Thermal conductivity measurement based on phase change material

Abstract

The disclosed technology can be implemented to provide a method of determining thermal conductivity of a sample. The method includes controlling a heat source to raise a temperature of the heat source to an elevated temperature that is higher than a phase transition temperature of a phase change material, placing the sample between and in thermal contact with the phase change material and the heat source below the phase transition temperature to allow thermal conduction through the sample from the heat source to the phase change material, thereby raising an initial temperature of the phase change material to the phase transition temperature to cause the phase change material to transition from a first phase to a second phase, performing a measurement on at least one of the sample or the phase change material, and determining the thermal conductivity of the sample based on the measurement.

Description

[0001] Cross-references to related applications

[0002] This patent document claims the benefit and priority of U.S. Patent Application No. 18 / 466,225, entitled "Measurement of Thermal Conductivity Based on Phase Change Materials," filed September 13, 2023, with the United States Patent and Trademark Office. The entire contents of the aforementioned patent application are incorporated herein by reference as part of the disclosure of this application. Technical Field

[0003] This patent document relates to methods and systems for measuring thermal conductivity. Background Technology

[0004] Thermal conductivity is an important material property used in various applications to integrate materials into structures, equipment, or systems that require thermal management. Summary of the Invention

[0005] This patent document includes a technique and its implementation for providing a method and system for measuring the thermal conductivity of samples of various shapes and configurations using phase change materials, including, for example, planar or non-planar samples that may or may not have rough surfaces suitable for various applications, including nuclear reactor environments and other applications requiring high-temperature performance across a wide range of temperatures. The method is applicable to samples that may have arbitrary surface roughness and samples that may be composed of heterogeneous materials, such as composite materials.

[0006] In one aspect, the disclosed technique can be implemented to provide a method for determining the thermal conductivity of a sample. The method includes controlling a heat source to raise its temperature to an elevated temperature above the phase transition temperature of the phase change material; placing and thermally contacting the sample between and the phase change material at an initial temperature below its phase transition temperature and the heat source at the elevated temperature to allow heat conduction through the sample from the heat source to the phase change material, thereby raising the initial temperature of the phase change material to the phase transition temperature, causing the phase change material to transform from a first phase to a second phase at the phase transition temperature; performing a measurement on at least one of the sample or the phase change material; and determining the thermal conductivity of the sample based on the measurement.

[0007] In an embodiment, the phase change material maintains a phase change temperature during the first phase change cycle to transform from the first phase to the second phase.

[0008] In one embodiment, during the first phase change cycle and in a second phase change cycle that lasts longer than the first phase change cycle, the heat source is at a constant temperature equal to or lower than the elevated temperature.

[0009] In an embodiment, the method further includes shaping the phase change material to conform to the shape of the sample, which may be a simple or complex shape, to ensure good thermal contact with the sample and to accurately determine the thermal conductivity of the sample.

[0010] In the embodiments, the phase change material has a curved shape to conform to the curved shape of the sample to ensure good thermal contact with the sample and to accurately determine the thermal conductivity of the sample.

[0011] In an embodiment, the step of performing a measurement on at least one of the sample or phase change material includes measuring a first phase change period of the phase change material between a first time when at least a portion of the phase change material transitions from a first phase to a second phase and a second time when substantially all of the phase change material transitions to the second phase, and wherein the thermal conductivity of the sample is determined by the following formula: , where k is the thermal conductivity of the sample, m1 is the mass of the phase change material, H1 is the latent heat of the phase change material, h is the thickness of the sample, A is the area of ​​the sample, T1 is the phase change temperature of the phase change material, T2 is the constant temperature of the heat source when the phase change material changes from the first phase to the second phase at the phase change temperature, and t is the first phase change period when the phase change material changes from the first phase to the second phase.

[0012] In an embodiment, the sample is a solid material sample having a tubular shape, and the phase change material is shaped to include contact with the tubular shape at the contact location of the solid material sample and to conform to a portion of the tubular shape.

[0013] In this embodiment, the thermal conductivity of the tube sample is determined by the following formula: Where k is the thermal conductivity of the sample, ρ is the density of the phase change material, H is the latent heat of the phase change material, and r i It is the inner radius of the curved shape of the sample, r o T1 is the outer radius of the curved shape of the sample, T2 is the phase transition temperature of the phase change material, T2 is the constant temperature of the heat source when the phase change material changes from the first phase to the second phase at the phase transition temperature, and t is the first phase transition period of the phase change material changing from the first phase to the second phase.

[0014] In an embodiment, the sample is a liquid or gas and is guided to flow in a fluid conduit between and in thermal contact with the heat source and the phase change material.

[0015] In one embodiment, the heat source includes a second phase change material having a second phase change temperature.

[0016] In an embodiment, the method further includes placing a reference structure between the sample and one of the heat source and the phase change material, such that the reference structure is in thermal contact with the sample and one of the heat source and the phase change material, and measuring a reference temperature of the reference structure during a first phase change cycle to determine the thermal conductivity of the sample at the reference temperature of the reference structure and the phase change temperature of the phase change material or the constant temperature of the heat source during the first phase change cycle of the phase change material.

[0017] In an embodiment, the method further includes placing a first reference structure in thermal contact with the sample and between the sample and the phase change material, placing a second reference structure between the sample and a heat source to be in thermal contact with the sample and the heat source, and measuring a first reference temperature of the first reference structure and a second reference temperature of the second reference structure to determine the thermal conductivity of the sample between the first reference temperature of the first reference structure and the second reference temperature of the second reference structure.

[0018] In this embodiment, the thermal conductivity of the sample between the first reference temperature and the second reference temperature is determined by one of the following expressions: Where k is the thermal conductivity of the sample, k r1 The thermal conductivity of the first reference structure, k r2 Here, m is the thermal conductivity of the second reference structure, H is the mass of the phase change material, A is the latent heat of the phase change material, and h is the area of ​​the sample. r1 It is the thickness of the first reference structure, h r2 T is the thickness of the second reference structure, T1 is the phase transition temperature of the phase change material, T2 is the constant temperature of the heat source, and T... r1 It is the temperature of the interface between the first reference structure and the sample, T. r2 It is the temperature of the interface between the second reference structure and the sample, and t is the first phase transition period from the first phase to the second phase of the phase change material.

[0019] In another aspect, the disclosed technique can be implemented to provide a system for determining the thermal conductivity of a sample. The system includes: a phase change material configured to transform from a first phase to a second phase at a phase change temperature; a heat source configured to be maintained at a constant temperature above the phase change temperature, the phase change material and the heat source being placed on different sides of the sample to allow heat conduction from the heat source to the phase change material and to cause the phase change material to transform from the first phase to the second phase; one or more sensors coupled to the phase change material and configured to perform a measurement on at least one of the sample or the phase change material; and a processor coupled to the one or more sensors and configured to determine the thermal conductivity of the sample based on at least one measurement of the sample and the phase change material.

[0020] In the embodiments, at least one of the heat source or phase change material has a shape that conforms to the shape of the sample to ensure good thermal contact with the sample and to determine the accuracy of the sample's thermal conductivity.

[0021] In one embodiment, one of the heat source or phase change material has a cylindrical shape.

[0022] In this embodiment, the heat source is a second phase change material having a second phase change temperature equal to a constant temperature.

[0023] In another aspect, the disclosed technique can be implemented to provide a method for determining the thermal conductivity of a sample. The method includes shaping a first phase change material to conform to the shape of the sample to ensure good thermal contact with the sample and accuracy in determining the thermal conductivity of the sample; placing the sample and the first phase change material, each in a solid phase, into thermal contact with a second phase change material in a liquid phase to allow heat conduction from the second phase change material to the first phase change material and to allow the first phase change material to transition from a solid phase to a liquid phase; measuring the duration between a first time when at least a portion of the first phase change material transitions from a solid phase to a liquid phase and a second time when substantially all of the first phase change material transitions to a liquid phase; and determining the thermal conductivity of the sample based at least on the duration.

[0024] In an embodiment, the step of shaping the first phase change material to conform to the shape of the sample includes: supplying heat to the first phase change material having a first melting point and the second phase change material having a second melting point higher than the first melting point, so that the first phase change material and the second phase change material each melt into a liquid phase; and placing at least a portion of the first phase change material in the liquid phase onto the sample, such that when cooled, the first phase change material changes from the liquid phase to the solid phase and binds to the sample.

[0025] In the embodiment, the thermal conductivity of the sample between the first melting point and the second melting point is determined by the following formula: Where k is the thermal conductivity of the sample, m1 is the mass of the first phase change material, H1 is the latent heat of the first phase change material, h is the thickness of the sample, A is the area of ​​the sample, T1 is the first melting point of the first phase change material, T2 is the second melting point of the second phase change material, and t is the measurement duration of the first phase change material changing from the solid phase to the liquid phase.

[0026] In the embodiments, the first phase change material is tin (Sn), lead (Pb), bismuth (Bi), eutectic copper-silver (Cu-Ag) alloy, silver (Ag), copper (Cu), or silicon (Si).

[0027] The above and other aspects and their embodiments are described in more detail in the accompanying drawings, description and claims. Attached Figure Description

[0028] Figure 1 This is a flowchart of an example method for measuring the thermal conductivity of a sample.

[0029] Figure 2 A schematic diagram illustrating the basic principle of heat conduction from a hot medium to a cold medium through a sample is shown.

[0030] Figure 3 An example of a thermal conductivity measurement system including a phase change material and a heat source is shown.

[0031] Figure 4A table showing some examples of phase change materials that can be used in thermal conductivity measurement systems is provided.

[0032] Figure 5A An example of the temperature change of the phase change material (solid line) and heat source (dotted line) with respect to time is shown in a thermal conductivity measurement system.

[0033] Figures 5B-5C An example of the temperature change of the first phase change material (solid line) and the second phase change material (dotted line) with respect to time is shown in the thermal conductivity measurement system.

[0034] Figure 6 An example of a thermal conductivity measurement system comprising two different phase change materials is shown.

[0035] Figure 7A and 7B Two different example thermal conductivity measurement systems are shown for measuring the thermal conductivity of samples with curved shapes.

[0036] Figure 8 This is a flowchart of an example method for measuring the thermal conductivity of a sample using two different phase change materials.

[0037] Figure 9A An example of a furnace configured to provide heat to a phase change material to transform it from a lower energy phase (e.g., solid) to a higher energy phase (e.g., liquid) is shown.

[0038] Figure 9B An exemplary thermal conductivity measurement system comprising two different phase change materials is shown.

[0039] Figures 10A to 10D Depict different examples of adjusting the temperature range to determine the thermal conductivity of a sample.

[0040] Figure 11 This is a schematic diagram of an example thermal conductivity measurement system configured to determine the thermal conductivity of a solid material sample with a tubular structure.

[0041] Figure 12 This is a schematic diagram of an example thermal conductivity measurement system configured to determine the thermal conductivity of a liquid or gas sample contained in a fluid conduit of the thermal conductivity measurement system.

[0042] Figure 13 An example of a hardware platform configured to implement some of the methods described in this disclosure is shown. Detailed Implementation

[0043] Various structures (such as heat exchangers, nozzles, nose cones, fuselages, flow channel inserts in fusion reactors, and nuclear blanket walls) and certain special liquids and gases can be used in a variety of heat transfer applications requiring high-temperature performance. Before mass production or actual use of these various structures and special liquids and gases, it is desirable to simulate and measure their thermal conductivity over the different temperature ranges required for the application. For example, various nuclear reactors use fissile materials as fuel to generate electricity. The fuel is typically held in a robust physical form (e.g., fuel rods) capable of withstanding high stress, elevated operating temperatures, and intense neutron radiation environments. The fuel structure needs to maintain its shape and integrity within the reactor core for a period of time (e.g., several years) to prevent fission products from leaking into the reactor coolant. The thermal conductivity of the fuel rods is a crucial parameter for selecting fuel rod materials and designing fuel rods.

[0044] As discussed above, the low thermal conductivity and complex shapes of samples, particularly those with specific liquids and gases, make accurately determining the thermal conductivity of such samples using existing methods technically challenging. Furthermore, while various existing thermal conductivity measurement methods can be applied to planar samples, factors must typically be applied to correct for samples with non-planar geometries or surface roughness, limiting their usability and accuracy. Additionally, some thermal conductivity measurement methods often use localized probes that may be insufficient to obtain volumetric measurements of materials composed of spatially distributed or heterogeneous material components or compositions, as the probe size may be insufficient to average the internal heterogeneous material components—for example, in cases where the laser spot size in a laser flash system is insufficient to sample the volume of the sample material components. The disclosed technology provides methods and systems for performing accurate thermal conductivity measurements on samples with complex shapes (e.g., curved, multi-curvature, tubular, or other complex geometries), and in some applications, the samples to be measured may have low thermal conductivity. Part of the technology disclosed in this patent document is based on the understanding that phase change materials remain at their phase change temperature during a phase change or transition from one phase to another. The constant temperature of the phase transition period can be used as a stable reference temperature for measuring the thermal conductivity of a sample, while transferring heat to or from the sample to measure its thermal conductivity.

[0045] In some embodiments of the disclosed technology, a method is provided for determining the thermal conductivity of a sample using one or more phase change materials. The method includes controlling a heat source to raise its temperature to an elevated temperature above the phase change temperature of the phase change material; placing the sample between and in thermal contact with the phase change material, whose initial temperature is below its phase change temperature, and the elevated heat source to allow heat conduction through the sample from the heat source to the phase change material, thereby raising the initial temperature of the phase change material to its phase change temperature, causing the phase change material to transform from a first phase to a second phase at the phase change temperature; performing a measurement on at least one of the sample or the phase change material; and determining the thermal conductivity of the sample based on the measurement.

[0046] In some embodiments of the disclosed technology, a system for determining the thermal conductivity of a sample is provided. The system includes: a phase change material configured to transform from a first phase to a second phase at a phase change temperature; a heat source configured to be maintained at a constant temperature above the phase change temperature, the phase change material and the heat source being placed on different sides of the sample to allow heat conduction from the heat source to the phase change material and to cause the phase change material to transform from the first phase to the second phase; one or more sensors coupled to the phase change material and configured to perform a measurement on at least one of the sample or the phase change material; and a processor coupled to the one or more sensors and configured to determine the thermal conductivity of the sample based at least on measurements of at least one of the sample and the phase change material.

[0047] In some embodiments of the disclosed technology, a method for determining the thermal conductivity of a sample is provided. The method includes shaping a first phase change material to conformally fit the shape of the sample to ensure good thermal contact with the sample and accuracy in determining the thermal conductivity of the sample; placing the sample and the first phase change material respectively in a solid phase to thermally contact a second phase change material in a liquid phase to allow heat conduction from the second phase change material to the first phase change material, and causing the first phase change material to transition from the solid phase to the liquid phase; measuring the duration between a first time when at least a portion of the first phase change material transitions from the solid phase to the liquid phase and a second time when substantially all of the first phase change material transitions to the liquid phase; and determining the thermal conductivity of the sample based at least on the duration.

[0048] Figure 1This is a flowchart of an example method 100 for measuring the thermal conductivity of a sample. In embodiments, the sample may have low thermal conductivity, for example, lower than that of the phase change material used in the measuring device. In embodiments, the sample is a solid having any shape or structure. In embodiments, the sample may be made of a general monolithic material. In embodiments, the sample may be a composite material with a heterogeneous internal structure. For example, the sample may include fibers, a matrix, voids, or any combination thereof. In embodiments, the sample may have a planar geometry. In embodiments, the sample may have a non-planar geometry. In embodiments, the sample may have a regular shape. For example, the sample may be a plate or a tube. In embodiments, the sample may have a homogeneous or non-homogeneous structure. For example, the sample may have a porous structure, such as a foam structure. In embodiments, the sample may have a very complex irregular structure. In embodiments, the sample may be a porous foam flow channel insert. In embodiments, the sample may be a silicon carbide composite nuclear fuel blanket tube. In embodiments, the sample is a liquid or gas to be placed in a thermally conductive container having any suitable shape or structure. In embodiments, the sample is a nuclear fusion reaction flow channel insert. In embodiments, the sample is a nuclear blanket wall. In embodiments, the sample is made of a heat exchange material. In the embodiments, the sample has a curved shape or a multi-curvature shape.

[0049] At step 110, a heat source is controlled to raise its temperature to an elevated temperature above the phase change temperature of the phase change material. In some embodiments, the phase change material and the heat source may be phase change materials 310, 710, 1010, 1110 and heat sources 340, 740, 1040, 1140. In embodiments, step 110 may be implemented by a furnace (e.g., furnace 900) that provides heat to raise the temperature of the heat source to the elevated temperature. In embodiments, the furnace (e.g., furnace 900) may be used to raise the temperature of the heat source to a temperature above the elevated temperature, and the heat source may be further cooled to the elevated temperature. In embodiments, the heat source may be configured, in use, to raise its temperature to the elevated temperature and maintain itself at the elevated temperature. The elevated temperature is above the phase change temperature of the phase change material to allow heat conduction from the heat source to the phase change material, as discussed in more detail below. The phase change temperature of the phase change material may be its melting point or boiling point.

[0050] In step 120, a sample is placed between and in thermal contact with the phase change material and a heat source. In some embodiments, the sample may be samples 230, 330, 730, 1030, 1130, and 1230. The sample is in thermal contact with the phase change material and the heat source to allow thermal conduction between the sample and the phase change material and between the sample and the heat source, each thermal conduction from one having a higher temperature to another having a lower temperature. In an embodiment, prior to performing step 120, the phase change material has an initial temperature below the phase change temperature. Because the temperature of the heat source is higher than that of the phase change material, thermal conduction occurs through the sample from the heat source to the phase change material, raising the temperature of the phase change material to the phase change temperature, thereby causing the phase change material to transform from a first phase to a second phase at the phase change temperature. The phase change temperature may also be referred to as the first temperature and is denoted by T1. In an embodiment, the first stage is a lower energy stage, and the second stage is a higher energy stage. The terms “lower” and “higher” are relative terms corresponding to the first and second phases at the respective phase change temperatures. For example, the first phase may be a solid, and the second phase may be a liquid. Therefore, the phase transition temperature is the melting point of the phase change material. Corresponding to the melting point of the phase change material, the solid phase is the lower energy phase, and the liquid phase is the higher energy phase. As another example, the first phase can be a liquid, and the second phase can be a gas. Therefore, the phase transition temperature is the boiling point of the phase change material. Corresponding to the boiling point of the phase change material, the liquid phase is the lower energy phase, and the gas phase is the higher energy phase.

[0051] In an embodiment, the heat source is a second phase change material that maintains a second phase change temperature during a phase change. In an embodiment, the second phase change material is second phase change material 640, 745, or 1045. In an embodiment, the second phase change material maintains a second phase change temperature during the measurement as it transitions from a higher energy phase to a lower energy phase. The second phase change temperature may also be referred to as a second temperature and is denoted by T2. In an embodiment, a first temperature T1 is lower than a second temperature T2. For example, the second phase change material transitions from a liquid to a solid. Therefore, the second phase change temperature is the melting point of the second phase change material. As another example, the second phase change material transitions from a gas to a liquid. Therefore, the second phase change temperature is the boiling point of the second phase change material. In an embodiment, the second phase change material is not connected to a controlled heater. Therefore, the heat source can maintain the second temperature during the phase change cycle of the second phase change material. As discussed in more detail below, the phase change cycle of the second phase change material must be longer than the phase change cycle of the phase change material.

[0052] In this embodiment, the heat source includes a controlled heater. For example, the controlled heater may be substantially similar to... Figure 3 The controlled heater 375 or Figure 11 and Figure 12The controlled heater 1125 is described above. In one embodiment, the controlled heater includes control circuitry (e.g., a feedback loop) that causes a heat source to raise its temperature to a second temperature T2 upon startup and maintain it at the second temperature T2 during operation. Examples of the heat source may include control circuitry, such as a feedback loop, coupled to the second phase change material to maintain the second temperature of the heat source by providing heat to the second phase change material within a predetermined range deviating from the second temperature. In this embodiment, the second phase change material may maintain the second temperature without undergoing a phase change. In some examples, as described above, the second temperature is greater than the second phase change temperature. In an embodiment, the controlled heater is a heating band. In an embodiment, the second phase change material is coupled to the controlled heater, which compensates for the heat loss of the second phase change material and maintains the phase change process at the second temperature for a relatively long time.

[0053] In step 130, a measurement is performed on at least one of the sample or phase change material. For example, when both the phase change material and the heat source are at constant temperatures, a measurement of the sample temperature is performed. In an embodiment, a measurement of a first phase change cycle is performed, during which the phase change material undergoes a phase change. In some embodiments, one or more dimensions of the sample are measured, such as the sample thickness and cross-sectional area. In an embodiment, the measurement is performed by a method similar to... Figure 3 One or more of the following sensors are used: a first temperature sensor 315, a second temperature sensor 335, a third temperature sensor 360, a timer 327, and a phase detector 325.

[0054] At step 140, the thermal conductivity of the sample is determined at least based on the measurement performed at step 130. In some embodiments, the thermal conductivity of the sample is determined over a temperature range between different constant temperatures of the phase change material (first temperature) and the heat source (second temperature).

[0055] In some embodiments, method 100 is implemented to determine the thermal conductivity of a sample within a specific temperature range for various applications. In some embodiments, a first temperature and a second temperature correspond to the lower and upper limits of the temperature range, respectively. Therefore, the phase change material and / or heat source at step 120 are selected based on the first and second temperatures corresponding to the requirements of the specific temperature range. For example, the sample may be a component (e.g., a core blanket) to be used in a light water reactor operating at 250°C–350°C. To approximate this temperature range for determining the thermal conductivity of the sample, the first phase material and / or heat source may be bismuth (Bi) with a melting point of 271°C or lead (Pb) with a melting point of 327°C. In an embodiment, the phase change material is bismuth (Bi), and the heat source is lead (Pb). As another example, the sample may be a core blanket to be used in a modular reactor operating at 700°C–900°C. To approximate this temperature range for determining the thermal conductivity of the sample, the phase change material and / or heat source may be a eutectic copper-silver (Cu-Ag) alloy with a melting point of 779°C. As another example, in the event of a high-temperature accident exceeding 900°C, it may be necessary to determine and evaluate the thermal conductivity of a sample. Therefore, the first-phase material and / or heat source could be silver (Ag) with a melting point of 962°C, copper (Cu) with a melting point of 1083°C, silicon (Si) with a melting point of 1414°C, or any combination thereof. As another example, the sample could be a flow channel insert wall structure for nuclear fusion coolant flow applications operating at 300-700°C. To approximate this temperature range for determining the thermal conductivity of the sample, the phase change material and / or heat source could be tin (Sn) with a melting point of 232°C or aluminum (Al) with a melting point of 660°C. In this embodiment, the phase change material is tin (Sn), and the heat source is Al. Sometimes, it is desirable to determine the thermal conductivity of a sample at a specific temperature. Therefore, the first-phase material may have a phase change temperature at or near a specific temperature. Furthermore, the heat source could be a different phase change material having a phase change temperature similar to but different from the phase change temperature. Alternatively or additionally, the heat source may be a heater configured to maintain a specific temperature, with or without a phase change material.

[0056] In some embodiments, the temperature range for determining the thermal conductivity of a sample can be adjusted by inserting one or more reference structures, such as... Figures 10A to 10D A more detailed description of the related information.

[0057] Figure 2 A schematic diagram 200 is depicted, illustrating the basic principle of heat conduction from hot medium 240 to cold medium 210 through sample 230. The terms "hot" and "cold" are relative terms, simply meaning that the temperature (T1) of the cold medium 210 is lower than the temperature (T2) of the hot medium 240. When both T1 and T2 are constant, the heat flux between the cold medium 210 and the hot medium 240 (e.g., ...) Figure 2(As shown in Figures 205, 215, and 235) are constant. The heat fluxes 205, 215, and 235 can be expressed as:

[0058] (1)

[0059] Where q is a constant heat flux of 205, 215 and 235, k is the thermal conductivity of sample 230 in the temperature range between T1 and T2, h is the thickness of sample 230, A is the cross-sectional area of ​​sample 230, T1 is a first temperature maintained by cold medium 210 and T2 is a second temperature maintained by hot medium 240.

[0060] By rearranging the terms in equation (1), the thermal conductivity k of sample 230 in the temperature range between T1 and T2 is obtained as follows:

[0061] (2)

[0062] Figure 3 An example of a thermal conductivity measurement system 300 is shown. The thermal conductivity measurement system 300 can be used to implement method 100 to determine the thermal conductivity of sample 330. As shown, the thermal conductivity measurement system 300 includes a phase change material 310 and a heat source 340. The thermal conductivity measurement system 300 also includes a first insulator 320 outside the phase change material 310 and a second insulator 350 outside the heat source 340 to prevent heat loss and maintain directional thermal conduction from the heat source 340 to the phase change material 310. In an embodiment, the first insulator 320 is disposed outside a first container surrounding the phase change material 310, and the second insulator 350 is disposed outside a second container surrounding the heat source 340. In an embodiment, the phase change material 310 is... Figure 2 The cold medium 210 and the heat source 340 are Figure 2 The thermal medium 240. The thermal conductivity measurement system 300 also includes one or more sensors 315, 325, 327, 335, and 360 for example in... Figure 1One or more measurements are performed at step 130 of method 100. For example, thermal conductivity measurement system 300 may include a first temperature sensor 315 configured to measure and monitor the temperature of phase change material 310, a second temperature sensor 335 configured to measure and monitor the temperature of sample 330, and a third temperature sensor 360 configured to measure and monitor the temperature of heat source 340. Thermal conductivity measurement system 300 may include timer 327 configured to measure the phase change period of phase change material 310 during which phase change material 310 undergoes a phase change. Specifically, time 327 is configured to measure the phase change period between a first time when at least a portion of phase change material 310 transitions from a first phase (e.g., a lower energy phase) to a second time when substantially all phase change material 310 transitions to the second phase (e.g., a higher energy phase). Optionally, thermal conductivity measurement system 300 may include phase detector 325 configured to detect the current phase (i.e., solid, liquid, or gas) of phase change material 310. In an embodiment, the first temperature sensor 315 can be used as a phase detector 325 based on the measured temperature of the phase change material 310. For example, when the measured temperature of the phase change material 310 is below its melting point, the phase change material 310 is a solid. When the measured temperature of the phase change material 310 is above its melting point but below its boiling point, the phase change material 310 is a liquid. When the measured temperature of the phase change material 310 is above its boiling point, the phase change material 310 is a gas. When the measured temperature of the phase change material 310 is equal to its melting point, the phase change material 310 is a mixture of solid and liquid. When the measured temperature of the phase change material 310 is equal to its boiling point, the phase change material 310 is a mixture of liquid and gas. Figure 3 As shown, the thermal conductivity measurement system 300 may further include a display 370, which shows the thermal conductivity measurement system in practice. Figure 1 The thermal conductivity of sample 330 is measured after step 140 of method 100. In an embodiment, the thermal conductivity measurement system 300 includes one or more processors coupled to a first temperature sensor 315, a second temperature sensor 335, a third temperature sensor 360, a timer 327, and a phase detector 325, and configured to implement... Figure 1Step 140 of method 100 involves determining the thermal conductivity of sample 330 using one or more equations, which will be discussed in detail below, based on one or more measurements from the first temperature sensor 315, the second temperature sensor 335, the third temperature sensor 360, the timer 327, and the phase detector 325. One or more processors may also be configured to send the determined thermal conductivity to a display 370 for display. In embodiments, one or more processors reside in a remote server or hardware platform (e.g., hardware platform 1300) communicating with the first temperature sensor 315, the second temperature sensor 335, the third temperature sensor 360, the timer 327, and the phase detector 325.

[0063] In implementation Figure 1 In step 130 of method 100, or prior to this step, the phase change material 310 may undergo a phase transition at a first temperature T1, while the heat source 340 may maintain a second temperature T2. In an embodiment, the first temperature T1 is lower than the second temperature T2. As described above, the phase change material 310 and the heat source 340 may be selected based on a specific desired temperature range for determining the thermal conductivity of the sample. Figure 4 Table 400 shows some examples of phase change materials 310 that can be used in thermal conductivity measurement system 300. Although not shown in Table 400, examples of phase change materials 310 may also include, but are not limited to, eutectic alloys such as copper-tin (Cu-Sn) alloys, aluminum-tin (Al-Sn) alloys, copper-gold (Cu-Au) alloys, copper-silver (Cu-Ag) alloys, tin-zinc (Sn-Zn) alloys, and aluminum-tin (Al-Sn) alloys.

[0064] In the embodiments, in the implementation Figure 1 In step 120 of method 100, or prior to this step, the phase change material 310 is provided in a lower energy phase with a temperature below a first temperature T1, while the heat source 340 is maintained at a second temperature T2. For example, the phase change material 310 may be provided as a solid with a temperature below its melting point. As another example, the phase change material 310 may be provided as a liquid with a temperature below its boiling point. Because the temperature of the heat source 340 is higher than that of the phase change material 310, heat conduction occurs from the heat source 340 through the sample 330 to the phase change material 310, causing the phase change material 310 to transition from a lower energy phase to a higher energy phase at the first temperature T1. In an embodiment, Figure 1 Step 130 in method 100 is by Figure 3 The timer 327 is implemented to measure the phase change cycle of the phase change material 310 undergoing a phase change (e.g., from solid to liquid, or from liquid to gas). To more clearly illustrate the thermal conductivity measurement process, Figure 5AThe figure illustrates the temperature changes of phase change material 310 (represented by solid lines) and heat source 340 (represented by dashed lines) with respect to time. As shown, heat source 340 maintains a stable constant temperature T2. When heat conduction begins from heat source 340 to phase change material 310 (e.g., due to sample 330 being placed and in thermal contact with phase change material 310 and heat source 340), phase change material 310 has an initial temperature T0 from time t0 to time t1. When phase change material 310 begins to transition from a lower energy phase to a higher energy phase, the temperature of phase change material 310 rises from T0 at time t1 to the phase transition temperature T1 at time t2, while maintaining the phase transition temperature T1 from time t2 to time t3. During the phase transition time period t = t3 - t2, phase change material 310 operates by storing energy from heat source 340 at a constant temperature T1 during the transition from a lower energy phase to a higher energy phase (e.g., from solid to liquid, or from liquid to gas). The stored energy can be converted into the kinetic energy of the atoms in the phase change material 310. The energy stored during the phase change cycle at a constant temperature is called the latent heat of the phase change material 310. Figure 5A In the example shown, the latent heat of the phase change material 310 is the energy difference between time t3 and time t2. In the embodiment, the phase change period t of the phase change material 310 is determined by... Figure 3 Timer 327 in Figure 1The measurement is taken at step 130 of method 100. After the phase change material 310 has completely transformed into a higher energy phase at time t3, the increased energy from the heat source 340 raises the temperature of the phase change material 310 until T2 at time t4, after which the phase change material 310 and the heat source 340 have the same temperature. In an embodiment, the first temperature T1 is the melting point of the phase change material 310. Therefore, the phase change material 310 is solid from time t0 to time t2, a mixture of solid and liquid during the phase change cycle t from time t2 to time t3, and a liquid after time t3 when the temperature of the phase change material 310 is below the boiling point of the phase change material. In an embodiment, the first temperature T1 is the boiling point of the phase change material 310. Therefore, the phase change material 310 is liquid from time t0 to time t2, a mixture of liquid and gas during the phase change cycle from time t2 to time t3, and a gas after time t3. In an embodiment, the heat source 340 may be a heater that provides a constant temperature T2. In one embodiment, heat source 340 may be a second phase change material connected to a controlled heater 375 to maintain the second phase change material at a constant temperature T2. In another embodiment, the controlled heater 375 is a heating band. In some embodiments, the second phase change material of heat source 340 may be the same as or different from phase change material 310, wherein the phase change temperature is not higher than T1. Thus, the controller heater 375 of heat source 340 can maintain the second phase change material of heat source 340 in a higher energy phase at a constant temperature T2. In some embodiments, the second phase change material of heat source 340 may be different from phase change material 310, whose phase change temperature is higher than T1. In this example, the phase change temperature of the second phase change material may be less than, equal to, or greater than the second temperature T2.

[0065] Figure 6 An example of a thermal conductivity measurement system 600 comprising two different phase change materials 310 and 640 is shown. Figure 3 The phase change material 310 in the system is renamed the first phase change material 310. In this embodiment, the heat source 340 in the thermal conductivity measurement system 300 is a phase change material. Therefore, the heat source 340 in the thermal conductivity measurement system 300 is transformed into a phase change material. Figure 6 The thermal conductivity measurement system 600 includes a second phase change material 640. In an embodiment, the second phase change material 640 maintains a phase change cycle at a second temperature T2, which is the phase change temperature of the second phase change material 640. The second temperature T2 may correspond to the upper limit of the temperature range that determines the thermal conductivity of the sample 330. The second phase change material 640 can be selected accordingly based on temperature range requirements. In some embodiments, the second phase change material 640 may, for example, be in... Figure 4 Choose from the phase change materials in Table 400.

[0066] To more clearly describe the thermal conductivity measurement process, Figures 5B-5C The diagram shows the temperature changes of the first phase change material 310 (solid line) and the second phase change material 640 (dotted line) relative to time. Figure 5B and 5C In the two examples, the first phase change material 310 is maintained at a first temperature T1 during a first phase change period t to transition from a lower energy phase to a higher energy phase, and the second phase change material 640 is maintained at a second temperature T2 during a corresponding second phase change period t', which is longer than the first phase change period t, to transition from a higher energy phase to a lower energy phase. Specifically in Figure 5B In this process, when the second phase change material 640 begins to transition from a higher energy phase to a lower energy phase (e.g., from gas to liquid, or from liquid to solid), the temperature of the second phase change material 640 decreases from T3 at time t0 to T2 at time t1. Then, the second phase change material 640 maintains a second temperature T2 until time t6 before the temperature decreases further. The second phase change material 640 operates by releasing energy during a second phase change period t' = t6 - t1 at the second phase change temperature T2 when the phase change occurs, for example, from a higher energy phase to a lower energy phase. The energy released during the second phase change period can be converted from the kinetic energy of the atoms in the second phase change material 640. The latent heat of the second phase change material 640 is the difference between the energy of the second phase change material 640 at time t1 and at time t6. When heat conduction begins from the second phase change material 640 to the first phase change material 310, and when the second phase change material 640 is a mixture of lower and higher energy phases during the phase change cycle, the first phase change material 310 has an initial temperature T0 from time t0 to time t2. As the first phase change material 310 begins to transition from the lower energy phase to the higher energy phase, its temperature rises from T0 at time t2 to the first phase change temperature T1 at time t3, while remaining at the first phase change temperature T1 from time t3 to time t4. During the first phase change cycle t = t4 - t3, the first phase change material 310 operates by storing energy from the second phase change material 640 at a constant temperature T1 during transitions from the lower energy phase to the higher energy phase (e.g., from solid to liquid, or from liquid to gas). The latent heat of the first phase change material 310 is the energy difference between time t4 and time t3. After the first phase change material 310 completely transforms into a higher energy phase at time t4, the additional energy from the second phase change material 640 causes the temperature of the first phase change material 310 to rise to T2 at time t5 and remain at T2 until time t6, after which the temperatures of the first phase change material 310 and the second phase change material 640 decrease together.

[0067] As Figure 5CAnother example is that when the second phase change material 640 begins to transition from a higher energy phase to a lower energy phase (e.g., from gas to liquid, or from liquid to solid), the temperature of the second phase change material 640 decreases from T3 at time t0 to the second phase change temperature T2 at time t2, and then remains constant until time t5 before decreasing. The second phase change material 640 operates by releasing energy at the second phase change temperature T2 during the second phase change period t' = t5 - t2, for example, from a higher energy phase to a lower energy phase. The latent heat of the second phase change material 640 is the difference between the energy of the second phase change material 640 at time t2 and at time t5. When heat conduction begins from the second phase change material 640 to the first phase change material 310, the first phase change material 310 has an initial temperature T0 from time t0 to time t1. This is in contrast to the second phase change material 640 being a mixture of a lower energy phase and a higher energy phase when heat conduction begins at time t1. Figure 5B different, Figure 5C The second phase change material 640 is provided to be fully in the higher energy phase at a temperature above the second phase transition temperature T2 when heat conduction begins. When the first phase change material 310 begins to transition from the lower energy phase to the higher energy phase, the temperature of the first phase change material 310 rises from T0 at time t1 to the first phase transition temperature T1 at time t3, while maintaining the first phase transition temperature T1 from time t3 to time t4. The first phase transition period t is equal to t4 - t3. The latent heat of the first phase change material 310 is the energy difference between time t4 and time t3. After the first phase change material 310 has fully transitioned to the higher energy phase at time t4, the additional energy from the second phase change material 640 causes the temperature of the first phase change material 310 to rise until T4 at time t6, after which the temperatures of the first and second phase change materials 640 decrease together. The temperature of the first phase change material 310 rises to T2 before the first phase change material completes its phase transition process. Figure 5B different, Figure 5C The first phase change material 310 was provided to fail to reach the same temperature as the second phase change material 640 before the second phase change material 640 completed the phase change process.

[0068] In an embodiment, Figure 5B or Figure 5C The first temperature T1 is the melting point of the first phase change material 310. Therefore, the first phase change material 310 is solid at the first temperature T1 before the first phase change period t, is a mixture of solid and liquid at the first temperature T1 during the first phase change period t, and is liquid after the first phase change period t when the temperature of the first phase change material 310 is below its boiling point. In the embodiment, Figure 5B or Figure 5CThe first temperature T1 is the boiling point of the first phase change material 310. Therefore, the first phase change material 310 is a liquid before the first phase change period t at the first temperature T1, a mixture of liquid and gas during the first phase change period t at the first temperature T1, and a gas after the first phase change period t.

[0069] In an embodiment, Figure 5B or Figure 5C The second temperature T2 is the melting point of the second phase change material 640. Therefore, the second phase change material 640 is a liquid before the second phase change cycle t' at the second temperature T2 when its boiling point is below that of the second phase change material 640; it is a mixture of solid and liquid during the second phase change cycle t' at the second temperature T2; and it is a solid after the second phase change cycle t'. In the embodiment, Figure 5B or Figure 5C The second temperature T2 is the boiling point of the second phase change material 640. Therefore, the second phase change material 640 is a gas before the second phase change period t' at the second temperature T2, a mixture of liquid and gas during the second phase change period t at the first temperature T2, and a liquid after the second phase change period t'.

[0070] In Figure 3 , Figures 5A-5C and Figure 6 In each of the associated examples, the constant heat flux q can be further determined relative to the phase change material 310 as:

[0071] (3)

[0072] Where m1 is the mass of phase change material 310 (or the first phase change material 310),

[0073] H1 is the latent heat of phase change material 310 (or the first phase change material 310), and

[0074] t is the phase change cycle during which the phase change material 310 (or the first phase change material 310) undergoes a phase change.

[0075] By substituting equation (3) into equation (2), the thermal conductivity of sample 330 in the temperature range between T1 and T2 can be determined as follows:

[0076] (4)

[0077] In the embodiments, m1, H1, h, A, T1, and T2 in equation (4) are all known or readily available constants. Therefore, Figure 1 Step 130 of method 100 may include measuring the phase change period of phase change material 310 (or first phase change material 310) by means of timer 327. Figure 1Step 140 of method 100 may include determining the thermal conductivity k of the sample by substituting the measured phase transition period t into equation (4).

[0078] Figure 7A Another example of a thermal conductivity measurement system 700 for measuring the thermal conductivity of sample 730 is shown. The thermal conductivity measurement system 700 is functionally similar to the thermal conductivity measurement system 300. The thermal conductivity measurement system 700 includes a first temperature sensor 715, a first insulator 720, a phase detector 725, a timer 727, a second temperature sensor 735, a second insulator 750, a third temperature sensor 760, and a display 770, which are substantially similar to the first temperature sensor 315, the first insulator 320, the phase detector 325, the timer 327, the second temperature sensor 335, the second insulator 350, the third temperature sensor 360, and the display 370. Furthermore, the thermal conductivity measurement system 700 includes a phase change material 710 and a heat source 740, which, apart from differences in shape, are substantially similar to the phase change material 310 and the heat source 360. As shown in the figure... Figures 7A-7B Sample 730 in the sample has a higher content than Figure 3 Sample 330 in the sample has a more complex shape. Specifically, in Figures 7A-7B In this study, sample 730 has a curved shape. To ensure good contact and accuracy in determining the thermal conductivity of sample 730, phase change material 710 and heat source 740 each have a curved shape conforming to the curved shape of sample 730, such as... Figure 7A As shown. When the phase change material 710 or heat source 740 is a liquid or gas, it is not challenging to conform the shape of the phase change material 710 or heat source 740 to the shape of the sample 730. In embodiments, when the phase change material 710 or heat source 740 is a solid, the phase change material 710 or heat source 740 has a pre-formed shape conforming to the shape of the sample 730. In embodiments, the phase change material 710 can be processed to have a shape conforming to the shape of the sample 730 to have good thermal contact with the sample 730. For example, the phase change material 710 can be first melted into a liquid and placed on the sample 730. When cooled, the phase change material 710 becomes a solid with a curved shape conforming to the shape of the sample 730. Sometimes, after cooling down, the phase change material 710 in the solid phase binds to the sample. Additionally or alternatively, the heat source 740 can be melted into a liquid, with the sample 730 located on top of the liquid phase heat source 740 and below the phase change material 710.

[0079] In this embodiment, the heat source 740 is as follows: Figure 7B The phase change material 710 shown is a different phase change material. Figure 7B The thermal conductivity measurement system 770 includes a phase change material 710 (in...) Figure 7BThe two phase change materials are renamed as first phase change material 710 and second phase change material 745. Except for their shape, second phase change material 745 is essentially similar to second phase change material 640. (The last sentence appears to be incomplete and possibly refers to a different material.) Figure 5B , Figure 5C and Figure 6 As described, in implementation Figure 1 Prior to step 130 of method 100, the first phase change material 310 may initially be provided in solid or liquid form, and the second phase change material 745 may initially be provided in liquid, gas, mixture of liquid and gas, or mixture of solid and liquid form.

[0080] Figure 8 This is a flowchart of an example method 800 for measuring the thermal conductivity of a sample using two different phase change materials. In this embodiment, the sample may be sample 330 or 730. In this embodiment, a method such as... Figure 9A The furnace 900 shown and as Figure 9B The thermal conductivity measurement system 950 shown performs one or more steps of method 800. In step 810, a first phase change material is shaped to conform to the shape of the sample to ensure good thermal contact with the sample and accuracy in determining the thermal conductivity of the sample. The first phase change material may be a first phase change material 310, 710. In an embodiment, the first phase change material is shaped to conform to the shape of the sample. For example, when the sample is similar to a sample 730 with a curved shape, the first phase change material may also have a curved shape conforming to the curved shape of the sample 730 to ensure good thermal contact between the sample and the first phase change material. In an embodiment, the first phase change material is shaped by supplying heat to a first phase change material having a first melting point and a second phase change material having a second melting point higher than the first melting point to melt the first and second phase change materials into liquid phases, respectively. For example, the first phase change material may be tin (Sn) with a melting point of 232°C, and the second phase change material may be aluminum (Al) with a melting point of 660°C. Figure 9AThe furnace 900 shown is used to provide heat to melt tin (Sn) in a thin-walled metal cup 915 into a liquid. Another furnace 900 can also be used to melt aluminum (Al) in a graphite crucible 945 into a liquid. Both the thin-walled metal cup 915 and the graphite crucible 945 may have good thermal conductivity, allowing for efficient heat conduction. After the aluminum (Al) has been completely melted into a liquid, the furnace 900 can be shut off or maintained at a low heating power to overcome heat loss from the aluminum (Al) and maintain a relatively stable temperature in the graphite crucible 945. In an embodiment, the first phase change material is further shaped by placing at least a portion of the first phase change material in a liquid phase onto the sample, such that upon cooling, the first phase change material transforms from a liquid phase to a solid phase and bonds with the sample. For example, at least a portion of the tin (Sn) in the liquid phase can be placed onto the sample 935 so that the tin (Sn) has a shape conforming to the shape of the sample 935 after cooling to a solid phase. In some embodiments, at least a portion of the tin (Sn) bonds with the sample 935 after cooling to a solid phase.

[0081] In step 820, the samples, each in the solid phase, and the first phase change material are placed in thermal contact with the second phase change material in the liquid phase to allow heat conduction from the second phase change material to the first phase change material and to cause the first phase change material to transition from the solid phase to the liquid phase. For example, a sample bonded to tin (Sn) is placed in thermal contact with liquid aluminum (Al) and on top of the liquid aluminum (Al) to allow heat conduction from the liquid aluminum (Al) to the liquid tin (Sn) through the liquid sample. This heat conduction can raise the temperature of the tin (Sn) to its melting point of 232°C and cause the tin (Sn) to transition from the solid phase to the liquid phase at 232°C. In an embodiment, while aluminum (Al) undergoes a phase transition from the liquid phase to the solid phase at 660°C, tin (Sn) undergoes a phase transition from the solid phase to the liquid phase at 232°C. In an embodiment, temperature changes of aluminum (Al) and tin (Sn) are monitored and recorded.

[0082] In step 830, the duration between a first time when at least a portion of the first phase change material transitions from a solid phase to a liquid phase and a second time when substantially all of the first phase change material transitions to a liquid phase is measured. In an embodiment, the measured duration is the phase transition cycle of tin (Si).

[0083] At step 840, the thermal conductivity of the sample is determined based on the duration. In an embodiment, for example, based on the duration measured at step 830, equation (4) is used to determine the thermal conductivity of the sample for a temperature range between the melting point of tin (Sn) at 232°C and the melting point of aluminum (Al) at 660°C.

[0084] Figures 10A to 10DDifferent examples of adjusting the temperature range for determining the thermal conductivity of a sample are described. Equation (4) calculates the thermal conductivity of the sample between constant temperatures (i.e., T1 and T2) on different sides of the sample. Sometimes, it is desirable to determine the thermal conductivity over different temperature ranges. However, it is difficult to adjust the constant temperatures T1 and T2 when selecting and employing a phase change material and a heat source. One solution to this problem is to insert one or more reference structures between the phase change material and the heat source. The inserted one or more reference structures each have a corresponding known thermal conductivity while the phase change material and the heat source are each kept at their respective constant temperatures. By varying the thickness of each of the one or more reference structures, the corresponding temperature difference of each of the one or more reference structures from one side to the other can be adjusted. Thus, the temperature range for adjusting the thermal conductivity of the sample can be achieved. In one embodiment, the one or more reference structures have the same thermal conductivity. In another embodiment, the one or more reference structures have different thermal conductivityes. In another embodiment, the one or more reference structures have the same thickness. In another embodiment, the one or more reference structures have different thicknesses. In another embodiment, the thermal conductivity of each of the one or more reference structures is known. In another embodiment, the one or more reference structures are one or more reference plates. In another embodiment, the one or more reference structures each have a shape conformal to the shape of the sample.

[0085] Figure 10A An example is shown of increasing the lower limit of the temperature range for determining the thermal conductivity of sample 1030 by inserting a first reference structure 1020 between phase change material 1010 and sample 1030 in thermal conductivity measurement system 1002. In an embodiment, phase change material 1010, sample 1030, and heat source 1040 may be substantially similar to phase change materials 310, 710, samples 330, 730, and heat sources 340, 740. In operation, phase change material 1010 is maintained at a first temperature T1 during a phase change period (denoted by t), during which phase change material 1010 transitions from a lower energy phase to a higher energy phase, for example, from a solid to a liquid or from a liquid to a gas. Heat source 1040 maintains a second temperature T2 at least longer than the duration of the phase change period. In an embodiment, at least one of the phase change period T or the temperature T of sample 1030 during the phase change period T is measured to determine... Figures 10A to 10D The thermal conductivity of sample 1030.

[0086] Similar to Figure 2 , Figure 3 and Figures 5A-5C as well as Figure 6 In related discussions, the heat flux q can be expressed by equations (5)-(7):

[0087] (5)

[0088] (6)

[0089] (7)

[0090] Where m is the mass of phase change material 1010, H is the latent heat of phase change material 1010, t is the phase change period of phase change material 1010 at the first temperature T1, and k r1 The thermal conductivity of the first reference structure is 1020, h. r1 It is the thickness of the first reference structure 1020, T r1 T1 is the constant temperature of the interface between the first reference structure 1020 and the sample 1030, A is the cross-sectional area of ​​the sample 1030, h is the thickness of the sample 1030, T1 is the constant temperature of the phase change material 1010, T2 is the constant temperature of the heat source 1040, and k is the thermal conductivity of the sample 1030 within the adjusted temperature range between T1 and T2. Because subsequent heat conduction occurs from the heat source 1040 through the sample 1030 and the first reference structure 1020 to the phase change material 1010, the constant temperature T on the sample-facing side of the first reference structure is... r1 Above the constant temperature T1 of the phase change material.

[0091] The formula for T can be calculated based on equations (5) and (7). r1 Thermal conductivity k of sample at 1030°C within the adjusted temperature range between T2:

[0092] (8)

[0093] Alternatively, the equations (6) and (7) can be used to calculate the expression for T. r1 Thermal conductivity k of sample at 1030°C within the adjusted temperature range between T2:

[0094] (9)

[0095] Figure 10B An example is shown of reducing the upper limit of the temperature range for determining the thermal conductivity of sample 1030 by inserting a second reference structure 1035 between the heat source 1040 and sample 1030 in the thermal conductivity measurement system 1004. In an embodiment, Figure 10A The second reference structure 1035 and the first reference structure 1020 have the same thickness. In the embodiment, Figure 10A The second reference structure 1035 and the first reference structure 1020 have different thicknesses. In the embodiment, Figure 10A The second reference structure 1035 and the first reference structure 1020 have the same thermal conductivity. In the embodiment, Figure 10A The second reference structure 1035 and the first reference structure 1020 have different thermal conductivity.

[0096] Similar to the discussion above, the heat flux q can be expressed by equations (5), (10), and (11):

[0097] (10)

[0098] (11)

[0099] Where k r2 The thermal conductivity of the second reference structure 1035 is h. r2 It is the thickness of the second reference structure 1035, T r2 It is the constant temperature of the interface between the second reference structure 1035 and the sample 1030, and k is the constant temperature between T1 and T2. r2 The thermal conductivity of sample 1030 within the adjusted temperature range. Because subsequent heat conduction occurs from heat source 1040 through second reference structure 1035 and sample 1030 to phase change material 1010, the constant temperature T on the sample-facing side of the second reference structure... r2 Below the constant temperature T2 of the heat source.

[0100] T1 and T can be calculated based on equations (5) and (11). r2 Thermal conductivity k of the sample at 1030°C within the adjusted temperature range:

[0101] (12)

[0102] Alternatively, T1 and T can be calculated based on equations (10) and (11). r2 Thermal conductivity k of the sample at 1030°C within the adjusted temperature range:

[0103] (13)

[0104] Figure 10C An example is shown of narrowing the temperature range for determining the thermal conductivity of sample 1030 by inserting a first reference structure 1020 between phase change material 1010 and sample 1030 and a second reference structure 1035 between heat source 1040 and sample 1030 in thermal conductivity measurement system 1006.

[0105] Similar to the discussion above, the heat flux q can be expressed by equations (5), (14), (15), and (16):

[0106] (14)

[0107] (15)

[0108] (16)

[0109] Where k is for T r1 With T r2 The thermal conductivity of sample 1030 within the adjusted temperature range. Because heat conduction occurs from heat source 1040 through second reference structure 1035, sample 1030, and first reference structure 1020 to phase change material 1010, the constant temperature T at the interface between the second reference structure and the sample subsequently... r2 The constant temperature T2 below the heat source, and the constant temperature T at the interface between the first reference structure and the sample. r1 Above the constant temperature T1 of the phase change material.

[0110] The equations (5) and (15) can be used to calculate the value for T. r1 With T r2 Thermal conductivity k of the sample at 1030°C within the adjusted temperature range:

[0111] (17)

[0112] Alternatively, the equations (14) and (15) can be used to calculate the expression for T. r1 With T r2 Thermal conductivity k of the sample at 1030°C within the adjusted temperature range:

[0113] (18)

[0114] Alternatively, the equations (15) and (16) can be used to calculate the expression for T. r1 With T r2 Thermal conductivity k of the sample at 1030°C within the adjusted temperature range:

[0115] (19)

[0116] In an embodiment, Figure 10C The heat source 1040 in the middle is as follows Figure 10D The phase change materials shown are, in which phase change material 1010 is renamed as first phase change material 1010, and heat source 1040 is replaced by second phase change material 1045 having a phase change temperature T2 in thermal conductivity measurement system 1050. In embodiments, first phase change material 1010 and second phase change material 1045 may be substantially similar to first phase change materials 310, 710 and second phase change materials 640, 745. The phase change temperature T2 can be calculated based on equations (17), (18) or (19). r1 With T r2 The thermal conductivity k of the sample at 1030 with an adjusted temperature range.

[0117] In the embodiments, each of the thermal conductivity measurement systems 1002, 1004, 1006, and 1050 includes components similar to Figure 3One or more sensors, including a first temperature sensor 315, a second temperature sensor 335, a third temperature sensor 360, a timer 327, and a phase detector 325, are used to perform actions such as... Figure 1 In step 130 of method 100, one or more measurements are taken to determine the thermal conductivity of sample 1030.

[0118] Figure 11 This is a schematic diagram of an example thermal conductivity measurement system 1100 configured to determine the thermal conductivity of a solid material sample 1130 having a tubular structure. Figure 11 As shown, the thermal conductivity measurement system 1100 includes a phase change material 1110, a heat source 1140, and a container 1120, wherein a controlled heater 1125 is coupled to the heat source 1140. In this example, the solid material sample 1130 has a tubular structure. Although not shown, the thermal conductivity measurement system 1100 may also include a display similar to display 370 to show the determined thermal conductivity of the solid material sample 1130. The thermal conductivity measurement system 1100 may further include components similar to... Figure 3 One or more sensors, including a first temperature sensor 315, a second temperature sensor 335, a third temperature sensor 360, a timer 327, and a phase detector 325, are used, for example, in... Figure 1 At step 130 of method 100, one or more measurements are performed to determine the thermal conductivity of the solid material sample 1130. In embodiments, the phase change material 1110 and the heat source 1140 may be substantially similar to phase change materials 310, 710, 1010 and heat sources 340, 740, 1040, except for differences in shape. In embodiments, the phase change material 1110 undergoes a phase change at a first temperature T1. In embodiments, a controlled heater 1125 is configured to supply heat to the heat source 1140 to maintain the heat source 1140 at a second temperature T2 above T1. In embodiments, the thermal conductivity measurement system 1100 does not necessarily contain an insulator because heat flows inward. In embodiments, the heat source 1140 is a different phase change material from the phase change material 1110. In embodiments, the phase change material of the heat source 1140 has a higher phase change temperature (e.g., melting point or boiling point) than the phase change material 1110. In one embodiment, the heat source 1140 is a phase change material 1110 connected to a controlled heater 1125, which maintains the phase change material of the heat source 1140 in a higher energy state (e.g., liquid or gas) to maintain a second temperature T2. In another embodiment, the controlled heater 1125 is a heating band. In yet another embodiment, the container 1120 is a granite crucible. As shown, the solid material sample 1130 has a tubular structure. Therefore, the heat source 1140 may also have a tubular structure, while the phase change material 1110 may have a cylindrical shape conforming to the shape of the solid material sample 1130 (e.g., cylindrical shape). Figure 11As shown), to ensure good thermal contact and accuracy in determining the thermal conductivity of the solid material sample 1130. In an embodiment, the phase change material 1110 can be pre-formed into a cylindrical shape conforming to the tubular shape of the solid material sample 1130. In an embodiment, it can be achieved by... Figure 8 A similar process to step 810 of method 800 involves processing the phase change material 1110 into a cylindrical shape conforming to the tubular shape of the solid material sample 1130. For example, the phase change material 1110 may be tin (Sn), and the solid material sample 1130 may have a quartz tubular shape. The phase change material 1110 may be completely melted into liquid tin (Sn) in a furnace (e.g., furnace 900) and placed on the surface of the solid material sample 1130. Upon cooling, the liquid tin (Sn) may become a solid cylindrical structure comprising portions that contact and conform to the tubular shape at contact points with the solid material sample 1130 to ensure good thermal contact with the solid material sample 1130. Sometimes, the phase change material 1110 with a cylindrical shape may be combined with the solid material sample 1130. Alternatively, the heat source 1140 may also be tin (Sn), and is completely melted into liquid tin (Sn) by a furnace (e.g., furnace 900), which is coupled to a controlled heater 1125 (e.g., a heating band) that allows the liquid tin (Sn) to remain liquid and at a second temperature T2 above T1. A solid material sample 1130 having a quartz tube shape and being bonded to the phase change material 1110 is placed in thermal contact with the heat source 1140 in the form of liquid tin (Sn) at the second temperature T2, so that heat conduction occurs from the heat source 1140 through the solid material sample 1130 to the phase change material 1110. Heat conduction can raise the temperature of the phase change material 1110 to the first temperature T1 to change phase, for example, from solid to liquid at T1. In an embodiment, one or more sensors of the thermal conductivity measurement system 1100 may be used to measure and monitor the temperatures of the phase change material 1110 and the heat source 1140. In an embodiment, the phase transition period t of the phase change material 1110 from a lower energy phase to a higher energy phase can be measured, for example, by a timer similar to timers 327 and 727.

[0119] The heat flux q can be expressed by equations (20) and (21):

[0120] (20)

[0121] (twenty one)

[0122] Where m is the mass of phase change material 1110, H is the latent heat of phase change material 1110, t is the phase change period of phase change material 1110 at the first temperature T1, ρ is the density of phase change material 1110, L is the length of phase change material 1110, and r iIt is the inner radius of the tubular shape of sample 1130, and r o T1 is the outer radius of the tube shape of sample 1130, T2 is the constant temperature of phase change material 1110, T2 is the constant temperature of heat source 1140, and k is the thermal conductivity of solid material sample 1130 in the temperature range between T1 and T2.

[0123] The thermal conductivity k of the solid material sample 1130 in the temperature range between T1 and T2 can be calculated based on equations (20) and (21):

[0124] (twenty two)

[0125] In one embodiment, the phase change material 1110 and the heat source 1140 can be arranged differently; for example, the phase change material can be placed between the container 1120 and the solid material sample 1130, and the heat source 1140 can have a cylindrical shape placed inside a tubular structure of the solid material sample 1130. In this arrangement, the thermal conductivity measurement system 1100 can include an insulator outside the container 1120 to prevent heat loss, as heat flows outward from the heat source 1140 to the phase change material 1110.

[0126] Figure 12 This is a schematic diagram of an example thermal conductivity measurement system 1200 configured to determine the thermal conductivity of sample 1230. Figure 11 Unlike the solid material sample 1130, sample 1230 is a liquid or gas contained in or guided to flow in a fluid conduit 1205, which is located between and in thermal contact with the phase change material 1110 and the heat source 1140 in the thermal conductivity measurement system 1200. Sometimes, sample 1230 is also referred to as liquid or gas sample 1230. In embodiments, fluid conduit 1205 is a tube structure. In embodiments, fluid conduit 1205 is a double thin-walled tube. Fluid conduit 1205 has good thermal conductivity, allowing the liquid or gas sample 1230 to be in thermal contact with the phase change material 1110 and the heat source 1140, and permitting heat conduction from the heat source 1140 to the phase change material 1110, although fluid conduit 1205 physically separates the liquid or gas sample 1230 from the phase change material 1110 and the heat source 1140.

[0127] In one embodiment, the thermal conductivity measurement system 1200 includes a component similar to... Figure 3 One or more sensors, including a first temperature sensor 315, a second temperature sensor 335, a third temperature sensor 360, a timer 327, and a phase detector 325, are used to perform one or more measurements, for example, in... Figure 1 The thermal conductivity of the liquid or gas sample 1230 is determined at step 130 of method 100.

[0128] In embodiments, each of the thermal conductivity measurement systems 600, 700, 770, 1002, 1004, 1006, 1050, 1100, and 1200 includes one or more processors coupled to one or more sensors and similar to one or more processors in the thermal conductivity measurement system 300 described above.

[0129] Figure 13 An example of a hardware platform 1300 configured to implement some of the methods 100, 800 described herein is shown. Hardware platform 1300 may include one or more processors 1310 that can execute executable programs 1325 to instruct and control one or more manufacturing tools to implement the methods. Hardware platform 1300 may include a non-transitory computer-readable storage medium 1320 that can be used to store one or more executable programs 1325 (i.e., executable computer code) and / or store data. Hardware platform 1300 may also include a communication interface 1330. For example, communication interface 1330 may implement one or more wired or wireless communication protocols (Ethernet, LTE, Wi-Fi, Bluetooth, etc.). Hardware platform 1300 may be used to implement an offline or online server that communicates with one or more thermal conductivity measurement systems 300, 600, 700, 770, 1002, 1004, 1006, 1050, 1100, 1200 as described herein. In some embodiments, one or more processors 1310 may communicate via a communication interface 1330 with one or more sensors of thermal conductivity measurement systems 300, 600, 700, 770, 1002, 1004, 1006, 1050, 1100, 1200. In some embodiments, one or more processors 1310 may be configured to determine the thermal conductivity of a sample based on one or more measurements performed by one or more sensors according to formulas (4), (8), (9), (12), (13), (17)-(19) and (22), which may be included in an executable program 1325 stored in a non-transitory computer-readable storage medium 1320.

[0130] While this patent document contains numerous details, these details should not be construed as limiting any invention or the scope of the claims, but rather as descriptions of features of particular embodiments of a particular invention. Certain features described in the context of individual embodiments in this patent document may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented individually or in any suitable sub-combination in multiple embodiments. Furthermore, although features may be described above as functioning in certain combinations and even initially claimed in this way, in some cases one or more features from the claimed combination may be removed from the combination, and the claimed combination may be for sub-combinations or variations thereof.

[0131] Similarly, although operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring these operations to be performed in the specific order shown or sequentially, or to perform all of the shown operations to achieve the desired result. Furthermore, the separation of various components in the embodiments described in this patent document should not be construed as requiring such separation in all embodiments.

[0132] Only a few implementation methods and examples have been described, and other implementation methods can be enhanced and varied based on what is described and shown in this patent document.

Claims

1. A method for determining the thermal conductivity of a sample, comprising: Control the heat source to raise its temperature to a temperature higher than the phase change temperature of the phase change material; The sample is placed between and in thermal contact with an initial temperature of the phase change material below the phase change temperature and a heat source at an elevated temperature, so as to allow heat conduction from the heat source to the phase change material through the sample, thereby raising the initial temperature of the phase change material to the phase change temperature, so that the phase change material transforms from the first phase to the second phase at the phase change temperature. Perform measurements on at least one of the sample or phase change material; and The thermal conductivity of the sample is determined based on measurements.

2. The method according to claim 1, wherein, The phase change material maintains the phase change temperature during the first phase change cycle in order to transform from the first phase to the second phase.

3. The method according to claim 2, wherein, During the first phase transition cycle and in the second phase transition cycle, which lasts longer than the first phase transition cycle, the heat source is at a constant temperature equal to or lower than the rising temperature.

4. The method of claim 1 further comprises shaping the phase change material to conform to the shape of the sample to ensure good thermal contact with the sample and to determine the accuracy of the thermal conductivity of the sample.

5. The method according to claim 1, wherein, Phase change materials have a curved shape to conform to the curved shape of the sample to ensure good thermal contact with the sample and to accurately determine the thermal conductivity of the sample.

6. The method according to claim 5, wherein, The thermal conductivity of the sample is determined by the following formula: Where k is the thermal conductivity of the sample, ρ is the density of the phase change material, H is the latent heat of the phase change material, and r i It is the inner radius of the curved shape of the sample, r o T1 is the outer radius of the curved shape of the sample, T2 is the phase transition temperature of the phase change material, T2 is the constant temperature of the heat source when the phase change material changes from the first phase to the second phase at the phase transition temperature, and t is the first phase transition period of the phase change material changing from the first phase to the second phase.

7. The method according to claim 6, wherein, The sample is a solid material sample with a tubular shape, and the phase change material is shaped to include a portion of the solid material sample that contacts the tubular shape and conforms to the portion of the tubular shape at the contact location.

8. The method according to claim 1, wherein, The sample is a liquid or gas and is guided to flow in a fluid conduit between a heat source and a phase change material and in thermal contact with both the heat source and the phase change material.

9. The method according to claim 2, wherein, The step of performing a measurement on at least one of the sample or phase change material includes measuring a first phase change period of the phase change material between a first time when at least a portion of the phase change material transitions from a first phase to a second phase and a second time when substantially all of the phase change material transitions to the second phase, and wherein the thermal conductivity of the sample is determined by the following formula: Where k is the thermal conductivity of the sample, m1 is the mass of the phase change material, H1 is the latent heat of the phase change material, h is the thickness of the sample, A is the area of ​​the sample, T1 is the phase change temperature of the phase change material, T2 is the constant temperature of the heat source when the phase change material changes from the first phase to the second phase at the phase change temperature, and t is the first phase change period when the phase change material changes from the first phase to the second phase.

10. The method according to claim 3, wherein, The heat source includes a second phase change material having a second phase change temperature.

11. The method according to claim 3, further comprising: The reference structure is placed between the sample and one of the heat source and the phase change material, such that the reference structure is in thermal contact with the sample and one of the heat source and the phase change material. as well as The reference temperature of the reference structure is measured during the first phase transition cycle to determine the thermal conductivity of the sample at the reference temperature of the reference structure and the phase transition temperature of the phase change material or the constant temperature of the heat source during the first phase transition cycle of the phase change material.

12. The method according to claim 1, further comprising: The first reference structure is placed in thermal contact with the sample and between the sample and the phase change material; The second reference structure is placed between the sample and the heat source to make thermal contact with both the sample and the heat source. as well as The first reference temperature of the first reference structure and the second reference temperature of the second reference structure are measured to determine the thermal conductivity of the sample between the first reference temperature of the first reference structure and the second reference temperature of the second reference structure.

13. The method according to claim 12, wherein, The thermal conductivity of the sample between the first reference temperature and the second reference temperature is determined by one of the following expressions: Where k is the thermal conductivity of the sample, k r1 The thermal conductivity of the first reference structure, k r2 is the thermal conductivity of the first reference structure, m is the mass of the phase change material, H is the latent heat of the phase change material, A is the area of ​​the sample, and h is the thickness of the sample. r1 It is the thickness of the first reference structure, h r2 T is the thickness of the second reference structure, T1 is the phase transition temperature of the phase change material, T2 is the constant temperature of the heat source, and T... r1 It is the temperature of the first interface between the first reference structure and the sample, T. r2 It is the temperature of the second interface between the second reference structure and the sample, and t is the first phase transition period from the first phase to the second phase of the phase change material.

14. A system for determining the thermal conductivity of a sample, comprising: The first phase change material is configured to transform from a first phase to a second phase at a phase change temperature; A heat source is configured to maintain a constant temperature above the phase change temperature, wherein the phase change material and the heat source are placed on different sides of the sample to allow heat conduction from the heat source to the phase change material and to cause the phase change material to change from the first phase to the second phase; One or more sensors are coupled to the phase change material and configured to perform measurements on at least one of the sample or the phase change material; and A processor, coupled to the one or more sensors and configured to determine the thermal conductivity of a sample based at least on measurements of at least one of the sample or phase change material.

15. The system according to claim 14, wherein, At least one of the heat source or phase change material has a shape that conforms to the shape of the sample to ensure good thermal contact with the sample and to accurately determine the thermal conductivity of the sample.

16. The system according to claim 14, wherein, One of the heat source or phase change material has a cylindrical shape.

17. The system according to claim 14, wherein, The heat source is a second phase change material with a second phase change temperature equal to a constant temperature.

18. A method for determining the thermal conductivity of a sample, comprising: The first phase change material is shaped to conform to the shape of the sample to ensure good thermal contact with the sample and to accurately determine the thermal conductivity of the sample. The samples, each in the solid phase, and the first phase change material are placed in thermal contact with the second phase change material in the liquid phase to allow heat conduction from the second phase change material to the first phase change material and to allow the first phase change material to change from the solid phase to the liquid phase. The duration between the first time when at least a portion of the first phase change material changes from a solid phase to a liquid phase and the second time when substantially all of the first phase change material changes to a liquid phase is measured. as well as The thermal conductivity of the sample is determined at least based on the duration of the test.

19. The method according to claim 18, wherein, The steps of shaping the first phase change material to conform to the shape of the sample include: Heat is supplied to a first phase change material having a first melting point and a second phase change material having a second melting point higher than the first melting point, so that the first phase change material and the second phase change material respectively melt into a liquid phase; and At least a portion of the first phase change material in the liquid phase is placed onto the sample, such that when cooled, the first phase change material changes from the liquid phase to the solid phase and binds to the sample.

20. The method according to claim 18, wherein, The thermal conductivity of the sample between the first and second melting points is determined by the following formula: Where k is the thermal conductivity of the sample, m1 is the mass of the first phase change material, H1 is the latent heat of the first phase change material, h is the thickness of the sample, A is the area of ​​the sample, T1 is the first melting point of the first phase change material, T2 is the second melting point of the second phase change material, and t is the measurement duration of the first phase change material changing from the solid phase to the liquid phase. Wherein, the first phase change material is tin (Sn), lead (Pb), bismuth (Bi), eutectic copper-silver (Cu-Ag) alloy, silver (Ag), copper (Cu), or silicon (Si).

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