly reliable, they are difficult to implement for widespread industrial and production applications. Another type of dynamic thermal conductivity meter uses wave theory, where the temperature of a high-temperature heat source varies harmonically, creating a heat wave that propagates dynamically and evenly along a metal rod. The velocity of the heat wave along the rod is then studied using wave theory to infer the metal's thermal conductivity. This method also has significant drawbacks: it requires a dynamic, constant heat flow, which raises the bar for instrument use and prevents its application in real-world scenarios where temperatures fluctuate. Summary of the Invention

[0006] In response to the problem that current thermal conductivity measuring instruments cannot achieve accurate measurement under unstable conditions such as variable temperature, the present invention provides a dynamic thermal conductivity measurement method.

[0007] To achieve the above object, the technical solution adopted by the present invention is a dynamic thermal conductivity measurement method, the steps of which include:

[0008] A. Arrange N temperature sensors on the metal material to be tested along a straight line with equal spacing, with a spacing of Δx, N ≥ 2;

[0009] B. The first temperature sensor is placed near the high temperature area, and the Nth temperature sensor is placed near the low temperature area;

[0010] C. Place a heat source ΔQ with a varying temperature in the high-temperature zone. The heat source provides a periodic stable heat source with a period of 2ΔT. Within the 2ΔT period, the heat source works for a period of ΔT and rests for a period of ΔT.

[0011] D. Record the real-time temperature changes of N temperature sensors and obtain the temperature change function Ti(t) of the i-th temperature sensor over time, where i = 1, 2, ..., N;

[0012] E. Read the temperature fluctuation amplitude ΔKi corresponding to the Ti(t) function curve when the temperature is Ki from the period 2ΔT;

[0013] F. Substitute the expression N-1 thermal conductivities κ can be obtained i (i=1, ..., N-1) measurement value;

[0014] H. Calculate N-1 thermal conductivities κ i The average value of (i=1, ..., N-1) is taken as the final measurement value K.

[0015] The following describes the specific measurement principle of the present invention in detail, taking a long metal rod as the measurement object. Starting from a certain position along the length of the metal rod close to the high-temperature heat source, a plurality of temperature measuring holes are set at equal intervals, and a micro-thermocouple is inserted to measure the real-time temperature of each temperature measuring hole point, and the temperature change information of each temperature measuring hole point obtained by measurement is transmitted to the LCD screen on the instrument chassis or the external computer screen through the signal line, thereby displaying the temperature change curve of each temperature measuring point. When intermittent heat flow comes from the high-temperature heat source, the temperature rise ΔTi of any temperature measuring point on the metal rod during a heating period is measured and the product of the mass and specific heat capacity of the metal rod being measured between the temperature measuring point and the high-temperature heat source can be used to calculate the incoming heat value ΔQ. Then, the time ΔT of this heating process is measured from the screen curve to calculate the heat transferred per unit time. In addition, the temperature gradient of the metal rod during heat conduction can be calculated based on the ratio of the temperature rise peak difference between the temperature measuring point and the adjacent temperature measuring points to the distance between the temperature measuring points.

[0016] The beneficial effects of the present invention are as follows: first, there is no need to construct complex constant temperature or steady-state thermal equilibrium measurement conditions, and the thermal conductivity of objects in a temperature non-thermal equilibrium state can be measured; second, as long as an additional temperature-changing heat source is provided and N temperature sensors are placed, the thermal conductivity measurement can be achieved, which is suitable for use in industrial production practices such as when the measurement object is immovable or inconvenient to disassemble. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a schematic diagram of the measuring device of the present invention. Explanation of the accompanying figures: 1. Metal rod to be measured; 2. Thermal insulation sleeve; 3. Temperature measuring hole; 4. Microthermocouple; 5. High-temperature heat source holder; 6. High-temperature heat source; 7. Low-temperature heat source holder; 8. Main unit case; 9. LCD control panel; 10. Communication port; 11. Main unit power switch; 12. Operation and alarm indicator lights; 13. Cooling water tank.

[0018] Figure 2 This is the temperature measurement change curve of the present invention.

[0019] Figure 3 This is the temperature measurement change curve within one change cycle of the present invention.

[0020] Figure 4It is a schematic diagram of dynamic TX changes of the present invention.

[0021] Figure 5 Schematic diagram of the dynamic temperature change amplitude of the present invention.

[0022] Figure 6 Schematic diagram of heat transfer according to the present invention.

[0023] Figure 7 Table 1 is the experimental measurement results of the present invention.

[0024] The embodiments of the present invention will be further described below with reference to the accompanying drawings. DETAILED DESCRIPTION

[0025] Example 1

[0026] The following describes how to use the measurement method of the present invention to measure the thermal conductivity of a metal copper rod, using the metal copper rod as the measurement object. The method includes the following steps:

[0027] A. Arrange N temperature sensors along a straight line with equal spacing, with a spacing of Δx, where N ≥ 2. Here, Δx is 0.02 m or 0.04 m. See Table 1 for details.

[0028] B. The first temperature sensor is placed near the high temperature area, and the Nth temperature sensor is placed near the low temperature area; here N = 4, see Figure 1 .

[0029] C. Place a temperature-varying heat source ΔQ in the high-temperature zone. The heat source provides a periodic stable heat source with a period of 2ΔT. Within the 2ΔT period, the heat source operates for a period of ΔT and rests for a period of ΔT. Here, ΔT is 90 seconds, 120 seconds, 180 seconds, and 240 seconds, respectively. For the specific structure, see Table 1.

[0030] D. Record the real-time temperature changes of N temperature sensors and obtain the temperature change function Ti(t) of the i-th temperature sensor, where i = 1, 2, ..., N. For details, see Figure 2 .

[0031] E. Read the temperature fluctuation amplitude ΔKi corresponding to the Ti(t) function curve at temperature Ki from the period 2ΔT; see Figure 3 .

[0032] F. Substitute the expression N-1 thermal conductivities κ can be obtained i (i=1, ..., N-1) measured values.

[0033] Find N-1 thermal conductivities κ i The average value of (i=1, ..., N-1) is taken as the final measurement value K, see Table 1 for details.

[0034] Figure 1 The two ends of the metal rod (1) to be tested are processed into a rectangular or trapezoidal shape and clamped between the clamping groove (5) of the high-temperature heat source and the elastic clamping groove (7) of the low-temperature heat source. The elastic clamping groove (7) of the low-temperature heat source is designed to be elastic so that the metal rod to be tested can be in close contact with the clamping grooves at both ends and can be easily removed from the clamping groove and replaced with other metal rods at any time. On the right side of the clamping groove (5) of the high-temperature heat source is a cover (6) of the high-temperature heat source to prevent accidental contact and burns during experimental operation. The side of the metal rod (1) to be tested is wrapped with an insulating sleeve (2) to reduce heat loss. Starting from a certain position on the side close to the high-temperature heat source, a plurality of temperature measuring holes (3) are set along the length direction of the metal rod to be tested. The number of temperature measuring holes can be slightly more than 1 to 2 thermocouples. The spacing between the temperature measuring holes is required to be appropriately close, but must be biased towards the high-temperature heat source side. The distribution range of the temperature measuring holes does not exceed 2 / 3 of the length of the metal rod. A micro thermocouple (4) with a signal line can be flexibly inserted into the temperature measuring hole (3) according to the needs of the experiment. Figure 1 In a typical embodiment, there are 8 temperature measuring holes (3) and 6 micro thermocouples (4) with signal lines. The temperature change information of each temperature measuring point is transmitted to the inside of the instrument chassis (8) through the signal line. A color LCD screen (9) is set on the instrument chassis (8) to display the real-time temperature change curve of each temperature measuring point. There is a small cooling water tank (11) near the instrument to continuously cool the elastic card slot (7) of the low-temperature heat source through the water pipe (10) of low-temperature cooling circulating water. Figure 1 The metal rod to be measured is placed in a slot on the top of the instrument. To the right of the rod is a high-temperature heat source, and to the left is a low-temperature heat source (cooled by circulating water). The intermittent heat generated by the high-temperature heat source is transferred to the low-temperature heat source in the form of heat waves along the rod. Starting near the high-temperature heat source, there are multiple temperature measurement holes spaced 2.00 cm apart. Thermocouples are inserted into these holes to measure the temperature at various locations on the rod in real time. During experiments, a number of micro-thermocouples can be selected based on the specific requirements and inserted into different temperature measurement holes for independent measurement research. The instrument's front panel features a color LCD touchscreen. Through interactive mode, users can select different high-temperature heat source heating times, display coordinates, and access secondary calculation interfaces. A communication port on the side of the chassis allows simultaneous transmission of measurement curves displayed on the LCD to the computer screen, facilitating on-screen capture, precise measurements, and calculations.

[0035] The following is a measured curve of copper material using the instrument using the dynamic method. Figure 2 .exist Figure 2The temperature measurement curves of 4 temperature measurement points are displayed in the figure. The horizontal axis is the time axis, in seconds; the vertical axis is the voltage value after the temperature measured by the thermocouple is converted and amplified. Because the voltage displayed after the thermocouple temperature measurement is approximately proportional to the temperature, it is more convenient to use the "counting grids" method to represent the temperature change in calculation. According to the height of the curve in the figure, it can be seen that the temperature measurement point represented by the top curve is closest to the heat source and has the highest temperature. As the distance between the temperature measurement point and the hot end increases, the height of the curve of each temperature measurement point decreases in turn. In order to facilitate analysis Figure 2 The curve in Figure 2 We intercept a part of the heating curve and sort it out a little bit to get Figure 3 .exist Figure 3 There are four curves in the figure, from top to bottom. To facilitate the following analysis, the readings of these four curves are defined as follows: T1: The absolute height of the peak of the first curve, representing the highest temperature reached by the first measuring point relative to room temperature; T2, T3, T4: The absolute heights of the second, third, and fourth curves, representing the highest temperatures reached by these measuring points relative to room temperature; ΔT1: The difference between the peak and valley values ​​of the first curve, representing the high and low fluctuations in the temperature at the first measuring point; ΔT2, ΔT3, ΔT4: The difference between the peak and valley values ​​of the second, third, and fourth curves, representing the temperature fluctuations at these measuring points; Δt: The period of time during which the temperature of a particular curve rises.

[0036] M1, M2, M3, M4: are the midpoints of the rising segments of the four curves. Since each heating curve is approximately a sine curve, a simple integral calculation shows that the temperature of these midpoints is the average temperature of each corresponding curve in the Δt period.

[0037] from Figure 3 The geometric relationship of the midline curve shows that:

[0038]

[0039]

[0040] according to Figure 3 From the two points M1 and M2 in the figure, we can get the average temperature difference between the first and second temperature measurement points, and use the ratio of this difference to ΔX to approximate the temperature gradient near the first temperature measurement:

[0041]

[0042] The average temperature and average temperature gradient of other points can be calculated by simply changing the corresponding subscripts based on equations (2), (3), and (4). Where ΔX is the distance between two adjacent temperature measurement points.

[0043] For reading the above parameters, please refer to Figure 3 As shown in .

[0044] With the above regulations, we can conduct further analysis.

[0045] Taking into account Figure 3 The temperature of the first temperature measuring point in the figure produces a temperature rise of ΔT1 due to the change in the temperature in the metal rod in front of it. Then, the temperature and temperature rise of this temperature measuring point affect and determine the temperature and temperature rise of other temperature measuring points in the metal rod behind it. From the theory of molecular thermal motion, it can be known that the transmission of temperature in a metal body is essentially the result of the transfer of momentum and energy of molecular thermal motion in the metal body. Only when the momentum and energy of molecular thermal motion are transferred from a high temperature to a low temperature can the temperature of the original low temperature be increased. Therefore, the temperature rise of the metal temperature measuring point at a high temperature is the reason for the temperature rise of the temperature measuring point at the low temperature behind it. The relationship between the influence of the front and rear temperatures during this heat transfer can be used Figure 4 express.

[0046] exist Figure 4 When the temperature of point X1 rises from the dotted line position to the height of T1, the temperature rise of ΔT1 at point X1 will cause the temperature of point X2 to rise by ΔT2. Similarly, the temperature rise of ΔT2 at point X2 is the cause of the temperature rise of ΔT3 at point X3. The temperature rise of the subsequent temperature measuring point has an inseparable causal relationship with the temperature rise of the previous temperature measuring point. Without the temperature fluctuation of the previous point, there will be no temperature fluctuation of the subsequent point. In actual measurement, if Figure 4 As shown in , the influence of ΔT1 on ΔT2, ΔT3, etc. is nonlinear. Since the functional relationship of this influence is not easy to give, when the error is allowed, according to the principle of error matching, the errors with little influence are ignored. We can approximate the influence of these temperature fluctuations by Figure 5 To express. Figure 5 The relationship between the temperature rises of ΔT1 and ΔT2 is approximated by a linear triangle relationship, roughly deriving the rearward impact distance L1 of ΔT1. The rearward impact distance L2 of ΔT2 is calculated using the triangle between ΔT2 and ΔT3. This simplifies complex problems.

[0047] exist Figure 5 According to the proportional line segment relationship of similar triangles, we can get:

[0048]

[0049] (5) In the formula, L1 represents the distance that the ΔT1 temperature fluctuation affects the temperature fluctuation behind it, and ΔX is the distance between two adjacent temperature measurement points. Figure 5 It can be seen that the influence distance of L1 only needs to consider the geometric relationship between ΔT1 and ΔT2, without taking into account the geometric relationship with the temperature rise of other temperature measuring points.

[0050] From formula (5), we can get:

[0051]

[0052] Similarly, from Figure 5 It can be deduced that the influence of ΔT2, ΔT3, etc. on the rear temperature rise is:

[0053]

[0054] Next, let's discuss the calculation of the heat transferred to the rear through a certain point X1 interface of the metal rod within the time Δt.

[0055] Assume that the density and specific heat capacity of the metal material are ρ and C, respectively, and the cross-sectional area of ​​the metal rod is S. The distance to the rear affected by the temperature rise at point X1 is actually the heat transfer distance L1 during this temperature rise period. Therefore, the heat transferred from the interface at point X1 to the rear during this temperature rise period can be considered as:

[0056]

[0057] The physical meaning of formula (8) can be Figure 6 It can be represented as follows: the heat within the distance L1 that is transferred backward in one dimension through the interface at point X1 within the time Δt is available Figure 6 The volume of the cylinder in .

[0058] In formula (2), Substituting L1 in formula (6) into formula (8), we get:

[0059]

[0060] As for the amount of heat transferred backward from the interface at points X2 and X3 during the time Δt, simply replace the subscripts "1" in equation (6) with "2" and "2" with "3." And so on. The significance of equation (9) is that we can use the dynamic temperature rise analysis method to determine the heat transfer distance during a temperature rise period, from which we can infer the amount of heat transferred through the interface at point X1 during this temperature rise period. To make the temperature fluctuation curve clear and reduce the relative measurement error, the heating time we usually choose should be greater than 90 seconds.

[0061] Finally, we substitute the above equations (4) and (9) into the original Fourier heat conduction law (1), and after sorting it out, we get the thermal conductivity expression obtained from the relevant parameters at point X1:

[0062]

[0063] If the measurement parameters of the remaining temperature measurement points are substituted into formula (10), the calculated thermal conductivity values ​​of the corresponding points can be obtained by changing the subscripts in sequence, and then the average value is taken and summarized.

[0064] To verify the correctness of this experimental theory, we chose pure copper as the metal rod to be tested. The purpose was to use the known standard values ​​of density, specific heat capacity, and thermal conductivity of pure copper for reference and comparison. We also compared the relative error Er of the thermal conductivity of pure copper. We selected heating times Δt of 90 seconds, 120 seconds, 180 seconds, and 240 seconds, and ΔX of 0.02m and 0.04m, respectively, to measure the curve and use the results. Figure 3 The measured parameters Ti and ΔTi for each curve were read from the screen, and formula (12) was substituted into the calculation table of Excel software to calculate the thermal conductivity κi obtained by different heating times, different measurement point spacings, and different temperature measurement point parameters. Finally, the results were summarized and averaged. The processing results are shown in Table 1. Except for the temperature unit in the table, which uses "grid", all other units are in the International System of Units. As can be seen from Table 1, the overall evaluation of the thermal conductivity of pure copper calculated under different measurement conditions is in good agreement with the theoretical standard value, and the overall deviation is less than 10%.

Claims

1. A method for measuring dynamic thermal conductivity, comprising the steps of: A. Arrange N temperature sensors on the metal material to be tested along a straight line with equal spacing, with a spacing of Δx, N ≥ 2; B. The first temperature sensor is placed near the high temperature area, and the Nth temperature sensor is placed near the low temperature area; C. Place a heat source ΔQ with a varying temperature in the high-temperature zone. The heat source provides a periodic stable heat source with a period of 2ΔT. Within the 2ΔT period, the heat source works for a period of ΔT and rests for a period of ΔT. D. Record the real-time temperature changes of N temperature sensors and obtain the temperature change function T of the i-th temperature sensor over time. i (t), i=1,2,...,N; E. Read T from the period 2ΔT i (t) function curve at temperature K i The corresponding temperature fluctuation amplitude ΔK i ; F. Substitute the expression , N-1 thermal conductivities can be calculated The measured values, where i=1,...,N-1, the density and specific heat capacity of the metal material to be measured are ρ, C, T i is the temperature of the i-th temperature sensor, ΔT i It is the temperature rise of any temperature measuring point on the metal material to be tested during a heating period; G. Calculate N-1 thermal conductivities The average value of i=1,...,N-1 is taken as the final measurement value κ.

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