CN113191047A - Regulation and control method for realizing super-structure material soaking substrate - Google Patents
Regulation and control method for realizing super-structure material soaking substrate Download PDFInfo
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Abstract
The invention belongs to the related technical field of thermodynamics and discloses a regulation and control method for realizing a soaking substrate of a metamaterial. The regulation and control method comprises the following steps: s1, setting the coefficient of thermal conductivity of the homogeneous substrate and the position and the size of the phantom heat source on the substrate; s2, dividing the positions of the non-heat sources in the homogeneous substrate and the soaking substrate to be solved into a plurality of areas, and corresponding the areas one to one; constructing a coordinate conversion relation between the homogeneous substrate and the soaking substrate to be solved so as to obtain a conversion matrix between the homogeneous substrate and the soaking substrate; s3, a relation between the conversion matrix and the thermal conductivity coefficient of each area on the soaking substrate to be solved is established, the thermal conductivity coefficient of each area on the soaking substrate to be solved is calculated, and the corresponding material of each area on the soaking substrate to be solved is selected according to the thermal conductivity coefficient, so that the regulation and control of the thermal conductivity of the soaking substrate to be solved are realized. According to the invention, the temperature distribution of the substrate is changed, the effect of uniform temperature at the top of the substrate is realized, and the function of a vapor chamber is achieved.
Description
Technical Field
The invention belongs to the related technical field of thermodynamics, and particularly relates to a regulation and control method for realizing a soaking substrate of a metamaterial.
Background
The thermal metamaterial can generate various novel thermal physical characteristics based on a special structure which can be artificially designed, and has great influence on the field of thermal management. At present, the research of the thermal metamaterial in the heat conduction direction is mainly heat flow control, namely, the heat flow is quantitatively and directionally controlled by designing the geometric structure of the metamaterial. The study is currently based in large part on the functions of thermal stealth, thermal transparency, thermal illusion, and the like. Huazhong university of science and technology Hu et al propose that a single internal original heat source can be disguised as multiple virtual heat source signals based on heat flow control, and that an observer cannot discern the actual heat source from the external heat distribution. In other words, the position, the shape, the size and the number of the actual heat source are hidden, the camouflage of the position of the heat source is realized, and the heat coding is realized based on the heat flow control; de et al introduced basic experimental studies on heat flow control, extended to various electronic applications including equipment temperature control, heat energy collection, thermoelectric circuit design, etc., using basic building blocks of thermal cloak, thermal aggregation, thermal rotation, based on standard Printed Circuit Board (PCB) technology. Chinese invention patent CN110826265A discloses a thermal stealth cloak designed based on the theory of transformed thermal radiation and thermal conduction, which is used for object stealth and is not discovered by external infrared detection. The Chinese patent CN 110600087A disclosed by the invention is an isotropic double-shell structure which presents a thermal chameleon phenomenon and the implementation method thereof is based on the Fourier heat conduction law, designs a thermal chameleon effect which actively adapts to the background temperature distribution, and is used for hiding in the background and not influencing the temperature distribution of the background. Although the research on the thermal metamaterial at home and abroad has been greatly progressed, most of the research is still in the theoretical level, and the practical application of the anisotropic substrate based on the thermal metamaterial is not fully considered.
The existing vapor chamber is developed from a heat pipe technology, is a vacuum chamber with a fine structure on the inner wall, achieves the purpose of vapor chamber by means of steam flow and phase change heat transfer of a working medium, and belongs to a liquid VC (polyvinyl chloride) plate. The chinese invention patent CN111637772A discloses an ultra-thin soaking plate with symmetrical structure, in which the upper and lower cover plates can be used as condensing surface or evaporating surface, aiming at the problem that the upper and lower cover plates of a common soaking plate are different in structure because the lower cover plate is used as evaporating end and is attached to the chip, and the upper cover plate is used as condensing end. The Chinese patent invention CN111669939A discloses a soaking plate made of composite metal material, aiming at the phenomena of surface point damage, bending deformation, poor flatness and the like easily caused by the insufficient integral strength and hardness of the traditional soaking plate in the using process, comprising an upper soaking plate cover and a lower soaking plate cover which are assembled together, wherein the inner side of the upper soaking plate cover is provided with a capillary structure, the inner side of the lower soaking plate cover is provided with a support pillar, the upper soaking plate cover and the lower soaking plate cover are compounded by at least two materials selected from metal materials and alloy materials, and the compounding mode comprises rolling, spraying, high-temperature sintering and electroplating. The design of the existing vapor chamber is generally provided with a vacuum cavity consisting of an upper cover plate, a middle capillary layer, a lower cover plate and an internal working medium. The structure that thus distinguishes the upper and lower cover plates can be extremely complex in the design, process flow manufacturing and use stages. And the working medium flow is needed in the liquid soaking plate, so that the corrosion and the leakage are easy to generate. In conclusion, most of the existing vapor chambers have the defects of high manufacturing cost, difficult assembly and disassembly, difficult operation and incapability of long-term use.
In order to solve the problems, realize free regulation and control of heat conduction and promote practical application, the invention provides a soaking substrate based on a thermal metamaterial by changing a thermal theory, which is used for realizing a solid soaking substrate.
Disclosure of Invention
Aiming at the defects or improvement requirements in the prior art, the invention provides a regulation and control method for realizing a soaking substrate made of a metamaterial, which comprises the steps of setting a common homogeneous substrate, establishing a conversion relation between the homogeneous substrate and the soaking substrate to be solved, determining a corresponding thermal conductivity coefficient in each area on the soaking substrate to be solved, selecting materials corresponding to each area according to the thermal conductivity coefficient, regulating and controlling the heat conduction and heat conduction characteristics of the soaking substrate to be solved, changing the temperature distribution of the substrate, realizing the effect of uniform temperature at the top of the substrate and achieving the function of the soaking substrate.
In order to achieve the above object, according to the present invention, there is provided a control method for realizing a soaking substrate of a metamaterial, the control method comprising the steps of:
s1, setting the coefficient of thermal conductivity of the homogeneous substrate and the position and the size of the phantom heat source on the substrate;
s2, dividing the positions of the non-heat sources in the homogeneous substrate and the soaking substrate to be solved into a plurality of regions respectively, and enabling the regions in the homogeneous substrate to correspond to the regions in the soaking substrate to be solved one by one; constructing a coordinate conversion relation between the homogeneous substrate and the soaking substrate to be solved so as to obtain a conversion matrix between the homogeneous substrate and the soaking substrate;
s3, using the conversion matrix to construct a relation between the conversion matrix and the thermal conductivity coefficient of each region on the soaking substrate to be solved, calculating and obtaining the thermal conductivity coefficient of each region on the soaking substrate to be solved, and selecting the corresponding material of each region on the soaking substrate to be solved according to the thermal conductivity coefficient to realize the regulation and control of the thermal conductivity of the soaking substrate to be solved.
Further preferably, in step S3, the relation between the transformation matrix and the thermal conductivity coefficient of each region on the soaking substrate to be solved is performed according to the following expression:
wherein, k'iIs the second-order thermal conductivity tensor, J, of the region i on the soaking substrate to be solvediIs a transformation matrix, kappa, between the region i on the homogeneous substrate and the region i on the soaking substrate to be solved0Is the coefficient of thermal conductivity on a homogeneous substrate.
Further preferably, in step S2, the transformation matrix J is two-dimensional for the case where the homogeneous substrate and the substrate to be solved are both two-dimensionaliThe following expression is followed:
wherein x isiAnd yiRespectively the abscissa and the ordinate of a point in a region i on a homogeneous substrate，x′iAnd y'iRespectively representing the abscissa and the ordinate of a point in a region i on the soaking substrate to be solved;
for the case where the homogeneous substrate and the substrate to be solved are both three-dimensional, the transformation matrix JiThe following expression is followed:
wherein x isi,yiAnd ziAre coordinates, x 'of points in area i in x, y and z directions on the homogeneous substrate'i,y′iAnd z'iThe coordinates of the points in the region i on the soaking substrate to be solved in the x, y and z directions, respectively.
Further preferably, in step S1, the homogeneous substrate is a thermal metamaterial, and the phantom heat source is a copper or aluminum heat plate.
Further preferably, in step S1, the phantom heat source is located on top of the homogeneous substrate at a distance of 1% to 30% of the thickness of the homogeneous substrate.
Further preferably, in step S1, the size and shape of the phantom heat source are different from those of the heat source on the soaking substrate to be solved, and the length of the phantom heat source is 50% to 100% of the length of the homogeneous substrate; the width is 1% -30% of the thickness of the homogeneous substrate.
Further preferably, in step S1, the length of the phantom heat source is 90% to 100% of the length of the homogeneous substrate.
Further preferably, in step S1, the shape of the phantom heat source is one of circular, triangular, rectangular, polygonal, and irregular.
Generally, compared with the prior art, the technical scheme of the invention has the following beneficial effects:
1. the soaking substrate based on the thermal metamaterial comprises a thermal metamaterial base material substrate and an illusion heat source, wherein the real heat source on the soaking substrate to be solved is converted into the illusion heat source positioned at the top of the substrate by establishing the relation between the homogeneous substrate and the soaking substrate to be solved, then the conversion relation between areas at positions of non-heat sources is established, and the change of the space is converted into the change of the thermophysical property of the material, so that the material parameters of the soaking substrate based on the thermal metamaterial are determined, the heat conduction and conduction characteristics of the substrate are regulated and controlled, the temperature distribution of the substrate is changed, the effect of uniform temperature at the top of the substrate is realized, and the function of the soaking plate is achieved;
2. the effect of top temperature uniformity is realized by heat transfer of the phantom heat source, the length is long, the temperature of each point on the top is more and more consistent, the condition of region division needs to be met, and the length of the phantom heat source is set to be 50-100% of the length of the soaking substrate; in order to avoid the scattered heat transfer effect, the width and the distance from the top of the substrate are 1 to 30 percent of the thickness of the soaking substrate;
3. the substrate is divided into a plurality of areas according to the heat source vertex position and the coordinate corresponding relation for obtaining the transposition matrix coefficient.
Drawings
FIG. 1 is a schematic diagram of a soaking substrate to be solved and a homogeneous substrate conversion principle constructed in accordance with a preferred embodiment of the present invention;
FIG. 2 is a schematic diagram of a two-dimensional steady state simulation comparison of example 1 and comparative example 1 constructed in accordance with a preferred embodiment of the present invention and a comparison of temperature values on a top cross-section of the substrate; wherein, (a) is a simulation result chart of the homogeneous isotropic FR4 substrate in comparative example 1, (b) is a simulation result chart of the substrate in example 1, and (c) is a quantitative comparison chart of temperature values on top section lines of the two substrates in comparative example 1 and example 1;
FIG. 3 is a comparison graph of three-dimensional steady state simulation of example 2 and comparative example 2 constructed in accordance with a preferred embodiment of the present invention and temperature values on the top surface of the substrate; wherein, (a) is an axial comparison chart of simulation results of two substrates in example 2 and comparative example 2, (b) is a top comparison chart of simulation results of two substrates in example 2 and comparative example 2, (c) is a bottom comparison chart of simulation results of two substrates in example 2 and comparative example 2, and (d) is a quantitative comparison chart of temperature values on top cross sections of two substrates in example 2 and comparative example 2.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The homogeneous substrate of the metamaterial constructed by the invention is a common substrate in appearance, but is processed by the thermal metamaterial, and a heat source can be a heating plate of copper, aluminum and the like, preferably a copper heating plate.
The position of the phantom heat source on the homogeneous substrate is positioned at the top of the substrate space, the distance from the upper surface of the substrate is 1-30% of the thickness of the substrate, and the distance from the upper surface of the substrate is preferably 1-3 mm. The size, the shape and the like of the phantom heat source are different from those of a real heat source, and the size and the length can be 50-100%, preferably 90-100% of the length of the upper surface; the width is 1-30% of the thickness of the substrate, preferably 1-3 m; the shape may be one of circular, triangular, rectangular, polygonal, irregular, preferably rectangular.
The homogeneous substrate based on the thermal metamaterial provided by the invention can be suitable for two-dimensional situations and also suitable for three-dimensional situations.
The conditions for achieving top temperature uniformity for thermal substrates based on thermal metamaterials are further derived as follows:
the transport process taking into account the heat transfer, the thermodynamic evolution of which is given by Fourier's law as formula (1):
wherein, k is the thermal conductivity of the material,
is the laplacian operator.
Virtually transforming the position of a real heat source of the soaking substrate to be solved to the top of the homogeneous substrate and the position of a phantom heat source by a coordinate transformation method, dividing the homogeneous substrate and the non-heat-source area of the soaking substrate to be solved into a plurality of subareas, and carrying out coordinate transformation in each subarea in the substrate, wherein the coordinate transformation method specifically comprises the following steps:
considering the two-dimensional situation, the soaking substrate to be solved is divided into four regions each having different anisotropic thermal conductivity, and based on the transformed thermal theory, the coordinate change (x ', y') from the virtual space (x, y) on the homogeneous substrate to the physical space on the soaking substrate to be solved is as shown in equation (2):
wherein i is the sequence number of the region, and the two-dimensional Jacobian transformation determinant can be obtained through the geometrical coordinates before and after transformation, and is shown in formula (3):
through Jacobian transformation matrix J, corresponding material change, namely transformed thermal conductivity k 'of the invention can be obtained'iDetermined by equation (4):
wherein, κ0For isotropic thermal conductivity, JiAs determinant of Jacobian transformation matrix, Ji TIs transpose of the Jacobian transform matrix, κ'iThe second order thermal conductivity tensor.
To this end, the thermal conductivity, which is a key parameter for designing a soaking substrate to be solved, has been determined, i.e., equation (4), and these parameters are expressed in a cartesian coordinate system.
The method can be popularized to the three-dimensional situation, the soaking substrate to be solved is divided into eighteen regions, each region has different anisotropic thermal conductivity, and the coordinate change from the virtual space (x, y, z) of the soaking substrate to be solved to the physical space (x ', y ', z ') of the soaking substrate to be solved is changed from a formula (5) to a formula (6) on the basis of a heat conversion theory:
the Jacobian transformation matrix J of the formula (5) is directly transformed from the formula (3) to the formula (6):
through Jacobian transformation matrix J, corresponding material change, namely transformed thermal conductivity k 'of the invention can be obtained'iDetermined by equation (4):
the three-dimensional case differs from the two-dimensional case only by the Jacobian transformation matrix J, the remaining and two-dimensional cases being exactly the same algorithm, i.e. thermal conductivity κ'iThe transformation of (c) is shown in equation (7).
The present invention will be further illustrated with reference to specific examples.
Example one-two dimensional Steady State simulation
A two-dimensional schematic diagram of a substrate to be solved for soaking is shown in FIG. 1, wherein the gray region P'1Q'1M'1N'1The heat source position is the heat source position, and the heat source of the soaking substrate to be solved is arranged at the lower left corner of the bottom. The functional mode for realizing the regulation and control of heat conduction of the soaking substrate to be solved is as follows:
in order to show the correctness of the theory, the invention utilizes a finite element simulation analysis method for verification. The given substrate is a rectangular heat-conducting substrate, the length of the substrate is 100mm, the width of the substrate is 5mm, and the parameter of the soaking substrate to be solved is setThe device is designed according to equation (4). The results of the two-dimensional steady-state simulation are shown in fig. 2. In the simulation process, the upper boundary and the left and right boundaries are set as the convective heat transfer boundary conditions, and the convective heat transfer coefficient is 5W/(m)2K), the lower boundary is set as an adiabatic boundary condition.
Fig. 1 is a schematic diagram of the conversion from the soaking substrate to be solved to the homogeneous substrate according to the present invention. According to the theory of transformed thermal, we make a virtual phantom heat source that appears on top so that the heat source at the bottom of the soaking substrate to be solved appears to be on top of the soaking substrate to be solved, i.e. the heat source is represented by the bottom edge square P 'at the bottom left corner in the left diagram of fig. 1'1Q'1M'1N'1The actual position shown is changed to the right picture P of figure 11Q1M1N1The phantom position of the substrate is designed and regulated by carrying out coordinate transformation on each area in the soaking substrate to be solved and designing the anisotropic thermal conductivity of the material required by each area of the substrate, so that the overall temperature distribution is changed by regulating the anisotropic thermal conductivity, and the temperature field detected by the thermal infrared imager is the temperature field formed by the structure of the right graph of the figure 1.
Observing the simulation result, it can be found that the top temperature of the soaking substrate to be solved is uniform in fig. 2 (b), and the temperatures of all points on the sectional line of the top of the soaking substrate to be solved are substantially equal in fig. 2 (c), which shows that the top temperature of the soaking substrate to be solved is uniform, thereby achieving the effect of the soaking plate.
Example two-three-dimensional Steady-State simulation
The invention also performs three-dimensional steady state simulation, at this time, the soaking substrate to be solved is a three-dimensional cuboid, we give the substrate as a cuboid heat-conducting substrate, the length of the substrate is 200mm, the width is 200mm, and the height is 10mm, and the result is shown in fig. 3. In the simulation process, six surfaces of the device are boundary conditions of convective heat transfer, and the convective heat transfer coefficient is 5W/(m)2K), the parameter settings of the thermal-metamaterial soaking substrate are designed according to equation (7).
Observing the simulation result, as can be seen from fig. 3, similar to the two-dimensional result, the temperature on the top section of the soaking substrate to be solved in (b) of fig. 3 is uniform, the temperature of all points on the top section of the soaking substrate to be solved in (d) of fig. 3 is substantially equal, and the temperature values of all points are substantially equal, which indicates that the temperature on the top section of the soaking substrate to be solved is uniform, thereby achieving the effect of the soaking plate.
Comparative example 1 two-dimensional Steady State simulation
A uniform isotropic substrate made of FR4 was selected for comparison, and given that the substrate was a rectangular heat-conducting substrate, we assumed that the substrate was a rectangular heat-conducting substrate, the substrate was 100mm long and 5mm wide, and the material parameter coefficient of thermal conductivity κ was 0.3W/(m · K). In the simulation process, the upper boundary and the left and right boundaries are set as the convective heat transfer boundary conditions, and the convective heat transfer coefficient is 5W/(m)2K), the lower boundary is set as an adiabatic boundary condition.
As a result of simulation of uniform isotropic substrate of FR4, it can be seen that the substrate temperature distribution is significantly different in fig. 2 (a), and the temperature of the top section line of the substrate of FR4 in fig. 2 (c) is parabolic, so that the temperature values of all points on the top section line cannot be substantially equal.
Comparative example 2 three-dimensional Steady State simulation
A uniform isotropic substrate made of FR4 was selected as a comparison, and the given substrate was a rectangular parallelepiped heat-conducting substrate with a length of 200mm, a width of 200mm, and a height of 10 mm. The coefficient of thermal conductivity of the material parameter kappa is 0.3W/(m.K). In the simulation process, six surfaces of the device are boundary conditions of convective heat transfer, and the convective heat transfer coefficient is 5W/(m)2·K)。
Observing the simulation result of the uniform isotropic substrate made of FR4, it can be seen from the left diagram in fig. 3 (b) that the temperature value of the middle part and the temperature value of the rest part of the top cross section of the substrate are greatly different, i.e. the difference between the highest temperature value and the lowest temperature value is large, and the temperature value mutation on the top cross section of the FR4 material substrate in the left diagram in fig. 3 (d) is obvious, and the temperature values of all points on the top surface cannot be substantially equal.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A regulation and control method for realizing a metamaterial soaking substrate is characterized by comprising the following steps:
s1, setting the coefficient of thermal conductivity of the homogeneous substrate and the position and the size of the phantom heat source on the substrate;
s2, dividing the positions of the non-heat sources in the homogeneous substrate and the soaking substrate to be solved into a plurality of regions respectively, and enabling the regions in the homogeneous substrate to correspond to the regions in the soaking substrate to be solved one by one; constructing a coordinate conversion relation between the homogeneous substrate and the soaking substrate to be solved so as to obtain a conversion matrix between the homogeneous substrate and the soaking substrate;
s3, using the conversion matrix to construct a relation between the conversion matrix and the thermal conductivity coefficient of each region on the soaking substrate to be solved, calculating and obtaining the thermal conductivity coefficient of each region on the soaking substrate to be solved, and selecting the corresponding material of each region on the soaking substrate to be solved according to the thermal conductivity coefficient to realize the regulation and control of the thermal conductivity of the soaking substrate to be solved.
2. A control method for realizing a metamaterial soaking substrate as claimed in claim 1, wherein in step S3, the relation between the transformation matrix and the thermal conductivity coefficient of each region on the soaking substrate to be solved is performed according to the following expression:
wherein, k'iIs the second-order thermal conductivity tensor, J, of the region i on the soaking substrate to be solvediIs a transformation matrix, kappa, between the region i on the homogeneous substrate and the region i on the soaking substrate to be solved0Is the coefficient of thermal conductivity on a homogeneous substrate.
3. A method of conditioning a metamaterial soaking substrate as in claim 2 wherein in stepIn S2, the transformation matrix J is used for the case where the homogeneous substrate and the soaking substrate to be solved are both two-dimensionaliThe following expression is followed:
wherein x isiAnd yiAre respectively the abscissa and ordinate, x ', of a point in a region i on a homogeneous substrate'iAnd y'iRespectively representing the abscissa and the ordinate of a point in a region i on the soaking substrate to be solved;
for the case where the homogeneous substrate and the substrate to be solved are both three-dimensional, the transformation matrix JiThe following expression is followed:
wherein x isi,yiAnd ziAre coordinates, x 'of points in area i in x, y and z directions on the homogeneous substrate'i,y′iAnd z'iThe coordinates of the points in the region i on the soaking substrate to be solved in the x, y and z directions, respectively.
4. A method according to claim 1 or 2, wherein in step S1, the homogeneous substrate is a thermal metamaterial, and the phantom heat source is a copper or aluminum heat plate.
5. A method according to claim 1 or 2, wherein in step S1, the phantom heat source is located on top of the homogeneous substrate at a distance of 1-30% of the thickness of the homogeneous substrate.
6. A method for regulating a soaking substrate of a metamaterial according to claim 1 or 2, wherein in step S1, the size of the phantom heat source is different from the actual heat source on the soaking substrate to be solved, and the length of the phantom heat source is 50% -100% of the length of the homogeneous substrate; the width is 1% -30% of the thickness of the homogeneous substrate.
7. A method according to claim 6, wherein in step S1, the length of the phantom heat source is 90% -100% of the length of the homogeneous substrate.
8. A method for conditioning a metamaterial heat spreader substrate as in claim 6 wherein in step S1, the phantom heat source is one of circular, triangular, rectangular, polygonal, and irregular.
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| CN110826265A (en) * | 2019-10-01 | 2020-02-21 | 复旦大学 | Heat stealth cloak designed based on heat radiation conversion and heat conduction theory |
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