Heat transport or heat exchange working fluid and heat transport or heat exchange system

Abstract

[Problem] To provide a working fluid in which the efficiency of heat transport or heat exchange is further enhanced. Furthermore, generally contradictory functions such as reducing the power required for flow are solved at the same time. [Solution] The present invention is a heat transport or heat exchange system in which there is used one or more types of working fluids selected from: heat dissipation working fluids for semiconductors, automobiles, and computers; working fluids for immersion lithography; working fluids for temperature regulation; and working fluids for air conditioning machines, air conditioners, heat pump water heaters, refrigerators, and freezers. The working fluid properties and operation conditions are such that the heat transfer coefficient h of the working fluid has a value greater than kNu / d. In the aforementioned relationship, h is the heat transfer coefficient of the working fluid, k is the thermal conductivity, Nu is the Nusselt number, and d is the tube diameter.

Description

Heat transport or heat exchange working fluid and heat transport or heat exchange system

[0001] The present invention relates to a heat transport or heat exchange working fluid and a heat transport or heat exchange system.

[0002] Dispersion media containing dispersed particles are required in a wide range of industrial systems. For example, in the semiconductor industry, immersion lithography requires increasingly finer processing, and the radiation source required for this is increasingly using shorter wavelengths in the extreme ultraviolet range. Furthermore, to improve the precision of the molding process, it is necessary to suppress the refraction of the light source. Lutetium oxide lenses are used, and refraction due to the refractive index difference with air is a problem. While this problem has been solved by using a solvent such as water or decane (immersion), a high concentration of lutetium oxide nanoparticles can be further dispersed therein to reduce the refractive index difference and suppress refraction. A high concentration of lutetium oxide nanoparticles is desirable to reduce the refractive index difference, but achieving a high concentration of transparent dispersion is difficult. Furthermore, to remove heat generated by devices, working fluids must have high thermal conductivity and high heat capacity. Furthermore, reducing the viscosity of working fluids is expected to reduce power requirements.

[0003] Power devices are becoming smaller and smaller every year, while their output power continues to increase. As a result, the amount of heat generated per device is increasing, making heat removal essential to maintaining device performance. Development of high thermal conductivity sheets and mat materials is progressing, but heat removal from these or heat sinks is also becoming increasingly important. Air cooling is generally used, but water cooling is also available, and in both cases, improving the thermal conductivity and heat transport properties is an important issue. However, there is no effective solution.

[0004] Heat removal from the semiconductor industry, automobiles, and computers is an important issue. Generally, air cooling is used, but some liquid phase cooling is also used. Fins are designed for heat removal in semiconductor manufacturing systems, automobiles, and large computers. The development of heat transport media is also an important issue, but no effective solution has yet been found.

[0005] To address these issues, a method has been proposed to improve conventional heat transport properties by using nanofluids. However, because the thermal conductivity of nanofluids directly depends on the concentration of highly thermally conductive nanoparticles, a high concentration is required, but achieving this is difficult and many challenges remain. Furthermore, in some cases it is desirable to reduce the increase in power required due to increased viscosity.

[0006] Temperature control is also important in analytical fields, where heat transport media are commonly used. Transparency is required for optical analysis, and heat transport performance has been a major issue from the perspective of temperature control. Fluorinated solvents have been commonly used in analytical fields. One reason for this is their high specific gravity. In the analysis of aqueous systems, including blood, leaking water also has the advantage of easily removing the water because it phase-separates and floats on top of the heat transfer solvent. There are high expectations for the use of nanofluids in this field as well. In addition to heat transport properties, nanoparticle filling can also increase specific gravity. However, in this case, it is important to be able to achieve transparent dispersion even at high concentrations, and ensuring high heat transport performance has been an important challenge. Reducing the required power is also desirable in this case.

[0007] In large-scale heat transport systems, such as heat pumps used in air conditioning systems, the dispersion of nanoparticles in the heat pump system can improve heat transport efficiency. In some cases, a secondary heat transfer medium is used in both the cooling and heating sections. In such systems, the same heat transport performance is required while reducing power consumption. Unlike the above, achieving both thermal conductivity and power consumption simultaneously is a key challenge. Adding highly thermally conductive nanoparticles can increase the thermal conductivity of nanofluids, but this also increases viscosity and power consumption. Nanofluids have never been designed with these two objectives in mind. Theories about the effect of nanoparticle addition on heat transport itself have been limited to improving thermal conductivity at best. Little experimental or theoretical discussion of heat transport in the flow field, which is actually required, has been conducted, much less from the perspective of power consumption. Even researchers who have experimentally investigated this issue have found it extremely difficult to simultaneously achieve these opposing functions.

[0008] As mentioned above, the use of nanofluids has attracted attention as an important fundamental technology for achieving high thermal conductivity, and various basic research results have been reported. For example, adding nanoparticles to a base fluid at room temperature and pressure increases the thermal conductivity and heat transfer coefficient. It has been reported that a nanofluid with a volume fraction of CuO nanoparticles of 5 vol% had a thermal conductivity that was 60% higher than that of pure water (Non-Patent Document 1). Another example has been reported in which a nanofluid with a volume fraction of Cu nanoparticles of 2.0 vol% had a convective heat transfer coefficient that was 39% higher than that of the base fluid water (Non-Patent Document 2).

[0009] The effect of dispersing highly thermally conductive particles in a fluid mixture to increase its thermal conductivity has been theoretically explained.

[0010] The Maxwell-Eucken model is one of the most basic models and is used to calculate the thermal conductivity of a dispersed system. It is evaluated from the thermal conductivity of the solvent (fluid), the thermal conductivity of the particles, and the volume fraction of the particles (proportion of particles).

[0011] The Hamilton-Crosser model is a modified model that takes into account cases where the particle shape is not spherical or where the particle shape is complex, and takes into account the effect of the particle shape factor.

[0012] The Brugge equation is also an empirical model used for highly concentrated slurries, and takes into account the proportionality constant (empirical value) depending on the characteristics of the system. There are also models that take into account the Brownian motion of nanoparticles and interfacial effects.

[0013] When using microfluids and nanofluids, the power required for their transport is also an important consideration. Regarding viscosity, the Einstein equation and the Bachelor equation have been reported. Recently, Arai et al. have reported a viscosity evaluation equation for higher concentration ranges (Non-Patent Document 3).

[0014] These studies on heat conduction and viscosity are related to physical properties, but in reality, it is necessary to consider the effects of flow in the flow field within the heat transport system. There have been very few reports on these topics.

[0015] SK Das, et al., Heat Transfer Engineering, 27 (2006), 3-19Y. micro- and nanoparticles, Journal of Molecular Liquids, Volume 411, 2024, 125659, https: / / doi.org / 10.1016 / j.molliq.2024.125659.

[0016] Adding nanoparticles or other fine particles to a solvent can impart the functionality of the particles. For example, it can impart refractive index, thermal conductivity, and magnetism. Increasing the concentration of these particles is expected to improve these properties. However, for optical applications, transparent dispersion is required to prevent light scattering, but higher concentrations lead to increased aggregation. Furthermore, adding fine particles generally increases the viscosity of the fluid, increasing the energy consumption required for fluid transport. Therefore, when using nanofluids as a heat transport system, these conflicting functions must be resolved. There have been no reports of a heat transport medium that can completely disperse nanofluids without aggregation, while simultaneously achieving high thermal conductivity and low viscosity.

[0017] Regarding thermal conductivity, the effect of adding fine particles on thermal conductivity has been discussed, but the effect of the change in flow state in the flow field through which the working fluid is transported has not been examined.In the case of nanofluid transport, not only the effect of increased viscosity but also the increase in energy loss due to the change in flow state has not been examined.

[0018] The present invention has been made in view of the above problems, and aims to provide a working fluid with improved efficiency in heat transport or heat exchange, aiming to realize functions such as refractive index, thermal conductivity, and magnetism, while simultaneously achieving a high concentration dispersion, which is one of the conflicting functions, or a reduction in the power required for flow, which is another conflicting function, and generally achieving multiple conflicting functions simultaneously.

[0019] A first aspect of the present invention is a heat transport or heat exchange system that uses one or more working fluids selected from the group consisting of working fluids for heat dissipation in semiconductors, automobiles, and computers, working fluids for immersion lithography, working fluids for temperature control, and working fluids for air conditioners, air conditioners, heat pump water heaters, refrigerators, and freezers, and that has physical properties and operating conditions such that the heat transfer coefficient h of the working fluid is greater than kNu / d (h is the heat transfer coefficient of the working fluid, k is the thermal conductivity, Nu is a value predicted by the commonly used Nusselt equation, and d is the pipe diameter).

[0020] In general, the addition of nanoparticles with high thermal conductivity improves the thermal conductivity of nanofluids. The thermal conductivity of nanofluids can be roughly predicted using various models, including the Maxwell model, Hamilton-Crosser model, Bruggeman model, Yu-Choi model, and Jang-Choi model. From the perspective of heat transport, the thickness δ of the thermal boundary layer formed near the wall, where heat moves to and from the wall in the flow field, is important in addition to the thermal conductivity constant.

[0021] The heat transport rate Q is determined by the interfacial area A, the temperature difference ΔT, and the heat transfer coefficient h, and is expressed as Q = AhΔT, where the heat transfer coefficient h is expressed as h = k / δ.

[0022] δ is generally expressed as the Nusselt number Nu as a function of the Reynolds number Re and the Prandtl number Pr: Nu = δ / d = f(Re, Pr).

[0023] There are several proposed prediction values ​​for the Nusselt number Nu using the commonly used Nusselt equation. For example, the Nusselt number for laminar flow is Nu = 4.36 for fully developed laminar flow, regardless of Re or Pr, and Nu = 3.66 under constant wall temperature conditions.

[0024] In addition, the Dittus-Boelter equation is often used for turbulent flows, where Nu = 0.023Re 0.8 Pr n where n = 0.4 for the heating fluid and n = 0.3 for the cooling fluid.

[0025] We have been studying the effect of adding nanoparticles on the thermal conductivity and the thermal boundary layer δ. As a result, we found that it is possible to obtain h that is greater than the theoretical formula and Nu number expression.

[0026] That is, it is a heat transport working fluid in which h of the heat transport working medium is greater than Nuk / d, which is expressed using Nu, k and the representative diameter d, which are predicted values ​​by the commonly used Nusselt equation.

[0027] Furthermore, it has been discovered that it may be possible to achieve nanofluids that not only achieve high thermal conductivity but also other physical properties and functions.

[0028] In the case of optical materials, dispersibility and transparency are important. Regarding dispersibility, it is known that high-concentration dispersion can be achieved through a patent application already filed (JP Patent Publication No. 2024-165976). However, achieving high thermal conductivity simultaneously is extremely difficult. As a result of extensive research into the competitive and contradictory relationship between thermal conductivity and high-concentration transparent dispersion, we have discovered that it is possible to achieve both simultaneously.

[0029] That is, the present invention can provide a heat transport or heat exchange system that has high thermal conductivity and transparent dispersion at a dispersibility of 5% or more, 10% or more by volume, and more preferably 15% or more by volume.

[0030] A second feature of the invention is the first feature of the invention, in which the working fluid contains nanoparticles.

[0031] Although it is generally not easy to disperse nanofluids in a solvent, a prior patent (JP 2024-165976 A) has made it possible to achieve a transparent dispersion of nanoparticles at high concentrations. That is, by taking into consideration the affinity of the organic molecules of the organically modified nanoparticles with the solvent, the molecular size, and the incorporation of the solvent and third components into the modified organic molecules, it is possible to achieve a high-concentration dispersion.

[0032] Generally, there are theories that roughly predict the thermal conductivity, refractive index, magnetism, and other properties that can be imparted by adding fine particles, and these can be used to make rough estimates. Furthermore, the viscosity of such nanofluids and microfluids can be predicted in a publicly known paper by Arai et al. (Non-Patent Document 3). In this way, it is possible to create a basic design for each physical property function.

[0033] However, working fluids are required to simultaneously exhibit multiple functions as described above. In the case of working fluids for heat transport or heat exchange, they are required to simultaneously achieve high thermal conductivity, high heat capacity, and low viscosity. However, high thermal conductivity and heat capacity, and low viscosity are contradictory functions, and achieving both is not easy. To date, materials informatics (MI) has been utilized to explore alternative working fluids, but a fundamental solution has yet to be found. In particular, in large-scale heat transport systems where power consumption is important, including those that use a secondary heat transfer medium from the cooling and heating sections, no design method other than a comprehensive search has yet been established to simultaneously achieve the above-mentioned contradictory functions, even in such simple systems.

[0034] To begin with, these methods do not include the estimation of physical properties such as thermal conductivity and viscosity, nor do they provide the scientific theory to discuss the influence of nanoparticles on heat transport coefficients (heat transfer coefficient, flow resistance coefficient, etc.) that accompany changes in the state of the flow field. It can be said that even in basic research, there has been almost no consideration from this perspective.

[0035] In the case of working fluids with dispersed particles, the function is expressed by controlling the dispersibility.

[0036] According to the present invention, it is possible to obtain high thermal conductivity, which is an effect of nanofluids, in a hydrocarbon-carbon dioxide mixed system or the like.

[0037] The third feature of the invention is the second feature of the invention, wherein the nanoparticles are any one of a high refractive index material, a magnetic material, an electrically conductive material, a dielectric material, a highly thermally conductive material, and a fluorescent / luminescent material.

[0038] A fourth feature of the invention is the second or third feature of the invention, in which the nanoparticles are transparently dispersed.

[0039] The fifth aspect of the invention is a heat transport or heat exchange working fluid selected from the group consisting of a heat dissipation working fluid for semiconductors, automobiles, and computers, a working fluid for immersion lithography, a temperature control working fluid, and a working fluid for air conditioners, air conditioners, heat pump water heaters, refrigerators, and freezers, which contains nanoparticles, and the addition of the nanoparticles makes the heat transfer coefficient of the working fluid higher than that of the dispersion medium in which the nanoparticles are dispersed, at a Reynolds number (Re) of 500 or more, and also higher than that of a nanofluid taking into account the effect of adding nanoparticles to improve thermal conductivity.

[0040] A sixth aspect of the present invention is one or more types of heat transport or heat exchange working fluid selected from the group consisting of working fluids for heat dissipation in semiconductors, automobiles, and computers, working fluids for immersion lithography, working fluids for temperature control, and working fluids for air conditioners, air conditioners, heat pump water heaters, refrigerators, and freezers, which contain nanoparticles and have a thermal conductivity improvement effect / viscosity increase effect value of 1 or more due to the addition of the nanoparticles.

[0041] According to the present invention, the value of the thermal conductivity improvement effect / viscosity increase effect due to the addition of nanoparticles can be made to be 1 or more, that is, high thermal conductivity can be achieved without increasing viscosity.

[0042] The seventh aspect of the invention is the fifth or sixth aspect of the invention, in which the effect of increasing the heat transfer coefficient h is greater than the effect of increasing the pressure loss ΔP, compared to when the nanoparticles are not contained.

[0043] According to the seventh aspect of the invention, it is possible to significantly improve the heat transfer coefficient with low pressure loss, and when applied as a heat transport or heat exchange working fluid, it may be possible to transport heat efficiently with low energy.

[0044] The invention according to an eighth feature is an invention according to any one of the fifth to seventh features, wherein the nanoparticles are dispersed in a solvent, and the content of the nanoparticles is 1 part by mass or more and 70 parts by mass or less per 100 parts by mass of the working fluid.

[0045] The ninth aspect of the invention is the invention according to any one of the fifth to eighth aspects, wherein the nanoparticles are dispersed in a gas or supercritical medium, and the content of the nanoparticles is 1 part by mass or more and 70 parts by mass or less per 100 parts by mass of the working fluid.

[0046] In the eighth and ninth aspects of the invention, the content of nanoparticles is 1 part by mass or more and 70 parts by mass or less per 100 parts by mass of the working fluid, which is due to the fact that a high-concentration transparent dispersion of up to 80 wt% is possible according to the prior patent (JP 2024-165976 A).

[0047] Increasing the thermal conductivity k and decreasing the viscosity μ are contradictory requirements.

[0048] In the eighth and ninth aspects of the invention, the content of nanoparticles is limited to a low filling ratio range of 1 to 70 parts by mass per 100 parts by mass of the working fluid, so high thermal conductivity can be achieved without increasing viscosity. This is thought to be due to the difference in the filling ratio dependence of thermal conductivity and viscosity.

[0049] The details are explained below. In nanofluids, when the filling rate Φ is increased, the thermal conductivity increases by 1 + AΦ, but the viscosity increases by 1 + αΦ + βΦ. ２ At a high filling rate Φ, the viscosity increases more than the improvement in thermal conductivity, and the adverse effect of the decrease in operability becomes greater.

[0050] On the other hand, at a low filling rate Φ of around 1%, the viscosity remains almost unchanged. However, the thermal conductivity increases. According to the Einstein equation, the viscosity is 1 + 2.5Φ, and when Φ is 0.01, the viscosity is 1.025 times greater than when Φ is 0. On the other hand, when the thermal conductivity of the nanoparticles is greater than that of the solvent, the thermal conductivity is 1 + 3.0Φ, and when Φ is 0.01, the thermal conductivity is 1.03 times greater than when Φ is 0.

[0051] In nanofluids, the thermal conductivity is even higher than the theoretical value mentioned above. This is thought to be due to the structured liquid layer (with thermal conductivity intermediate between that of a solid and a liquid) that forms on the surface of the nanoparticles. There are other effects as well. These effects result in a thermal conductivity higher than that of a solvent. Although the experimental accuracy is thought to be low, this can also be seen from the results of the Data Bank for Thermophysical Properties of Fluids (Dortmund Data Bank, DDB).

[0052] As shown in the examples, even higher thermal conductivity than predicted by existing theories is obtained in the low nanoparticle loading range. At loadings on the order of 100%, an increase in thermal conductivity of several percent is obtained compared to the thermal conductivity of the solvent.

[0053] Furthermore, it has been found that when a supercritical fluid is used as the working fluid, high thermal conductivity can be obtained, particularly near the critical point.

[0054] A working fluid is required to have high thermal conductivity, high heat capacity, and low viscosity at the same time. However, high thermal conductivity and heat capacity, and low viscosity are contradictory functions, and it is not easy to achieve all of these simultaneously.

[0055] In contrast, in this invention, a method for simultaneously analyzing heat conduction and viscosity has been developed based on chemical engineering design methods. On the heat transfer surface, fast heat conduction is desirable. In reality, the constant pressure heat capacity C against viscosity μ is ｐ (molar specific heat at constant pressure) ratio C ｐ It is important to increase the thermal conductivity k while increasing / μ. More specifically, since it is important to increase the heat transfer coefficient (μ -0.5 k 2 Cp 1) ^(1 / 3) It is important to increase C. Nanofluids can achieve high thermal conductivity. However, the loading of nanoparticles ｐ The coefficient of thermal conductivity k decreases. Also, the viscosity increases. Generally, adding particles increases the thermal conductivity, but also increases the viscosity. In other words, increasing the thermal conductivity k and decreasing the viscosity μ are contradictory requirements.

[0056] According to the eighth and ninth features of the invention, high thermal conductivity can be achieved without increasing viscosity.

[0057] The above viewpoint is based on the idea of ​​achieving contradictory functions according to the purpose from the viewpoint of physical property values ​​such as thermal conductivity and viscosity.

[0058] However, we also conducted extensive research into the heat conduction and energy loss (pressure loss) in the flow field of an actual heat transport working fluid, and found conditions that can improve heat transport in the flow field while reducing energy loss, i.e., energy consumption.

[0059] A tenth feature of the invention is the invention according to any one of the fifth to ninth features, wherein the nanoparticles are organically modified nanoparticles having organic modifying groups on the surface thereof.

[0060] Based on the technique described in the prior patent (JP 2024-165976 A), optimizing the organic modification group enables high-concentration dispersion. For example, it is not possible to disperse organically modified nanoparticles in hydrocarbons that do not contain carbon dioxide. This is because the van der Waals volume of the hydrocarbon is larger than the volume of the voids created by the organic modification group, or the free volume of the organic modification layer is too small to contain solvent molecules, making it difficult to dissolve the organically modified nanoparticles, or the dispersion force term δ of the Hansen solubility parameters Ｄ Regarding the dispersion force term δ of the organic modifying group under the dispersion treatment temperature and pressure Ｄ The value of and the dispersion term δ of poorly dispersible solvents Ｄ The absolute value of the difference between the values ​​is 1.2 MPa 1 / 2 It means exceeding.

[0061] On the other hand, when carbon dioxide is added to the solvent, the carbon dioxide coordinates with the modification groups of the organically modified nanoparticles, and the dispersion force terms δ Ｄ The absolute value of the difference between the values ​​is 1.2 MPa. 1 / 2 If carbon dioxide coordinates to the modified organic molecules, the self-organization of the modified organic molecules can be suppressed, thereby increasing the free volume of the organic molecule layer and promoting the coordination of solvent molecules, thereby dramatically improving the affinity of the organically modified nanoparticles with the solvent.

[0062] An eleventh feature of the invention is the invention according to any one of the fifth to tenth features, in which the average particle size of the nanoparticles is 1 nm or more and 100 nm or less.

[0063] This allows for sufficient suppression of scattering of light of that wavelength by making the thickness about a fraction to one-tenth of the wavelength of the target light. For example, it is desirable that the thickness be a few tens of nanometers or less in the visible light region, 10 nm or less in the extreme ultraviolet region, and about 100 nm or less in the infrared region.

[0064] Furthermore, when the non-azeotropic composition is used as a working fluid in a heat pump cycle that repeats compression and expansion, it is possible to prevent the sedimentation of nanoparticles, especially during the expansion process. This is thought to be because the gas contained in the non-azeotropic composition circulates, and the circulation speed is faster than the sedimentation speed of the nanoparticles.

[0065] The technical concept of the present invention can be applied not only to the working fluid of a heat transport system but also to the working fluid of a heat exchange system.

[0066] The present invention provides a working fluid with improved heat transport efficiency, and also provides a working fluid that achieves contradictory functions such as transparency, high thermal conductivity, high refractive index, and high magnetism while reducing the required power.

[0067] FIG. 1 is a schematic diagram of the apparatus used in Test Example 1 and the like. FIG. 2 is a diagram showing the pressure setting conditions in Test Example 1. FIG. 3 is a diagram showing the test results of Example 1-1. FIG. 4 is a diagram showing the heat transfer coefficient of nanofluid at 40°C. FIG. 5 is a schematic diagram of the apparatus used to measure the heat transfer coefficient. FIG. 6 is a comparison of the experimental and calculated values ​​of Nu number as the Re number changes (pure water, average temperature 365°C to 390°C). FIG. 7 is a comparison of the experimental and calculated values ​​of Nu number as the Re number changes (pure water, average temperature 395°C to 420°C). FIG. 8 is a comparison of the experimental and calculated values ​​of Nu number as the temperature changes (pure water, average temperature around 395°C to 420°C). FIG. 9 is a comparison of the experimental and calculated values ​​of Nu number as the temperature changes (pure water, mass flow rate: 15 g / min, average temperature around 360°C to 420°C). Figure 10 compares the experimental and calculated Nu numbers with changes in Re (pure water and nanofluid, average temperature 365°C to 388°C, Re number 4700 to 5700). Figure 11 compares the experimental and calculated Nu numbers with changes in Re (pure water and nanofluid, average temperature 365°C to 388°C, Re number 7600 to 9600). Figure 12 compares the experimental and calculated Nu numbers with changes in Re (pure water and nanofluid, average temperature 365°C to 390°C, Re number 10200 to 13200). Figure 13 compares the experimental and calculated Nu numbers with changes in temperature (pure water and nanofluid, Re number 4700 to 5700). Figure 14 compares the experimental and calculated Nu numbers with changes in temperature (pure water and nanofluid, Re number 7600 to 9600). Figure 15 shows a comparison of the experimental and calculated Nu numbers with temperature (pure water / nanofluid, Re number 10200-13200). Figure 16 shows a comparison of the experimental and calculated Nu numbers with Re number (pure water / nanofluid, average temperatures 375, 383, and 388°C, Re number 4700-5700). Figure 17 shows a comparison of the experimental and calculated Nu numbers with Re number (relative viscosity considered, mass concentration: 1.8 wt%, average temperature 365°C-388°C, Re number before correction: 4600-5600). Figure 18 shows a comparison of the experimental and calculated Nu numbers with Re number (relative viscosity considered, mass concentration: 1.8 wt%, average temperature 365°C-388°C, Re number before correction: 4600-5600).Figure 19 shows a comparison of the experimental and calculated values ​​of Nu number as the Re number changes (relative viscosity considered, mass concentration: 1.8 wt%, average temperature 365°C to 388°C, Re number before correction: 7600 to 9600). Figure 20 shows a comparison of the experimental and calculated values ​​of Nu number as the Re number changes (relative viscosity considered, mass concentration: 3.6 wt%, average temperature 365°C to 388°C, Re number before correction: 7600 to 9600). Figure 21 shows a comparison of the experimental and calculated values ​​of Nu number as the Re number changes (relative viscosity considered, mass concentration: 1.8 wt%, average temperature 365°C to 388°C, Re number before correction: 10200 to 13200). FIG. 22 compares the experimental and calculated Nu numbers with changes in Re number (relative viscosity considered, mass concentration: 3.6 wt %, average temperature 365°C to 388°C, Re number before correction: 10,200 to 13,200). FIG. 23 shows the relative viscosity versus particle concentration for particle dispersions of various particle sizes. FIG. 24 is a continuation of FIG. 23. FIG. 25 shows the relative viscosity versus particle size, relative to the particle volume fraction φ, for a particle size of 10 nm. FIG. 26 shows the change in order corresponding to particle size. FIG. 27 shows the change in the difference between the measured value and the value calculated from the Batchelor equation versus the particle volume fraction for a particle size of 10 nm (order n = 3). FIG. 28 shows the change in coefficient corresponding to particle size. FIG. 29 shows the correlation between calculated and measured values ​​(particle concentration 10 vol % or higher). FIG. 30 shows the change in coefficient versus particle size. FIG. 31 is a diagram showing the correlation between measured values ​​and calculated values. FIG. 32 is a diagram showing the change in relative viscosity with respect to the change in particle concentration for particle dispersions in different solvents. FIG. 33 is a diagram showing the change in relative viscosity with respect to the change in particle concentration for particle dispersions at different viscosity measurement temperatures. FIG. 34 is a diagram showing the same graph as FIG. 32, but with the vertical axis represented as absolute viscosity. FIG. 35 is a diagram showing the change in coefficient with respect to particle size. FIG. 36 is a diagram showing the correlation between predicted values ​​and measured values ​​when the order m' is 6. FIG. 37 is a schematic diagram showing a simulation of the relationship between the average particle size of nanoparticles and their sedimentation. FIG. 38 shows the relationship between rotation speed (share rate) and shear stress (share stress) in <Test 5> Rheological analysis.Figure 39 shows the relationship between rotation speed (share rate) and viscosity in <Test 5> rheological analysis. Figure 40 shows the results of heat transfer coefficient measurements in <Test 6> (CeO2 nanofloids with octanoic acid). Figure 41 shows the results of heat transfer coefficient measurements in <Test 6> (CeO2 nanofloids with hexanoic acid or decanoic acid). Figure 42 is a schematic diagram of the flow system used in <Test 7>. Figure 43 shows the relationship between Reynolds number Re and heat transfer coefficient h (40°C). Figure 44 shows the relationship between Reynolds number Re and heat transfer coefficient h (15°C). Figure 45 is a schematic diagram illustrating how the addition of nanoparticles changes the flow field. Figure 46 shows the relationship between heat transfer coefficient h and pressure drop ΔP in <Test 8> (40°C). Figure 47 shows the relationship between heat transfer coefficient h and pressure drop ΔP in <Test 8> (15°C).

[0068] Specific embodiments of the present invention will be described in detail below, but the present invention is not limited to the following embodiments and can be implemented with appropriate modifications within the scope of the object of the present invention.

[0069] <Heat Transport or Heat Exchange Working Fluid> The heat transport or heat exchange working fluid contains nanoparticles, and the value of the thermal conductivity improvement effect / viscosity increase effect due to the addition of the nanoparticles is equal to or greater than 1. Furthermore, the nanoparticles are preferably dispersed in a solvent or gas medium.

[0070] [Nanoparticles] Nanofluids are expected to be used to achieve high thermal conductivity, and research is underway (Hammad Younes et al., Nanofluids: Key parameters to enhance thermal conductivity and its applications, Applied Thermal Engineering, 207 (2022) 118202).

[0071] It is impossible to disperse nanoparticles in hydrocarbons, which are inherently difficult to disperse. However, in the present invention, the dispersion power term δ of the Hansen solubility parameters of the mixed solvent and nanoparticles is Ｄ The absolute value of the difference between the values ​​is 1.2 MPa. 1 / 2 The affinity can be dramatically improved.

[0072] According to the present invention, it is possible to obtain high thermal conductivity, which is an effect of nanofluids, in a hydrocarbon-carbon dioxide mixed system.

[0073] The type of nanoparticles is not particularly limited, and SiO ２ , Fe ２ O ３ , CeO ２ , TiO ２ , Y ２ O ３ , InO, ZnO, SnO ２ , Nb ２ O ３ , Cu, Ag, Al, Co, Fe, B ４ C, AlN, TiB ２ , C (CNT (carbon nanotube), graphene, graphite core-shell nanoparticles, etc.), or other known materials may be used.

[0074] The nanoparticles are preferably dispersed in a medium. The medium may be a solvent, a gas, or a medium in a supercritical state. Examples of the medium include water, alcohol, glycol, hydrocarbons having 2 to 6 carbon atoms, CO ２ , and N ２ It is preferable that the medium is one or more selected from O. Among these, it is preferable that the medium contains alcohol and / or glycol, which makes it easy to realize an azeotropic mixture composition using a mixture system of hydrocarbon-carbon dioxide or the like.

[0075] A working fluid is required to have high thermal conductivity, high heat capacity, and low viscosity. However, high thermal conductivity and heat capacity, and low viscosity are contradictory functions, and achieving both is not easy. Materials informatics (MI) has been utilized to explore alternative working fluids, but a fundamental solution has yet to be found. In large-scale heat transport systems, a secondary heat transfer medium may be used in both the cooling and heating sections. However, even in such cases, achieving both of these contradictory functions remains a challenge.

[0076] On the heat transfer surface, fast heat conduction is desirable. In reality, the constant pressure heat capacity C isｐ (molar specific heat at constant pressure) ratio C ｐ It is important to increase the thermal conductivity k while increasing / μ. More specifically, since it is important to increase the heat transfer coefficient (μ -0.5 k 2 Cp 1 ) ^(1 / 3)　 It is important to increase C. Nanofluids can achieve high thermal conductivity. However, the loading of nanoparticles ｐ The coefficient of thermal conductivity k decreases. Also, the viscosity increases. Generally, adding particles increases the thermal conductivity, but also increases the viscosity. In other words, increasing the thermal conductivity k and decreasing the viscosity μ are contradictory requirements.

[0077] According to the present invention, the value of the thermal conductivity improvement effect / viscosity increase effect due to the addition of nanoparticles can be made to be 1 or more, that is, high thermal conductivity can be achieved without increasing viscosity.

[0078] Among these, the nanoparticles are preferably organically modified nanoparticles having organic modifying groups on the surface.

[0079] Organically modified nanoparticles cannot be dispersed in hydrocarbons that do not contain carbon dioxide. This is because the van der Waals volume of the hydrocarbon is larger than the volume of the voids created by the organic modification group, or the free volume of the organic modification layer is too small to contain solvent molecules, making it difficult to dissolve organically modified nanoparticles, or the dispersion force term δ of the Hansen solubility parameters Ｄ Regarding the dispersion force term δ of the organic modifying group under the dispersion treatment temperature and pressure Ｄ The value of and the dispersion term δ of poorly dispersible solvents Ｄ The absolute value of the difference between the values ​​is 1.2 MPa 1 / 2 It means exceeding.

[0080] On the other hand, when carbon dioxide is added to the solvent, the carbon dioxide coordinates with the modification groups of the organically modified nanoparticles, and the dispersion force terms δ Ｄ The absolute value of the difference between the values ​​is 1.2 MPa. 1 / 2If carbon dioxide coordinates to the modified organic molecules, the self-organization of the modified organic molecules can be suppressed, thereby increasing the free volume of the organic molecule layer and promoting the coordination of solvent molecules, thereby dramatically improving the affinity of the organically modified nanoparticles with the solvent.

[0081] According to the present invention, carbon dioxide can be used not only as an alternative to fluorine compounds but also to improve the affinity of organically modified nanoparticles with solvents, thereby making it possible to obtain high thermal conductivity, an effect of nanofluids, in hydrocarbon-carbon dioxide mixed systems.

[0082] The type of organic modifying group is not particularly limited, and examples thereof include an optionally substituted linear or branched alkyl group, an optionally substituted cyclic alkyl group, an optionally substituted aryl group, an optionally substituted aralkyl group, and an optionally substituted saturated or unsaturated heterocyclic group.

[0083] Examples of the substituent include a carboxy group, a cyano group, a nitro group, a halogen atom, an ester group, an amide group, a ketone group, a formyl group, an ether group, a hydroxyl group, an amino group, a sulfonyl group, -O-, -NH-, and -S-.

[0084] The organically modified nanoparticles may have one type of organic modifying group on the surface, or may have multiple types of organic modifying groups.

[0085] The average particle size of the nanoparticles is preferably 100 nm or less, more preferably 50 nm or less, and even more preferably 20 nm or less. This prevents the nanoparticles from settling, particularly during the expansion process, in a heat pump cycle that repeats compression and expansion. This is thought to be because the gas contained in the azeotrope-like composition circulates, and the circulation rate is greater than the settling rate of the nanoparticles.

[0086] There is no particular lower limit to the average particle size of the nanoparticles, but in consideration of workability, it is preferably 1 nm or more, and more preferably 5 nm or more.

[0087] The content of nanoparticles is preferably 1 part by mass or more, more preferably 3 parts by mass or more, per 100 parts by mass of the working fluid. The content of nanoparticles is preferably 70 parts by mass or less, more preferably 40 parts by mass or less, even more preferably 20 parts by mass or less, even more preferably 10 parts by mass or less, and particularly preferably 7 parts by mass or less. This is due to the fact that a high-concentration transparent dispersion of up to 80 wt% is possible according to the prior patent (JP 2024-165976 A).

[0088] [Dispersion Medium] The nanoparticles are preferably dispersed in a solvent or gas medium.

[0089] When the nanoparticles are dispersed in a solvent, the solvent may be water, alcohol, glycol, hydrocarbons having 2 to 6 carbon atoms, or high-pressure CO ２ , high pressure N ２ and O.

[0090] When the nanoparticles are dispersed in a gaseous medium, the gas may be air, nitrogen, oxygen, hydrogen, hydrocarbons, chlorofluorocarbons, inert gases, N ２ O, CO ２ It is one or more selected from the following.

[0091] As described above, increasing the thermal conductivity k and decreasing the viscosity μ are contradictory requirements.

[0092] In the present invention, the nanoparticle content is limited to a low filling rate range, so the value of the thermal conductivity improvement effect / viscosity increase effect due to the addition of nanoparticles can be made greater than or equal to 1, i.e., high thermal conductivity can be achieved without increasing viscosity. This is thought to be due to the different filling rate dependencies of thermal conductivity and viscosity. In actual fluid fields and systems, it is important to ensure that the ratio of the increase in heat transfer coefficient to the increase in viscosity is greater than or equal to 1.

[0093] The details are explained below. In nanofluids, when the filling rate Φ is increased, the thermal conductivity increases by 1 + AΦ, but the viscosity increases by 1 + αΦ + βΦ. ２ At a high filling rate Φ, the viscosity increases more than the improvement in thermal conductivity, and the adverse effect of the decrease in operability becomes greater.

[0094] On the other hand, at a low filling rate Φ of around 1%, the viscosity remains almost unchanged. However, the thermal conductivity increases. According to the Einstein equation, the viscosity is 1 + 2.5Φ, and when Φ is 0.01, the viscosity is 1.025 times greater than when Φ is 0. On the other hand, when the thermal conductivity of the nanoparticles is greater than that of the solvent, the thermal conductivity is 1 + 3.0Φ, and when Φ is 0.01, the thermal conductivity is 1.03 times greater than when Φ is 0.

[0095] In nanofluids, the thermal conductivity is even higher than the theoretical value mentioned above. This is thought to be due to the structured liquid layer (with thermal conductivity intermediate between that of a solid and a liquid) that forms on the surface of the nanoparticles. There are other effects as well. These effects result in a thermal conductivity higher than that of a solvent. Although the experimental accuracy is thought to be low, this can also be seen from the results of the Data Bank for Thermophysical Properties of Fluids (Dortmund Data Bank, DDB).

[0096] As shown in the examples, even higher thermal conductivity than predicted by existing theories is obtained in the low nanoparticle loading range. At loadings on the order of 100%, an increase in thermal conductivity of several percent is obtained compared to the thermal conductivity of the solvent.

[0097] Furthermore, it has been found that when a supercritical fluid is used as the working fluid, high thermal conductivity can be obtained, particularly near the critical point.

[0098] A working fluid is required to have high thermal conductivity, high heat capacity, and low viscosity at the same time. However, high thermal conductivity and heat capacity, and low viscosity are contradictory functions, and it is not easy to achieve all of these simultaneously.

[0099] In contrast, in this invention, a method for simultaneously analyzing heat conduction and viscosity has been developed based on chemical engineering design methods. On the heat transfer surface, fast heat conduction is desirable. In reality, the constant pressure heat capacity C against viscosity μ is ｐ (molar specific heat at constant pressure) ratio C ｐ It is important to increase the thermal conductivity k while increasing / μ. More specifically, since it is important to increase the heat transfer coefficient (μ -0.5 k2 Cp 1 ) ^(1 / 3) It is important to increase C. Nanofluids can achieve high thermal conductivity. However, the loading of nanoparticles ｐ The coefficient of thermal conductivity k decreases. Also, the viscosity increases. Generally, adding particles increases the thermal conductivity, but also increases the viscosity. In other words, increasing the thermal conductivity k and decreasing the viscosity μ are contradictory requirements.

[0100] According to the present invention, high thermal conductivity can be achieved without increasing viscosity.

[0101] In the present invention, the effect of adding nanoparticles to improve thermal conductivity is evaluated based on the results of the Data Bank for Thermophysical Properties of Fluids (Dortmund Data Bank, DDB).

[0102] The heat transfer coefficient h in a flow field is evaluated from the temperature difference in the heat transfer field and the fluid temperature (ΔT and Tw-Tnf in equation 184).

[0103] The viscosity-increasing effect of adding nanoparticles will be evaluated from the actual measured values ​​in the operating temperature range using a rotational viscometer.

[0104] In addition, when it is difficult to obtain data, the effect of adding nanoparticles on improving thermal conductivity can be estimated from the results of the Fluid Thermophysical Properties Data Bank (Dortmund Data Bank, DDB) or by using the viscosity estimation formula for fine nanoparticles described in this patent.

[0105] [Method for Producing a Working Fluid Containing Nanoparticles] A working fluid containing nanoparticles can be obtained by dispersing nanoparticles in a solvent by applying a predetermined pressure to the solvent.

[0106] The solvent contains carbon dioxide and a hydrocarbon having a carbon number of 3 to 6. The predetermined pressure is a pressurized state of 0.5 MPa or more, or a pressure equal to or greater than the saturated vapor pressure at the dispersion treatment temperature (however, if the dispersion treatment temperature is equal to or greater than the critical temperature, then equal to or greater than the critical pressure).

[0107] By pressurizing a hydrocarbon-containing solvent to a certain pressure in the presence of carbon dioxide, the carbon dioxide dissolves in the solvent, and the free volume of the mixed solvent increases compared to before pressurization. Furthermore, the gas is distributed to the modifying groups of the organically modified nanoparticles, increasing the free volume of the organically modified layer. The dispersion force term δ of the Hansen solubility parameter of the modifying group also increases. Ｄ and the dispersion force term of the mixed solvent δ Ｄ The absolute value of the difference between the two also becomes lower. As a result, it becomes possible to disperse organically modified nanoparticles in a solvent that would not normally be able to disperse them. At normal pressure (0.1 MPa), the gas desorbs and diffuses out, but high dispersibility can be maintained for 1 to 14 hours or more.

[0108] [Uses of working fluids] Heat transport or heat exchange systems Working fluids are used as heat transport fluids for temperature control, heat dissipation, temperature control, and heat pumps. Examples of heat transport systems include heat dissipation media for semiconductor manufacturing equipment, automobiles, and large computers, heat dissipation media for power devices, air conditioners, air conditioners, heat pump water heaters, refrigerators, and freezers.

[0109] The working fluid can be used as a working fluid for immersion lithography, and can simultaneously exhibit thermal conductivity, heat transport properties, low viscosity, and transparency.

[0110] The working fluid can be used to remove heat from large computers and semiconductor manufacturing plants. It can simultaneously exhibit thermal conductivity, heat transport properties, and low viscosity.

[0111] The working fluid can be used as a working fluid for power devices, and can simultaneously exhibit thermal conductivity, heat transport properties, low viscosity, and transparency.

[0112] The working fluid can be used as a working fluid for temperature control in analytical equipment, and can simultaneously exhibit thermal conductivity, heat transport properties, low viscosity, and transparency.

[0113] The present invention will be specifically explained below with reference to examples, but the present invention is not limited to these examples.

[0114] <Test 1> Solvent dispersion of organically modified nanoparticles Example 1-1: Solvent dispersion of organically modified nanoparticles in decane Here, we will explain the solvent dispersion of organically modified nanoparticles in decane. Decane has 10 carbon atoms, but if they can be dispersed in a solvent in decane, they can naturally be dispersed in hydrocarbons with 2 to 6 carbon atoms, so we will explain this as a test example here.

[0115] [Preparation of Organically Modified Nanoparticles with Decanoic Acid] In this test, CeO was used as a model nanoparticle. ２ Using decanoic acid (DA) as a modifier, organically modified CeO nanoparticles were synthesized by supercritical hydrothermal synthesis. ２ Nanoparticles (hereinafter also referred to as "OM nanoparticles") were synthesized.

[0116] Ce(OH) ４ was dispersed in distilled water by ultrasonic treatment, and 0.1 M Ce(OH) ４ Then, 0.10 M Ce(OH) ４ The aqueous suspension (2.5 mL) and DA (molar ratio 1:3) were placed in a 5 mL Hastelloy tubular batch reactor. The reactor was placed in a furnace and heated at 150 °C for 20 minutes, then at 400 °C for 10 minutes. The reactor was then rapidly cooled to terminate the reaction, after which the product was recovered using hexane and the aqueous layer was removed. An equal volume of ethanol was added to the remaining organic layer, and the mixture was centrifuged (9600 rpm, 20 minutes) to remove unreacted materials, yielding OM nanoparticles.

[0117] [Dispersion of OM Nanoparticles in Decane] The solvent dispersion was carried out under the following conditions using the apparatus shown in FIG. 1. Nanoparticles: the above-mentioned decanoic acid-modified CeO ２ Nanoparticles (OM nanoparticles) Nanoparticle concentration: 1 wt% Solvent: Decane Temperature: 40°C Additive: Carbon dioxide gas Pressure: As shown in Figure 2 (2, 4, 6 MPa)

[0118] [Results] The results are shown in Figure 3. When the carbon dioxide gas pressure was 2 MPa, the OM nanoparticles were not dispersed in the solvent (decane), but when the pressure was 4 MPa, the OM nanoparticles were uniformly dispersed in the solvent (decane). This uniform dispersion state was maintained even when the pressure was increased to 6 MPa, and was also maintained when the pressure was subsequently returned to normal pressure.

[0119] Comparative Example 1-1 An attempt was made to disperse OM nanoparticles in decane using the same method as in Example 1-1, except that carbon dioxide gas was not added. However, it was not possible to uniformly disperse the OM nanoparticles in decane.

[0120] <Test 2> Heat transfer performance of nanofluid [Heat transfer coefficient at 40°C] TiO in water ２ The heat transfer coefficient at 40°C was measured for nanofluids containing 1 wt% nanoparticles (average particle size 135 nm).

[0121] The results are shown in Figure 4. An increase in the heat transfer coefficient h was observed by adding nanoparticles to the solvent.

[0122] [Heat transfer coefficient near the supercritical point] While research on the heat transfer performance of nanofluids and pure base fluids near the critical point at room temperature and pressure has progressed, there is little knowledge about the thermal conductivity and heat transfer coefficient of nanofluids near the critical point. Therefore, we measured the heat transfer coefficient of nanofluids near the critical point and investigated the effect of adding nanoparticles on the heat transfer performance of fluids near the critical point.

[0123] [Reagents] The following reagents were used in the experiment: TiO ２ Sol (STS-01, particle size 7.0 nm), Ishihara Sangyo Co., Ltd. Purified water H ２ O, resistivity 8,000,000 Ω cm or more, Daiwa Pharmaceutical Co., Ltd.

[0124] [Apparatus] Figure 5 shows an outline of the apparatus used to measure the heat transfer coefficient. Distilled water was pumped through a high-pressure pump (NP-KX-500 manufactured by Nippon Seimitsu Co., Ltd.), a sample nanofluid (TiO ２ The sol was delivered to the test section using a syringe pump (Teledyne Isco 260D). All piping was made of SUS316. Distilled water preheated by a heater and TiO２ The sol was mixed. A cartridge heater (HLT3141, manufactured by Hakko Electric Co., Ltd.) was used to preheat the distilled water. After mixing, the mixture was passed through a pipe with an inner diameter of 0.8 mm or 1.755 mm and a length of 0.17 m and heated using a mantle heater (PK, manufactured by Tokyo Technical Research Institute Co., Ltd.). The fluid temperature before and after this heating section and the pipe wall temperature were measured using a K-type thermocouple (KTO-16300M3, manufactured by AS ONE). A double-pipe heat exchanger was then used, and cooling water was circulated through the outer pipe using a small cooling water circulator (Cool Man C580, manufactured by Shibata Scientific Co., Ltd.). The temperatures of the preheated water and the mantle heater were monitored and adjusted using temperature controllers (TR-KN-T, manufactured by AS ONE, ST-300K, manufactured by Sansho Co., Ltd., and SR83, manufactured by Shimaden Co., Ltd.). The pressure in the system was monitored immediately after mixing and after heating with a mantle heater, and was adjusted to 30 MPa using a back pressure valve (26-1762-24, manufactured by TESCOM). Heat insulating material (NM-8602, manufactured by Nichias Corporation) and glass wool (Fine Flex Blanket, manufactured by Nichias Corporation) were used to insulate the preheating zone and heating zone.

[0125] [Experimental Method] A base fluid (distilled water) and TiO ２ A sample nanofluid, consisting of nanoparticles (agglomeration diameter less than 100 nm) dispersed in water, was mixed with preheated water and heated to 365°C to 385°C. The particle mass fraction of the nanofluid after mixing was set to 1.8 and 3.6 wt%, and the test section was further heated using a mantle heater to raise the fluid temperature by 10°C to 20°C. The fluid flow rate was set so that the Reynolds number (Re number) was in the turbulent range of 4,500 to 14,000. While the preheated water temperature was changed, the tube wall temperature and the fluid temperatures at the inlet and outlet were measured using thermocouples attached to the test section. The following analysis was performed based on the average temperatures at the inlet and outlet.

[0126] Furthermore, measurements were also carried out using pure water only, with the same procedure being repeated under conditions of mass flow rates of 15, 20, 25 and 30 g / min, with the inlet temperature raised to around 410° C. and then further heating with a mantle heater.

[0127] [Theoretical formula] Assuming that the heat flux given to the fluid from the pipe wall in the heating section is equal to the amount of heat that contributed to the temperature rise of the fluid at the inlet and outlet of the heating section, the convection heat transfer coefficient h is calculated from [Equation 1]. ｎｆ asked for.

[0128] Here, C ｐ is the constant pressure heat capacity, ΔT ｎｆ is the temperature rise before and after the heating section, w is the mass flow rate, S is the heat transfer area, h ｎｆ is the convection heat transfer coefficient, T ｗ and T ｎｆ is the average temperature of the tube wall and nanofluid in the heated section.

[0129] Measured h ｎｆ In order to evaluate this, we compared the definition equation for the Nu number obtained from experimental values ​​(Equation 2) with the correlation equation for the Nu number in a turbulent flow field (Equation 5) calculated from each dimensionless number obtained from (Equation 3) and (Equation 4).

[0130] Here h ｎｆ is the convection heat transfer coefficient, d is the pipe diameter, k ｎｆ is the thermal conductivity, ρ ｎｆ is the density, v is the linear velocity, μ ｎｆ is the viscosity. ｎｆ , Re ｎｆ , Pr ｎｆ The physical properties used to determine the above were calculated from [Equation 6] to [Equation 9].

[0131] where φ is the volume fraction of the particles, and n in Equation 9 is a coefficient that varies depending on the particle shape, with n = 3 being used for spherical particles. The subscripts for each physical property value indicate that nf is the value for the nanofluid, p is the value for the particle, and bf is the value for the base fluid.

[0132] [Results and Discussion] [Considerations on mixing of preheated water and nanofluid] Before evaluating the heat transfer coefficient of the fluid near the critical point, we will discuss the mixing of preheated water and the sample nanofluid. The distance from the mixing point of the preheated water and the sample nanofluid to the inlet of the heating section is 9.80 cm, and mixing of the two fluids must be fully completed while flowing through this section.

[0133] The following equation (10) proposed by Yoko is the mixing rate constant k of a substance near the critical point. ｍｉｘ [1 / s] is calculated as a function of fluid temperature and Re number (A. Yoko, et al., J. Phys. Chem. C., 124(8)(2020)4772-4780).

[0134] The reciprocal of this rate constant is the time required for the materials to mix, and if this is shorter than the time required for the materials to flow from the mixing point to the entrance of the heated section, mixing is considered to be sufficiently complete.

[0135] Here, the experimental conditions of fluid temperature T = 374°C, Re = 4768, and linear flow velocity v = 0.308 m / s are taken as an example, and the calculation results will be explained. First, the mixing rate constant obtained by substituting each value into [Equation 10] is k ｍｉｘ = 6.184 s －１ The reciprocal of this, the time required for mixing, was 0.161 s. On the other hand, the time required for flow was calculated to be 0.318 s, which is longer than the time required for mixing, so it is believed that mixing was sufficiently completed under these conditions. Furthermore, when similar calculations were performed for all fluid temperatures, Re numbers, and linear flow velocities in this experimental system, the mixing time was shorter than the flow time, so it is believed that the heat transfer coefficient was measured in a state where the nanofluid and preheated water were sufficiently mixed.

[0136] [Measurement of Convective Heat Transfer Coefficient (Pure Water)] Figure 6 compares the Nu number (plot) obtained from experimental values ​​for pure water in a supercritical state with the Nu number (dotted line) calculated using Equation 5, which is commonly used for base fluids in turbulent flows.

[0137] [Equation 5] is 0.7≦Pr≦120 and 10 ４ ≦Re≦1.2×10 ５turbulent flow region, but at 365°C and 370°C in Figure 13, Re≦10 ４ However, at higher temperatures of 380°C and 390°C, the deviation of the experimental values ​​from the calculated values ​​increased with increasing Re number.

[0138] This is thought to be due to the fact that in addition to convective heat transfer, a phenomenon similar to boiling heat transfer (pseudo-boiling), in which a large amount of heat is transported by bubbles near the heat transfer surface, occurs when the liquid changes to a supercritical state.

[0139] Next, FIG. 7 shows a comparison of the experimental values ​​(plots) of the Nu number of pure water in the high temperature range of 395° C. to 420° C. from FIG. 6 with the calculated values ​​(dotted line) of [Equation 5].

[0140] As in Figure 6, the deviation of the experimental values ​​from the calculated values ​​increases as the Re number increases at all fluid temperatures, which is also thought to be due to the pseudo-boiling phenomenon. Figure 8 shows the relationship between the experimental values ​​and temperature in the vicinity of 395°C to 420°C, and Figure 9 shows the relationship between the experimental values ​​and temperature in the vicinity of 360°C to 420°C at 15g / min.

[0141] In Figure 8, the Nu number exhibits a behavior in which it takes on a maximum value with respect to temperature at all flow rates, and at flow rates other than 20 g / min, it takes on a maximum value around 410 to 415°C. From this, it is expected that the effect of promoting heat transfer by pseudo-boiling at 30 MPa is maximized around 410 to 415°C, and that this effect weakens as the temperature increases further.

[0142] [Convective Heat Transfer Coefficient Measurement (Nanofluid)] Figures 10 to 12 show a comparison of the experimental (plot) and calculated (dotted line) Nu numbers for nanofluids and pure water with changes in Re number near the critical point. Figures 13 to 15 also show a comparison of the experimental (plot) and calculated (dotted line) Nu numbers for nanofluids and pure water with changes in temperature near the critical point. The results are for a tube with an inner diameter of 0.80 mm for the Re number ranges of 4700 to 5700 and 7600 to 9600, and a tube with an inner diameter of 1.755 mm for the Re number range of 10200 to 13200.

[0143] In Figure 10, the addition of particles increased the Nu number compared to pure water, and this effect became greater as the particle concentration increased. On the other hand, in the region where the Re number was about 9,000 in Figure 11 and about 11,000 in Figure 12, the addition of particles decreased the Nu number compared to pure water. Furthermore, as seen in Figures 13 to 15, the Nu number increased with increasing temperature, as in the case of pure water alone.

[0144] FIG. 16 shows the results of the analysis of the TiO concentration in pure water and at various concentrations from the graph in FIG. ２ + 375°C, 383°C, and 388°C were selected for water nanofluid, and the experimental and calculated values ​​are compared.

[0145] For each concentration of nanofluid, the experimental values ​​did not match the calculated values, and the discrepancy became larger as the temperature increased from 375°C near the critical point to 383°C and 388°C. The reason for the larger discrepancy at temperatures above 375°C is thought to be the pseudo-bubbles that occur during pseudo-boiling. Pseudo-bubbles are similar to bubbles in nucleate boiling, and this is thought to be due to the increased diffusion of nanoparticles in the fluid, which in turn promotes heat transfer through the particles. Furthermore, conventional correlation equations could not take into account the effects of adding these particles over a wide temperature range near the critical point, and therefore could not be applied to nanofluids.

[0146] As shown in Figure 10, the addition of particles increased the Nu number when the Re number was around 5,000, while the addition of particles reduced the Nu number below that of pure water when the Re number was around 9,000 in Figure 11 and around 11,000 in Figure 12. Furthermore, the calculated values ​​using the conventional correlation equation were higher than the experimental values ​​and did not match. The possible reasons for this are as follows:

[0147] First, the addition of particles increased viscosity and suppressed turbulence. This is also observed in nanofluids at room temperature and pressure, and it is thought that the effect of increased viscosity increases as the Re number increases.

[0148] The second point is that in a more turbulent flow field, the addition of particles suppressed the effect of pseudo-boiling, contrary to the above findings. It has been reported that, at room temperature and pressure, as the particle concentration in the fluid increased, the temperature near the wall increased (increased superheat) and the number of nucleate boiling sites decreased due to particles. A similar phenomenon also occurred near the critical point, and in regions with high flow velocities, a velocity distribution formed inside the pipe, and particles with a higher specific gravity than water flowed near the wall, which is thought to have exacerbated these effects.

[0149] [Calculation of relative viscosity using pressure loss and analysis of heat transfer coefficient (nanofluid)] Pressure loss was measured before and after the heating section, and the friction coefficient was calculated from the measured values ​​using [Equation 11].

[0150] where ΔP is the pressure loss, d ｔ is the pipe diameter, L is the pipe length, ρ is the density, and v is the linear flow velocity.

[0151] In addition, the turbulent flow conditions in a circular pipe (3 × 10 ３ ≦Re≦1×10 ５ ) the coefficient of friction is calculated by Blasius' formula (Blasius PRH, Forschungsheft., 131 (1913) 1-141) shown in [Equation 12].

[0152] By substituting the friction coefficient obtained from [Equation 11] into [Equation 12], the Re number and viscosity of the fluid can be determined.

[0153] The pressure loss measured in this experimental system was 0.5 MPa to 0.8 MPa for both pure water and nanofluid. When substituted into [Equation 10], the friction coefficient was 10 ３ From this, the Re number calculated using [Equation 11] is 10 －１８ The Re number under the conditions of this experiment is on the order of 10 ３ ~10 ４ Since it is expected that the Re number will be on the order of 1000, it was not possible to obtain an accurate Re number from the actual pressure loss measurements. This is thought to be due to measurement errors in the pressure gauge used in this experiment.

[0154] Since the above-mentioned method could not accurately determine the Re number of the nanofluid, the friction coefficient was calculated from the pressure loss of pure water and nanofluid at the same flow rate and fluid temperature, and the Re number ratio of pure water to nanofluid was calculated as shown in Equation 13.

[0155] The relative viscosity η of nanofluids at each concentration is calculated from the Re number ratio. ｎｆ / η ｂｆ Calculating the average value of [-], we got 1.946 at 1.8 wt% and 3.244 at 3.6 wt%, which are much larger than the relative viscosity calculated using Equation 8 (1.006 at 1.8 wt% and 1.012 at 3.6 wt%). Taking this viscosity ratio into consideration, Figs. 17 to 22 show a comparison of the experimental and calculated Nu numbers in the region (Re ≈ 9000, 11000) where nanofluids showed lower heat transfer performance than pure water in the section [Convective heat transfer coefficient measurement (pure water)].

[0156] When comparing the experimental values ​​of nanofluids at each concentration and Re number, taking into account relative viscosity, with the calculated values ​​of the nanofluids and base fluid (pure water), several experimental values ​​were found to be greater than the calculated values ​​for pure water. This suggests that, assuming that the viscosity of nanofluids calculated from pressure drop is greater than the value obtained using the correlation equation, the addition of particles enhances heat transfer more than pure water. However, the experimental values ​​did not match the calculated values ​​for nanofluids. The values ​​were generally smaller than the calculated values ​​in Figures 19 to 21, but larger in Figures 17, 18, and 22. This suggests that existing correlation equations cannot be applied to the heat transfer coefficient of nanofluids, even when viscosity is taken into account.

[0157] In this way, the heat transfer performance of the particle addition was improved compared to the base fluid when a viscosity greater than the value of the correlation equation was assumed, but since the calculation results change depending on the degree of increase in viscosity, it is thought that the accuracy of the obtained viscosity must also be evaluated.In addition to viscosity, it is also thought that it is necessary to measure thermal conductivity and compare it with the calculated value using the correlation equation, and to calculate the Nu number using the measured value.

[0158] <Test 3> Viscous behavior of nanofluids Nanofluids are prone to aggregation even at low concentrations, and changes in the dispersion state affect the transport property known as viscosity. If it is not possible to grasp the change in viscosity that accompanies changes in particle dispersion, even if it is possible to produce a nanofluid in which nanoparticles are dispersed in an unagglomerated state, there is concern that aggregation will occur during stirring or transport, causing adverse effects due to changes in viscosity. Therefore, the viscosity behavior of nanofluids was investigated.

[0159] [Viscosity of Particle Dispersion and Particle Size Dependence] Figure 23 shows viscosity data for particle dispersions of various particle sizes, from fine particles of a few nanometers to large particles of 100 μm or more. Using this viscosity data, a formula for predicting the viscosity of particle dispersions was investigated.

[0160] [Data Used] In this test, data that met the following conditions was used: Particle shape: spherical or nearly spherical Viscometer: rotational viscometer Measurement temperature: 25°C to 35°C

[0161] Regarding particle shape, spherical or nearly spherical shapes were selected because rod- or plate-like shapes may affect viscosity. Furthermore, to determine whether the particles exhibit non-Newtonian behavior, in which viscosity changes depending on the rotation speed, the results of measurements using a rotational viscometer were selected. This time, nano-sized particles (nanoparticles) were used for evaluation. Nanoparticles are expected to be thermally conductive materials, and have been evaluated at a variety of temperatures, from low (10°C) to high (70°C). Extreme temperature conditions were not included here, and the temperature was set to around room temperature (20°C to 35°C). After selecting particles under these conditions, the following three types were identified: - Surface-modified metal oxide (particle size d<10 nm) - Metal oxide (10 nm≦d≦450 nm) - Glass (1.3 μm≦d)

[0162] The data for a particle size of 25 nm shows that the surface is modified with organic molecules, but because the proportion of the modified layer is very low at 3 wt.%, it is treated as having no effect from the modified chains. In addition, for data with a range of particle sizes, the average value is used as the particle size.

[0163] The viscosity of the particle dispersion liquid with a particle size of 5.2 nm or less is newly obtained data. The particles used for evaluation were decanoic acid-modified cerium oxide (C10CeO ２ The particles were purchased from ITEC Co., Ltd. and pretreated to remove aggregates. In this study, the particle size was defined as the core size, and the particle volume was defined as the sum of the core volume and the volume of the modified chain.

[0164] [Viscosity Prediction Formula] As can be seen from Figure 23, the viscosity of a particle dispersion increases as the particle concentration increases. Up to a particle concentration of around 10 vol%, there is almost no difference in viscosity due to differences in particle size. Above 10 vol%, the change in viscosity as the particle concentration increases is more rapid for nanometer-sized particles than for micrometer-sized particles. This suggests that the viscosity of a particle dispersion is affected by particle size.

[0165] Furthermore, predicted values ​​calculated from an existing viscosity prediction formula are shown in Figure 30. The predicted values ​​and the measured values ​​are almost identical up to a particle concentration of approximately 10 vol%, which suggests that predictions can be made using the existing viscosity prediction formula when the particle concentration is low. On the other hand, at high particle concentrations, predictions can be made by introducing into the prediction formula a term that increases viscosity as the particle size decreases.

[0166] Figure 24 shows the change in relative viscosity when the particle concentration is fixed and particle size d is plotted on the horizontal axis using the data in Figure 23. Figure 24 also shows predicted values ​​calculated using the Einstein and Bachelor equations, which are existing viscosity measurement formulas. The relative viscosity in the Einstein and Batchelor equations depends only on the particle concentration, resulting in a constant value at each particle concentration. At a particle concentration of 5 vol%, there is no difference between the results of the Einstein and Bachelor equations, and they are consistent with the relative viscosity for particle sizes of 100 nm or larger. At a high particle concentration of 20 vol%, there is a difference between the two predicted values, and the Batchelor equation is in good agreement with the relative viscosity for particle sizes of 100 nm or larger. In other words, when the particle size is large, it may be possible to use existing prediction formulas to predict viscosity.

[0167] Furthermore, at any particle concentration, the relative viscosity increases as the particle size d decreases. Furthermore, looking at the data for particle concentrations of 10 vol% or more, the change in relative viscosity becomes steeper when the particle size becomes smaller than 100 nm (log d = 2). The higher the particle concentration, the more pronounced the change in relative viscosity when the particle size decreases. In other words, it can be said that the relative viscosity changes with particle size and particle concentration.

[0168] This is more easily seen from the graph for particle concentrations of 15 vol % or more. When the particle size becomes less than 10 nm (log d<1), the relative viscosity decreases once, and when the particle size becomes even smaller, the relative viscosity increases again.

[0169] A discontinuous change is observed around the particle size of 10 nm. The reason for this may be due to the way particle size is handled. In this test, the particle size was defined as the core size, but it can also be considered as the size including the surface modification chains (hydrodynamic size). However, although it is easy to consider the surface modification chains as extending radially from the core, various states are possible, such as when they are tilted or entangled.) Although it may be possible to express particle size and particle volume as a single curve by using appropriate expressions, in this test, prediction equations were examined for small particles without surface modification chains and relatively large particles with surface modification chains.

[0170] (Procedure for determining viscosity prediction formula) The viscosity prediction formula taking particle size dependency into consideration was determined according to the following procedure: (1) The form of the prediction formula is determined. (2) Determine the order n of the particle concentration of the term that expresses the particle size dependency. (3) Determine the coefficient a of the term that represents the particle size dependency. (4) Express the coefficient a as a function of particle size.

[0171] It was confirmed that the form of the prediction formula in step (1) is consistent with the experimental value when calculated from the Batchelor equation, an existing viscosity prediction formula, in the region where the particle size is 100 nm or more and the change in relative viscosity is small relative to the change in particle size. Therefore, the Batchelor equation was used as the base form of the prediction formula, and the part where the particle size dependency appears was defined as aφ ｎ Two prediction equations are examined depending on the particle size and the presence or absence of surface modification, and both prediction equations are examined in the form of [Equation 14].

[0172] In step (2), first, for each particle size, the difference obtained by subtracting the value calculated from the Batchelor equation from the measured value as shown in [Equation 15] is graphed against the change in particle concentration. Figure 25 shows the results when the particle size is 10 nm. The coefficient a and the order n are used as variables for the plot, and the difference between the measured value and the calculated value (R ２ ) was minimized. The RSQ values ​​in the figure indicate the correlation between the measured values ​​and the fitting results. For most particle sizes, the correlation value RSQ was 0.9 or higher, and it was determined that the fitting was performed without any problems.

[0173] Figure 26 shows the order n obtained by fitting as a change with respect to particle size. Looking at the plot in Figure 26, it appears that the order n is around 3 (average value: 3.1) for particle sizes of 10 nm or more, and around 2 (average value: 1.9) for particle sizes less than 10 nm. This is a similar trend to Figure 21. Here, the value of the order n is an integer, rather than a value containing a decimal point such as an average value, in order to consider its physical meaning.

[0174] Small particles with a particle size of less than 10 nm are assigned a value of 2, and large particles with a particle size of 10 nm or more are assigned a value of 3. In the following sections, we proceed to step (3) determining the coefficient a and step (4) expressing it as a function of the particle size d, first examining the case of large particles (particle size of 10 nm or more) and then the case of small particles (particle size of less than 10 nm).

[0175] (Large particles (particle size 10 nm or more)) When 3 is inserted into the order n of [Equation 14], the following is obtained.

[0176] In step (3), similar to step (2), the difference between the measured value and the calculated value from the Batchelor equation is plotted as a change in particle concentration for each particle size. Figure 27 shows a plot for a particle size of 10 nm. The fitting results showed a correlation value of 0.9 or higher, indicating a high correlation, so it was determined that there were no problems with the fitting.

[0177] Figure 28 is a plot of coefficient a, calculated for each particle size in the same manner as in Figure 27, against particle size. The plot shows that the coefficient increases as the particle size decreases. It also appears to remain constant as the particles increase. Based on these findings, we decided to separate coefficient a into a particle size-dependent portion c and an independent portion b. Since the coefficient increases as the particle size decreases, we set coefficient c as the numerator and the denominator to the mth power of particle size d. As a result, we considered that equation 17 would be as follows:

[0178] Next, fitting was performed with coefficients b and c as variables and the degree m changed in order from 1. As a result, the combination with the highest correlation was as follows:

[0179] FIG. 29 shows the correlation between the calculated values ​​obtained using the determined viscosity prediction formula (Equation 19) and the actually measured values.

[0180] Since the Batchelor equation can be used to make predictions at particle concentrations as low as 10 vol% (see Figure 23), values ​​above 10 vol% are displayed. Since the correlation value is high at 0.94, it is believed that there is a sufficient correlation. Furthermore, Equation 20 is expressed in the form of relative viscosity, which is the approach used in conventional viscosity prediction equations. In other words, the viscosity of the particle dispersion is proportional to the viscosity of the solvent, and is expressed as the relationship between the particle and solvent interactions.

[0181] The movement of particles in a liquid due to particle-solvent interactions is known as Brownian motion. When the diffusion coefficient of the particles is D, the Brownian motion in a particle dispersion is expressed as follows: where k and T are the Boltzmann constant and absolute temperature, respectively. When the temperature remains constant, the diffusion coefficient D changes depending on the particle size. The particle size dependence of the viscosity of particle dispersions is thought to be due to Brownian motion, which also suggests that the increase in viscosity at high particle concentrations when the particle size is large is due to particle-solvent interactions. Alternatively, when nanoparticles are formed, a solvation structure is formed, and its influence is greater than that of larger particles. In other words, it is thought that the distance between particles, including solvation, becomes extremely short, which increases the viscosity-increasing effect.

[0182] (Small particles (particle size less than 10 nm)) Next, we will consider the viscosity of a particle dispersion of small particles. As with the case of large particles, the form of the prediction formula is based on the Batchelor equation. The order of the particle volume fraction Φ, which is the term that represents the difference between the actually measured value and the value calculated using the Batchelor equation, is set to 2 based on the results shown in Figure 26.

[0183] As with the large particles, the difference between the experimental value and the calculated value using the Batchelor equation was calculated for each particle size and plotted against the particle volume fraction. Fitting was then performed using the coefficient a' as a variable, and the values ​​obtained from the fitting were plotted as a function of particle size. The viscosity data for small particles included literature values ​​(particle sizes 6 nm or larger) and newly acquired data (particle sizes less than 6 nm), although the core particles were the same. The trends differed between these data. This may be due to differences in the synthesis method and pretreatment method, which resulted in differences in the surface modification state. Therefore, in examining the viscosity prediction formula, we decided to use the results of the newly acquired data shown in Figure 30, which were carefully selected by performing multiple pretreatments. Fitting was performed on this plot using c' as a variable, gradually increasing the order of particle size d from 1, as shown below.

[0184] The combination of coefficient c' and degree m' with the highest correlation is The correlation value was 0.95. Figure 31 shows the correlation between the calculated values ​​obtained using [Equation 24] and the measured values. As with Figure 29, only calculated values ​​for particle concentrations of 10 vol% or more are shown. The correlation value for particle concentrations of 10 vol% or more was low at 0.39, and Figure 31 also shows that the measured values ​​and calculated values ​​do not match, showing a variation without a clear trend. On the other hand, when the low particle concentration side was included, the correlation value was high at 0.71, and the experimental value and calculated value were relatively consistent. This suggests that the form of [Equation 24] does not adequately represent the high particle concentration side, where viscosity increases.

[0185] Conventional viscosity predictions for particle dispersions are expressed in terms of relative viscosity, which represents the influence of particle-solvent interactions. At high particle concentrations, the viscosity is no longer expressed in this way, which suggests that there may be influences other than particle-solvent interactions. To examine the influence of the solvent, Figures 32 and 33 show the relative viscosities when the same particles are dispersed in different solvents, and when the temperature during viscosity measurement is changed. These figures show the particle concentration range where the relative viscosities do not match due to differences in solvent and temperature during viscosity measurement.

[0186] When the solvent was changed, C10CeO with a particle size of 4.4 nm ２ This is the viscosity of a particle dispersion in which particles were dispersed in cyclohexane and hexane. The viscosity of the solvent was 0.87 mPa·s for cyclohexane and 0.29 mPa·s for hexane at a measurement temperature of 25°C. The results shown in Figure 39 confirm that Newtonian behavior is observed. If the influence of particle-solvent interactions were dominant, the results should be plotted on the same line or curve, but since they were different, they could not be expressed as relative viscosity, which suggests the possibility of influences other than particle-solvent interactions.

[0187] Similarly, to examine the effect of increasing particle concentration on the viscosity of the solvent, measurements were performed at different solvent temperatures during viscosity measurement (Figure 33). ２A particle dispersion liquid in which particles were dispersed in cyclohexane was used. The measurement temperatures were 25°C, 35°C, and 40°C, and the viscosities of cyclohexane at these temperatures were 0.87 mPa·s, 0.78 mPa·s, and 0.65 mPa·s (measured values). When the temperature during viscosity measurement was changed, as with different solvents, no difference in viscosity was observed depending on the measurement temperature when the particle concentration was low. However, as the particle concentration increased and exceeded 5 vol%, differences gradually appeared, and the viscosity of the solvent decreased, showing a tendency for the relative viscosity to increase as the measurement temperature increased.

[0188] These results indicate that the effect of the solvent is smaller at high particle concentrations, and that this cannot be expressed in terms of relative viscosity, a conventional concept for particle dispersions. Here, we consider absolute viscosity as an alternative to relative viscosity. Figure 34 shows the results of expressing the plots in Figure 32 in terms of absolute viscosity. When expressed in terms of relative viscosity, the difference in relative viscosity between different solvents is large (Figure 32), but when expressed in terms of absolute viscosity, the difference becomes smaller at high particle concentrations. These results suggest that at high particle concentrations, it may be more appropriate to express viscosity in terms of absolute viscosity rather than relative viscosity.

[0189] Based on these results, we once again considered a new prediction formula for the viscosity of small particle dispersions. Because the particle concentration is affected by the solvent when it is low, we took a form similar to relative viscosity at low particle concentrations, multiplying the Batchelor formula by the viscosity of the solvent. Then, if we express the portion that cannot be expressed by the Batchelor formula in absolute viscosity, Equation 22 takes the following form.

[0190] Using the coefficient a'' as a variable, fitting was performed to minimize the difference from the measured value, and the obtained results are plotted in Figure 35. Next, the obtained coefficient a'' is expressed as a function of the coefficient particle size d. To do this, the coefficient a'' is re-expressed in the following form.

[0191] Then, with the coefficient c'' as a variable, the order m' of the particle size d is changed in order from 1, and R ２Fitting was performed so that the correlation coefficient RSQ was minimized. When the order m' was from 6 to 9, the correlation value RSQ was almost unchanged, ranging from 0.83 to 0.84 (Figure 35). Therefore, the coefficient c' obtained by fitting was used to calculate the viscosity for each order m' from 6 to 9, and the correlation with the measured value was confirmed. Figure 36 shows the results when the order m' was 6, which showed the highest correlation between the experimental value and the calculated value. Only data for particle concentrations of 10 vol% or more are plotted.

[0192] The prediction formula for the viscosity of particle dispersion when the order m' is 6 is This becomes:

[0193] Here, we consider the particle volume fraction φ and particle size d in the term showing particle size dependency. ３ is the particle number concentration. In other words, this shows that viscosity is proportional to the square of the particle number concentration. Considering that similar expressions exist in chemical reactions and molecular theory, this may suggest the influence of particle-particle interactions. In other words, the reason why the conventional viscosity prediction formula, which assumes the influence of the solvent and describes the solvent-particle interaction only in terms of the particle packing rate, could not be applied was revealed to be that in such high concentration regions, the type of solvent is not affected and the inter-particle interaction is dominant.

[0194] [Summary] This study attempted to predict the viscosity of a dispersion of monodispersed particles. As the particle concentration increased, existing viscosity equations, which only use particle packing concentration, became inapplicable, revealing particle size dependence. Particle size dependence differs depending on the particle size. For dispersions of relatively large particles, the viscosity of the particle dispersion was expressed in terms of relative viscosity, a conventional viscosity prediction equation, suggesting that particle-solvent interactions are dominant. Meanwhile, for small particles, the viscosity could be predicted in terms of relative viscosity at low particle concentrations, suggesting particle-solvent interactions. However, as the particle concentration increased, the viscosity could no longer be expressed in terms of relative viscosity and was expressed in terms of absolute viscosity. The relationship between the particle volume fraction φ and particle size d in the particle size dependence term was expressed in a similar way to chemical reactions, suggesting that particle-particle interactions are influential. In other words, it was revealed that the viscosity of small particle dispersions could not be described as a relative viscosity that represents particle-solvent interaction, assuming the influence of the solvent, because in the high particle concentration region, there is no influence of the solvent and particle-particle interaction becomes dominant.

[0195] <Test 4> Average particle size of nanoparticles contained in nanofluids Because the heat pump cycle repeats compression and expansion, it is necessary to consider the sedimentation of nanoparticles, especially during the expansion process. Therefore, we investigated the relationship between the average particle size of nanoparticles and their sedimentation.

[0196] Figure 37 is a schematic diagram of the simulation. －７ m (100 nm), the average flow velocity of the nanofluid was 2.7 m / s, the inner diameter of the pipe was 0.01 m, and the pipe length was 10 m. In this case, the terminal velocity (the velocity at which a nanoparticle is balanced by a volume force such as gravity and a velocity-dependent drag force) was 1 × 10 －６ m / s, and the settling time of the nanoparticles is 10 ４ s, and the particle transit time inside the tube is 4 s. Therefore, it is considered that the settling time of the nanoparticles is much longer than the particle transit time inside the tube, and that the gas contained in the non-azeotropic composition is circulating, and the circulation speed is greater than the settling speed of the nanoparticles, so that the nanoparticles do not settle.

[0197] Therefore, if the average particle size of the nanoparticles is 100 nm or less, it is thought that the sedimentation of the nanoparticles can be prevented, particularly during the expansion process, in a heat pump cycle in which compression and expansion are repeated.

[0198] <Test 5> Rheological analysis Even if the thermal conductivity is high, if the viscosity becomes high, more pump power is required. Also, the higher the particle concentration, the higher the viscosity. Therefore, a rheological analysis was conducted.

[0199] The viscosity of the nanofluid was measured using a cone-and-plate viscometer. A nanofluid containing organic acid-modified CeO2 was added to a cell, and the cone-and-plate was rotated. The rotation speed (shear rate is determined by the rotation speed and the geometry of the cone) was changed, and the shear stress at each rotation speed was recorded to measure the viscosity (shear stress / shear rate) at different shear rates. The temperatures were set to 30°C and 40°C. The temperature of the measurement cell was controlled by circulating water in a circulating thermostatic bath.

[0200] Figure 38 shows the relationship between rotation speed (Share rate) and shear stress, and Figure 39 shows the relationship between rotation speed (Share rate) and viscosity. At a temperature of 30°C, for both nanofluids containing hexanoic acid-modified CeO2 and nanofluids containing decanoic acid-modified CeO2, the shear stress is proportional to the rotation speed (Share rate) up to a concentration of 18 vol%, and the viscosity (= shear stress / shear rate) is almost constant, so the nanofluids can be considered Newtonian fluids.

[0201] On the other hand, at a temperature of 40°C, if the concentration of hexanoic acid-modified CeO2 is 5 vol%, the shear stress is proportional to the share rate, and the fluid can be said to be a Newtonian fluid. However, if the concentration of hexanoic acid-modified CeO2 is 12 vol% or higher, the proportional relationship between the share rate and the shear stress is lost, and the viscosity changes depending on the shear rate, making the fluid a non-Newtonian fluid.

[0202] In this way, even with the same material, Newtonian / non-Newtonian behavior changes depending on conditions such as temperature, etc. If the fluid is considered to be a Newtonian fluid, the viscosity can be predicted for nanofluids of various particle sizes and concentrations using the prediction formula already mentioned.

[0203] <Test 6> Measurement of heat transfer coefficient [Apparatus] The sample nanofluid was delivered to the test section using a syringe pump (Teledyne Isco 260D). The heat transfer coefficient measurement section was a circular tube made of SUS316. The heat transfer coefficient measurement section was immersed in a constant temperature water bath. The fluid temperatures on the In and Out sides of the heat transfer coefficient measurement section were measured using a T-type thermocouple. The pipe wall temperature in the heat transfer coefficient measurement section was also measured using a T-type thermocouple. The fluid pressure was measured for the In and Out sides using a pressure gauge (manufactured by Nippon Seimitsu). The heat transfer coefficient measurement section was a circular tube with an inner diameter of 0.5 mm and a length of 0.2 m.

[0204] [Experimental Method] The temperature of the thermostatic water bath was set to 15°C or 40°C, and the experiment was carried out. ２ The experiment was conducted using octanoic acid-modified cellulose (C10) dispersed in cyclohexane at concentrations ranging from 1 to 25 wt % and at flow rates ranging from 20 to 100 mL / min.

[0205] [Theoretical formula] Assuming that the heat flux given to the fluid from the pipe wall in the heating section is equal to the amount of heat that contributed to the temperature rise of the fluid at the inlet and outlet of the heating section, the convection heat transfer coefficient h is calculated from [Equation 28]. ｎｆ asked for.

[0206] Here, C ｐ is the constant pressure heat capacity, ΔTｎｆ is the temperature rise before and after the heating section, w is the mass flow rate, S is the heat transfer area, h ｎｆ is the convection heat transfer coefficient, T ｗ and T ｎｆ is the average temperature of the tube wall and nanofluid in the heated section. The Re number was used for the analysis.

[0207] Here h ｎｆ is the convection heat transfer coefficient, d is the pipe diameter, k ｎｆ is the thermal conductivity, ρ ｎｆ is the density, v is the linear velocity, μ ｎｆ is the viscosity. ｎｆ and Re ｎｆ The physical properties used to determine the viscosity were calculated from [Equation 30] to [Equation 33]. The viscosity was also measured using the cone-plate rheometer mentioned above.

[0208] where φ is the volume fraction of the particles, and n in Equation 33 is a coefficient that varies depending on the particle shape, with n = 3 being used for spherical particles. The subscripts for each physical property value indicate that nf is the value for the nanofluid, p is the value for the particle, and bf is the value for the base fluid.

[0209] [Evaluation] The thermal diffusivity of the systems for which viscosity was evaluated was measured using the laser flash method. The results are shown in Figure 40. The nanofluid was sealed in a liquid cell, and after specifying the thickness, the thermal diffusivity was measured and converted to thermal conductivity using the heat capacity calculated from the theoretical formula (Equation 32).

[0210] As explained above, it has been confirmed that the concentration dependence of thermal conductivity can be predicted using the theoretical formula (Equation 33). In other words, the existence of a unique size effect is denied. It has also been confirmed that there is no temperature dependence. This indicates that Brownian motion does not have a significant effect on thermal conductivity.

[0211] Experiments were also conducted in which the nanoparticles were replaced with hexanoic acid-modified CeO2 or decanoic acid-modified CeO2, the nanoparticle concentration was set to 5 vol%, 12 vol%, or 18 vol%, and the measurement cell temperature was set to 25°C, 30°C, 35°C, or 40°C. The results are shown in Figure 41. When nanoparticles were replaced, a similar trend to that shown in Figure 40 was observed. This confirms that the concentration dependence of thermal conductivity can be predicted using the theoretical formula (Equation 33). It was also confirmed that there was no temperature dependence.

[0212] <Test 7> Evaluation in a flow system Thermal conductivity is a physical property, but the actual speed at which heat is transported, the heat transfer coefficient h, is determined by the fluid temperature T at the inlet and outlet. ｉｎ , T ｏｕｔ (i.e., ΔTw), the pipe wall temperature Tw, and the fluid average temperature Tf (calculated from Tin and Tout). Using the measurement system shown in Figure 42, the actual heat transfer rate and heat transfer coefficient h in a flow system were evaluated at different temperatures.

[0213] The results are shown in Figures 43 and 44. Theoretical h for Cyclohexane is the theoretical value of the heat transfer coefficient h of the solvent (cyclohexane), and the experimental results (Experimental h for Cyclohexane) shown with bars are in good agreement with the theoretical value. The horizontal axis is the Reynolds number (ρud / μ), and the viscosity is the measured result.

[0214] Theoretical h for CeO2 is the theoretical line of the result of adding nanoparticles. Thermal conductivity was evaluated using the theoretical formula (Equation 33), and h was calculated using that value. The amount added was 20 wt%, and the effect of adding nanoparticles on improving thermal conductivity was not very significant at this loading amount.

[0215] In contrast, the dotted line shows the results of actual measurements. The heat transfer coefficient of nanoparticles with various organic modifications is several times higher when compared at the same Reynolds number, a new discovery. This change cannot be expressed even with a theoretical line that takes into account the improvement in thermal conductivity due to the addition of nanoparticles; it is the effect of improved heat transport due to changes in flow. A similar trend was observed not only under the condition of 40°C, where heat is added to the nanofluid, but also at 15°C, where heat is removed from the nanofluid (Figure 44). This change can be seen in both heating and cooling.

[0216] The dependence of the particles on thermal conductivity is included in the calculation of h, and the improvement in heat transfer coefficient observed here is a significant effect that cannot be expressed simply by an increase in thermal conductivity, and serves as a new basis for nanofluid design.

[0217] By adding highly thermally conductive nanoparticles, the thermal conductivity k of the nanofluid increases according to the previously reported theoretical formula (Equation 33).

[0218] The newly discovered finding is that the inclusion of nanoparticles changes the flow field, which affects the heat transfer coefficient, as shown in Figure 45.

[0219] Heat conduction occurs through the wall, but a thin film called a boundary film is formed (boundary layer δ), and heat is transferred through this film with thermal conductivity k. The thinner the boundary layer δ, the easier the heat is transferred. This means that not only is the thermal conductivity k high, but the thermal resistance h = k / δ is also important. The newly discovered finding here is that the addition of nanoparticles to the boundary layer δ has a greater impact than the thermal conductivity k.

[0220] This new finding indicates that the technique is useful not only for air conditioning but also for liquid immersion, a method of improving performance by using liquid in optical systems, such as those used in semiconductor and microscope manufacturing, and as a heat transfer medium for temperature control.

[0221] The fact that the boundary layer δ is more important than the thermal conductivity k means that there is no need to go to the trouble of searching for particles with high thermal conductivity, making this a very effective heat transfer medium.

[0222] However, in practical applications such as air conditioning, it is important to keep power consumption low and improve performance.

[0223] The heat transport working fluid carries the heat with a flow rate F and heat capacity Cp. Q = FCpΔT in-out The heat is transported to and from the wall in the heat transfer section.

[0224] The heat transfer rate Q can be expressed as Q = AhΔT, where A is the heat transfer area, H is the heat transfer coefficient, and ΔT is the temperature difference. If h is increased for the same heat transfer area and temperature difference ΔT, more heat can be transferred, which is the original purpose. In addition, because heat is transferred faster by the wall, the heat transfer area A can be reduced, reducing the cost of the device.

[0225] Regarding operating costs, the energy consumption associated with transporting nanofluids is significant.

[0226] For this reason, up until now, emphasis has been placed on preventing the viscosity μ from becoming too high. However, this new finding has revealed that adding nanoparticles changes not only the thermal conduction boundary film but also the flow field boundary film.

[0227] When a fluid flows, a velocity gradient occurs, resulting in pressure loss. The shear force is proportional to μ·du / dx (velocity gradient), and multiplying this by the area of ​​the intervening wall is the energy lost, which appears as pressure loss ΔP. ​​It is presumed that as the boundary layer δ becomes thinner, u / δ becomes larger.

[0228] Until now, emphasis has been placed on balancing thermal conductivity k and viscosity μ, but it has been suggested that efficiency can be further improved by comparing thermal resistance h and pressure loss ΔP. ​​If the thermal resistance h increases but the pressure loss ΔP also increases, this is undesirable because it increases power consumption. However, this finding has shown that there are cases in which the degree to which thermal resistance h increases is greater than the degree to which pressure loss ΔP increases. This finding is extremely important when applying this to practical aspects such as air conditioning, immersion, and heat transfer media for temperature control.

[0229] <Test 8> Relationship between heat transfer coefficient h and pressure drop ΔP Figure 46 shows the relationship between the heat transfer coefficient h and pressure drop ΔP. ２ or octanoic acid modified CeO ２This figure shows the results of simultaneous measurements of heat transfer coefficient and pressure drop using a flowmeter. As shown above, by changing the flow rate and performing measurements, the heat transfer coefficient h increases. Conversely, the pressure drop also increases. Figure 46 shows the relationship between the heat transfer coefficient h and pressure drop ΔP. It was confirmed that the calculated results of pressure drop and heat transfer coefficient for the solvent cyclohexane were close to the measured results.

[0230] Experiments were conducted with concentrations ranging from 5 to 25 wt%, and it was found that there was no significant difference in the relationship between pressure drop and h. Furthermore, although h was not particularly high at low flow rates, it was found that for all nanofluids, h increased without increasing pressure drop compared to the solvent. It was also found that some nanofluids could achieve a higher h at the same ΔP compared to the solvent (Figure 47 (C8-17.44%)).

[0231] In addition to 40°C, experiments were also conducted at 15°C, and the same tendency was observed (Figure 47). This result suggests the possibility of significantly improving the heat transfer coefficient with low pressure loss, and indicates that efficient heat transport with low energy consumption may be possible when the material is used as a heat transfer medium through circulation.

Claims

1. A heat transport or heat transfer system in which one or more working fluids selected from heat transfer working fluids for semiconductors, automobiles, and computers, working fluids for immersion lithography, temperature control working fluids, or working fluids for air conditioners, air conditioners, heat pump water heaters, refrigerators, and freezers are used, wherein the physical properties and operating conditions of the working fluid are such that the heat transfer coefficient h of the working fluid is greater than kNu / d. (h is the heat transfer coefficient of the working fluid, k is the thermal conductivity, Nu is the predicted value according to the generally used Nusselt number formula, and d is the pipe diameter.) 2. The system according to claim 1, wherein the working fluid contains nanoparticles.

3. The system according to claim 2, wherein the nanoparticles are any one of a high refractive index material, a magnetic material, an electric conduction material, a dielectric material, a high thermal conductivity material, and a fluorescent / light emitting material.

4. The system according to claim 2, wherein the nanoparticles are transparently dispersed.

5. One or more heat transport or heat transfer working fluids selected from heat transfer working fluids for semiconductors, automobiles, and computers, working fluids for immersion lithography, temperature control working fluids, or working fluids for air conditioners, air conditioners, heat pump water heaters, refrigerators, and freezers, which contain nanoparticles, and wherein, due to the addition of the nanoparticles, at a Reynolds number (Re) of 500 or more, the heat transfer coefficient is higher than the heat transfer coefficient of the dispersion medium in which the nanoparticles are dispersed and higher than the heat transfer coefficient of the nanofluid considering the effect of improving the thermal conductivity by adding the nanoparticles.

6. One or more heat transport or heat transfer working fluids selected from heat transfer working fluids for semiconductors, automobiles, and computers, working fluids for immersion lithography, temperature control working fluids, or working fluids for air conditioners, air conditioners, heat pump water heaters, refrigerators, and freezers, which contain nanoparticles, and wherein the value of the thermal conductivity improvement effect / viscosity increase effect due to the addition of the nanoparticles is 1 or more.

7. The working fluid according to claim 5 or 6, wherein the effect of increasing the heat transfer rate h is greater than the effect of increasing the pressure loss ΔP compared to the case where the nanoparticles are not contained.

8. The working fluid according to claim 5 or 6, wherein the nanoparticles are dispersed in a solvent, and the content of the nanoparticles is 1 part by mass or more and 70 parts by mass or less with respect to 100 parts by mass of the working fluid.

9. The nanoparticles are dispersed in a gaseous or supercritical medium, and the content of the nanoparticles is 1 part by mass or more and 70 parts by mass or less with respect to 100 parts by mass of the working fluid. The working fluid according to claim 5 or 6.

10. The working fluid according to claim 5 or 6, wherein the nanoparticles are organically modified nanoparticles having an organic modification group on the surface.

11. The working fluid according to claim 5 or 6, wherein the average particle diameter of the nanoparticles is 1 nm or more and 100 nm or less.

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