CN107426946B - Direct contact heat dissipation method for vibrating device based on microarray structure - Google Patents

Direct contact heat dissipation method for vibrating device based on microarray structure Download PDF

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CN107426946B
CN107426946B CN201710521283.8A CN201710521283A CN107426946B CN 107426946 B CN107426946 B CN 107426946B CN 201710521283 A CN201710521283 A CN 201710521283A CN 107426946 B CN107426946 B CN 107426946B
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vibration
array structure
direct contact
contact heat
vibration device
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CN107426946A (en
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琚斌
张海姣
郭治华
申佳乐
刘永斌
刘方
陆思良
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Anhui University
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Anhui University
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    • HELECTRICITY
    • H05ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
    • H05KPRINTED CIRCUITS; CASINGS OR CONSTRUCTIONAL DETAILS OF ELECTRIC APPARATUS; MANUFACTURE OF ASSEMBLAGES OF ELECTRICAL COMPONENTS
    • H05K7/00Constructional details common to different types of electric apparatus
    • H05K7/20Modifications to facilitate cooling, ventilating, or heating
    • H05K7/2039Modifications to facilitate cooling, ventilating, or heating characterised by the heat transfer by conduction from the heat generating element to a dissipating body
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B82NANOTECHNOLOGY
    • B82YSPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y30/00Nanotechnology for materials or surface science, e.g. nanocomposites
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B82NANOTECHNOLOGY
    • B82YSPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y40/00Manufacture or treatment of nanostructures
    • HELECTRICITY
    • H05ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
    • H05KPRINTED CIRCUITS; CASINGS OR CONSTRUCTIONAL DETAILS OF ELECTRIC APPARATUS; MANUFACTURE OF ASSEMBLAGES OF ELECTRICAL COMPONENTS
    • H05K7/00Constructional details common to different types of electric apparatus
    • H05K7/20Modifications to facilitate cooling, ventilating, or heating
    • H05K7/2039Modifications to facilitate cooling, ventilating, or heating characterised by the heat transfer by conduction from the heat generating element to a dissipating body
    • H05K7/20436Inner thermal coupling elements in heat dissipating housings, e.g. protrusions or depressions integrally formed in the housing
    • H05K7/20445Inner thermal coupling elements in heat dissipating housings, e.g. protrusions or depressions integrally formed in the housing the coupling element being an additional piece, e.g. thermal standoff
    • H05K7/20472Sheet interfaces
    • HELECTRICITY
    • H05ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
    • H05KPRINTED CIRCUITS; CASINGS OR CONSTRUCTIONAL DETAILS OF ELECTRIC APPARATUS; MANUFACTURE OF ASSEMBLAGES OF ELECTRICAL COMPONENTS
    • H05K7/00Constructional details common to different types of electric apparatus
    • H05K7/20Modifications to facilitate cooling, ventilating, or heating
    • H05K7/2039Modifications to facilitate cooling, ventilating, or heating characterised by the heat transfer by conduction from the heat generating element to a dissipating body
    • H05K7/20436Inner thermal coupling elements in heat dissipating housings, e.g. protrusions or depressions integrally formed in the housing
    • H05K7/20445Inner thermal coupling elements in heat dissipating housings, e.g. protrusions or depressions integrally formed in the housing the coupling element being an additional piece, e.g. thermal standoff
    • H05K7/20472Sheet interfaces
    • H05K7/20481Sheet interfaces characterised by the material composition exhibiting specific thermal properties

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Chemical & Material Sciences (AREA)
  • Nanotechnology (AREA)
  • Microelectronics & Electronic Packaging (AREA)
  • Thermal Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Crystallography & Structural Chemistry (AREA)
  • Condensed Matter Physics & Semiconductors (AREA)
  • Manufacturing & Machinery (AREA)
  • Composite Materials (AREA)
  • Materials Engineering (AREA)
  • Cooling Or The Like Of Electrical Apparatus (AREA)
  • General Electrical Machinery Utilizing Piezoelectricity, Electrostriction Or Magnetostriction (AREA)

Abstract

The invention discloses a direct contact heat dissipation method and application of a vibration device based on a microarray structure, and provides an elastic microarray contact heat dissipation structure with low thermal resistance and high thermal conductivity coefficient, aiming at the problems that direct contact heat dissipation is large in contact thermal resistance, serious in device abrasion, and the like generally existing in a high-frequency vibration device similar to a piezoelectric transformer. The microarray structure with high length-diameter ratio and proper array density is grown on the substrate of the radiator in a large scale, and the microarray structure can be used for occasions where a vibrating device is not suitable for direct contact heat dissipation based on good longitudinal thermal conductivity and van der Waals force action and good transverse flexibility. The vibrating device heat management scheme has the advantages that the vibrating device heat management scheme has no relative sliding, does not generate contact wear, has high flexibility and small damping in the direction perpendicular to the heat transfer direction, has low influence on the vibration of the device, does not need additional acting force to fix in the heat transfer direction, has a simple structure, and can meet the requirement of the vibrating device on heat management to a certain extent.

Description

A kind of vibration device based on micro array structure is in direct contact heat dissipating method
Technical field
The present invention relates to the field of heat management more particularly to a kind of carbon nano pipe array of micro array structure and vibration device Structure piezoelectric transformer heat dissipation in application, i.e., a kind of vibration device based on micro array structure be in direct contact heat dissipating method and Using.
Background technology
As requirement of the people to product portability is higher and higher, miniaturization, cost effective becomes inevitable at lightweight Development trend.But people to the diversification requirement of function so that then higher and higher to the power requirement of product, therefore its power Density is also higher and higher, and the heat management of device also just becomes more and more important.And for some vibration devices, it is usually unsuitable It carries out being in direct contact heat dissipation, generally all with water cooling or oil cooling.But if vibration device also hot line job, these modes may It influences vibration performance and can not use, it is necessary to consider suitable heat-treatment protocol.
By taking the piezoelectric transformer in vibration device as an example, a kind of piezoelectric effect and inverse piezoelectric effect using material is realized From electric energy to mechanical energy, the energy transmission device of electric energy is reconverted into, it is small, light-weight, simple in structure, and with very high Energy density.But the various losses that piezoelectric transformer generates during the work time can cause Wen Sheng, when the work temperature of piezoelectric device Its piezoelectric property begins to decay before degree reaches Curie temperature;Meanwhile the loss of piezoelectric transformer is with the increase of Wen Sheng It can rapidly increase, form uncontrollable positive feedback effect, lead to piezoelectric device performance rapid attenuation.At present, it has proposed both at home and abroad The contact heat sink conception of piezoelectric transformer, by the way that piezoelectric transformer is directly connect with metal cooling device (such as copper sheet) The problem of touching, improving piezoelectric transformer self-radiating scarce capacity.
For this high-frequency vibration device of piezoelectric transformer, it is in direct contact heat dissipating method and there are problems that.Piezoelectricity transformation Contact between device and metal fin belongs to two rigid interfaces and is in direct contact, due to the influence of surface defect, roughness, contact It can not possibly be bonded completely between face, there are the air gaps, and thermal resistance is big, influence heat dissipation effect.Meanwhile piezoelectric transformer is in work There is the opposite working performance slided, piezoelectric transformer can be influenced between cooling fin in high-frequency vibration state;In addition this high frequency It is opposite to slide the contact fretting wear that cause piezoelectric transformer electrode surface, greatly reduce the service life and property of transformer Energy.Therefore, to carry out contact heat dissipation to vibration device, suitable thermal interfacial material is crucial.
Invention content
The technology of the present invention solves the problems, such as:Overcome the deficiencies of the prior art and provide a kind of vibration based on micro array structure Device is in direct contact heat dissipating method and application, is provided for high-frequency vibration device (can be to hundreds of kHz or even megahertz rank) A kind of elastic microarray contact radiator structure (thermal resistance of low thermal resistance, high thermal conductivity coefficient<0.1cm2K/W, thermal conductivity factor>10W/ m·K)。
The purpose of the present invention is what is be achieved through the following technical solutions:
The vibration device heat dissipating method based on micro array structure of the present invention, using laser ablation, lithography process or change The methods of learning vapor deposition prepares following any micro array structure:
Substrate is rectangle, disc, circular ring shape, triangle and the shapes such as trapezoidal, on the substrate processing vertical arrangement Micro array structure, unit size can be micron order or nanoscale, and material can be carbon nanotube, Huo Zhetong, but not only It is limited to the good metal material of heat conduction of copper.
The above-mentioned micro array structure of the present invention, the contact heat dissipation in working available for vibration devices such as piezoelectric transformers should With.
As seen from the above technical solution provided by the invention, the piezoelectricity provided by the invention based on micro array structure becomes Depressor contacts heat dissipating method and application has the following advantages:
(1) carbon nanotube of the longitudinal arrangement of grown on larger scale first, in the case of array density is suitable, has on longitudinal direction Excellent heat conductivility and the mechanical strength of superelevation.
(2) using processing carbon nano tube microarray in copper sheet substrate, hundred nanometers of single-root carbon nano-tube diameter, hundred microns of height Left and right, so high draw ratio cause there is very strong mechanical compliance as thermal interfacial material using it.When high-frequency vibration When piezoelectric transformer is bonded with micro array structure, due to vibration displacement generally in the micron-scale not, the carbon pipe of high flexibility can generate with It is dynamic so that will not to occur to slide relatively therebetween, eliminate or greatly reduce the fretting wear of piezoelectric device electrode surface, carry High service life.It is servo-actuated under this high flexibility state simultaneously, big damping will not be generated so that microarray radiator structure pair The vibration effect very little of transformer, ensure that working performance.
(3) carbon nano pipe array of micro/nano-scale can very easily fill the gap with piezoelectric transformer contact surface Or defect, it is not high to the surface roughness requirements of transformer, fully ensure that micro array structure and the direct of transformer bay connect Contacting surface is accumulated, and can reduce thermal resistance, heat radiation performance.
(4) the millions of carbon pipes grown in substrate, after being contacted with piezoelectric transformer surface, the model moral of generation Magnificent active force can guarantee that array carbon nanotube is closely contacted with transformer surface-stable, not needed to again in the transformer course of work The additional active force that applies is bonded the two, and radiator structure can be simpler, while reduces additional active force to transformer The influence of energy.
To sum up, in radiator substrate, such as copper sheet or silicon chip, it is close that draw ratio height, array are gone out by grown on larger scale Suitable micro array structure is spent, is not limited to the array structures such as carbon nanotube or copper nano-wire, based on its good heat conduction in longitudinal direction Property and van der Waals interaction and lateral good flexibility, it is unsuitable available for conventional vibration device especially high-frequency vibration device Carry out the occasion of contact heat dissipation.This vibration device thermal management scheme based on micro array structure, good heat conductivity, interface resistance It is low, it is slided without opposite, does not generate contact wear, it is small perpendicular to heat transfer direction flexibility high-damping, it is low to device vibration effect, and Additional active force is not needed on heat transfer direction to be fixed, it is simple in structure, vibration device can be met to a certain extent to heat The demand of management.
Description of the drawings
Fig. 1 a, Fig. 1 b are respectively that substrate provided in an embodiment of the present invention is rectangle, and microarray unit is cylinder, cuboid Microarray radiator structure schematic diagram;
Fig. 2 is Rectangular piezoelectric transformer planar expanded vibration shape schematic diagram in the embodiment of the present invention;
Fig. 3 is that carbon nanotube or copper nano-wire micro array structure are used for piezoelectric transformer planar expanded in the embodiment of the present invention Heat dissipation experiment under operation mode;
Fig. 4 a are heat dissipation experiment of the piezoelectric transformer under three kinds of hot boundary conditions of difference;
Fig. 4 b is under these three different hot boundary conditions, and the temperature of piezoelectric transformer rises experiment knot during same operating power Fruit;
Fig. 5 is piezoelectric ceramic tube torsion vibration mode schematic diagram in the embodiment of the present invention;A shows piezoelectric ceramic tube torsion vibration mode Schematic diagram;B is in circular substrate inner wall, radially grows the schematic diagram of carbon nanotube micro array structure;
Fig. 6 is that micro array structure in the cooling application of other vibration devices, is turned round with piezoelectric ceramic tube in the embodiment of the present invention Rotational oscillation move in radiator structure for, wherein a is to be made pottery using annular distribution microarray thermal interfacial material to the piezoelectricity of twisting vibration Porcelain tube carries out the overall structure figure of contact heat dissipation, and b is the vertical view of structure in a.
Specific embodiment
For high-frequency vibration device, certain Wen Sheng will be generated simply by the presence of loss.When Wen Sheng is reached a certain level It will influence performance and the service life of vibration device.The occasion to be radiated using grease type is not suitable for for some, the present invention carries Go out and contact heat dissipating method is carried out to vibration device using the micro array structure of a kind of high flexibility, low thermal resistance, high thermal conductivity coefficient.
The purpose of the present invention is what is be achieved through the following technical solutions:
The micro array structure of certain distribution density is prepared on metal or silicon chip substrate first, the array is with substrate in vertical In line column distribution, unit size can be micron order or nanoscale, material can be carbon nanotube or copper nano-wire and It is not limited only to the good metal material of other heat conduction of both materials.
The substrate of micro array structure can be planar, can also be in thin circular ring shape, in annulus growth inside perpendicular to table The micro array structure in face.
The above-mentioned micro array structure of the present invention, in can working directly as vibration devices such as piezoelectric transformers in contact heat dissipation Thermal interfacial material.Micro array structure is directly bonded with vibration device, it, should due to the superposition of extensive Van der Waals Structure will be directly adsorbed on device, not need to additionally apply pretightning force.Microarray unit size, can be well in micro-nano rank Cavity or the defect of device surface are filled, reduces thermal contact resistance;The high flexibility of micro array structure will not influence device simultaneously Vibration performance, slided between device without opposite, contact wear will not be generated.It is good to lead as long as array density is suitable Hot property can meet the needs of vibration device opposite heat tube reason to a certain extent.
The above-mentioned vibration device of the present invention, the characteristics of due to micro array structure anisotropy, vibration side when device works To vertical with array element.
Embodiment 1:
For below using carbon nanotube microarray as thermal interfacial material, explain in detail it and work in piezoelectric transformer and radiate In application:
Fig. 1 a show the carbon nanotube micro array structure grown in rectangular silicon piece substrate, and carbon nanotube is in substrate Vertical arrangement distribution, for unit to be cylindric, hundred ran of diameter is highly micron order, and array density leads to 1% or so It crosses laser interferance method and measures its thermal conductivity factor as 10-20W/mK.
Fig. 2 shows Rectangular piezoelectric transformer and its planar expanded vibration shape signals that radiating treatment is carried out in the present embodiment Figure.It is quiet if contact heat dissipation is directly carried out to it using rigid heat sink in high-frequency vibration state in piezoelectric transformer transverse direction There can be opposite slip between radiator and transformer only, influence transformer vibration performance;Contact wear can be generated simultaneously, when Between a long transformer and the wear to electrodes on radiator structure contact surface it is serious, substantially reduce the service life of transformer.
Fig. 3 is the structure diagram of carbon nanotube or copper nano-wire microarray for piezoelectric transformer contact heat dissipation.With carbon For nanotube microarray, piezoelectric transformer is directly contacted with being arranged vertically the carbon nano pipe array fitting of distribution in substrate.Battle array The end size of column unit can fill tiny flaw or the cavity on piezoelectric transformer contact surface well in nanoscale, Reduce contact surface thermal resistance.The millions of carbon pipes grown in substrate after being contacted with piezoelectric transformer surface, generate Model ylid bloom action power can guarantee that array carbon nanotube is closely contacted with transformer surface-stable, is not required in the transformer course of work Additionally to apply active force again is bonded the two, and radiator structure can be simpler.In addition, in the carbon nanotube transverse direction of high length-diameter ratio With very strong mechanical compliance, when the piezoelectric transformer of high-frequency vibration is bonded with micro array structure, due to vibration displacement one As in the micron-scale not, the carbon pipe of high flexibility can generate servo-actuated so that will not occur therebetween it is opposite slide, eliminate or significantly The fretting wear of piezoelectric device electrode surface is reduced, improves service life.It is servo-actuated under this high flexibility state simultaneously, it will not Generate big damping so that microarray radiator structure ensure that working performance to the vibration effect very little of transformer.
Fig. 4 a are that schematic diagram is tested in heat dissipation of the piezoelectric transformer under three kinds of hot boundary conditions of difference.(1) in Fig. 4 a exists It is bonded polypropylene film PP on silicon chip to contact with piezoelectric transformer as thermal interfacial material, is then placed on copper radiator and carries out Heat dissipation;(2) in Fig. 4 a are contacted in grown above silicon carbon nano pipe array as thermal interfacial material with piezoelectric transformer, Ran Houfang It puts and radiates on copper radiator;(3) in Fig. 4 a are directly using polypropylene film PP as thermal interfacial material and piezoelectricity transformation Device contacts, and is then placed on copper radiator and radiates.
Fig. 4 b are piezoelectric transformer under three kinds of hot boundary conditions of difference shown in Fig. 4 a and when being not added with any cooling measure, Under identical driving power its steady operation for a period of time after warm liter situation.As can be seen that when being not added with any cooling measure When, the Wen Sheng of piezoelectric transformer has reached 23 DEG C;When polypropylene film+silicon chip+copper sheet is as contact cooling measure, piezoelectricity becomes The temperature of depressor is upgraded to 13 DEG C;When without silicon chip, direct polypropylene film+copper sheet, which contact, radiates, the temperature of piezoelectric transformer It is upgraded to 10 DEG C;And during using carbon nano pipe array+silicon chip+copper sheet as contact cooling measure, it is only 8 that the temperature of piezoelectric transformer, which rises, ℃。
Embodiment 2:
Carbon nanotube micro array structure cooling application technical solution in column vibrating device:
Figure a in Fig. 5 shows piezoelectric ceramic tube torsion vibration mode schematic diagram.For this circular vibration device, due to not It is conventional plane motion state, is generally inconvenient to carry out radiating management to it.
Figure b in Fig. 5 is in circular substrate inner wall, radially grows the schematic diagram of carbon nanotube micro array structure.Base High-termal conductivity, high flexibility in above-mentioned carbon nano pipe array can reduce contact surface thermal resistance, and without phase in cooling application is contacted To slip, contactless abrasion, therefore available for the thermal management applications of circular vibration device.
Fig. 6 is that the piezoelectric ceramic tube of twisting vibration is connect using the carbon nanotube micro array structure of above-mentioned radial growth Touch the schematic diagram of cooling application.The circular heat dissipating substrate that inner wall, which is radially grown, certain density carbon nano pipe array is sleeved on On the outside of piezoelectric ceramic tube, carbon nano pipe array is in close contact with ceramic tube.The millions of carbon pipes grown in substrate, production Raw model ylid bloom action power can guarantee array carbon nanotube and ceramic tube surface-stable and closely contact, and provide good contact heat dissipation Condition, while do not need in the ceramic tube course of work additionally to apply active force again and be fixed.The carbon nanotube of high length-diameter ratio Along the circumferential direction there is very strong mechanical compliance, and the piezoelectric ceramic tube displacement of high-frequency vibration is generally in the micron-scale, therefore two It will not occur to slide relatively between person, not influence the vibration performance of device, while eliminate or greatly reduce piezoelectric device electricity The fretting wear of pole-face.
Embodiment 3:
For below using copper nano-wire microarray as thermal interfacial material, explain in detail it and work in piezoelectric transformer and radiate In application:
Fig. 1 b show the copper nano-wire microarray processed in rectangle copper sheet substrate by laser ablation or photoetching technique Structure, copper nano-wire perpendicular arranged distribution in substrate, unit are cuboid, and cross sectional dimensions is in hundred rans, height It spends for micron order, array density is 1% or so.
For piezoelectric transformer under planar expanded operation mode, contact heat dissipation is carried out using copper nano-wire micro array structure Embodiment, similary available Fig. 3 represents the radiator structure schematic diagram of the program.Piezoelectric transformer in substrate directly with being arranged vertically The Arrays of Copper Nanowires fitting contact of distribution.The end size of array element can fill piezoelectricity change well in nanoscale Tiny flaw or cavity on depressor contact surface reduce contact surface thermal resistance.High machine is similarly laterally gone up based on Arrays of Copper Nanowires High thermal conductivity coefficient in tool compliance, longitudinal direction, therefore with the contact heat dissipation advantage similar with carbon nano pipe array, neither influence to become The vibration performance of depressor in itself, and thermal losses transfer is carried out well.
In short, the present invention passes through in radiator substrate grown on larger scale draw ratio height, the suitable microarray knot of array density Structure, it is unsuitable available for vibration device based on its good thermal conductivity in longitudinal direction and van der Waals interaction and lateral good flexibility In the occasion for being in direct contact heat dissipation.This vibration device thermal management scheme due to being slided without opposite, does not generate contact wear, hangs down It is directly small in heat transfer direction flexibility high-damping, it is low to device vibration effect, and do not needed on direction of conducting heat additional active force into Row is fixed, simple in structure, can meet the needs of vibration device opposite heat tube reason to a certain extent.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto, Any one skilled in the art is in the technical scope of present disclosure, the change or replacement that can readily occur in, It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with the protection model of claims Subject to enclosing.

Claims (8)

1. a kind of vibration device based on micro array structure is in direct contact heat dissipating method, it is characterised in that:Using raw in substrate Micro array structure that is long or processing certain density is as thermal interfacial material, the directly vibration device to needing progress thermal losses transfer Contact heat dissipation;
Array element of the direction of vibration of the vibration device in micro array structure;
If substrate is planar, the direction of vibration of vibration device is parallel to base plane, and vertical with array element;
If substrate is cylindric or circular, the direction of vibration and substrate circumferencial direction of vibration device are tangent, and and array Unit is vertical.
2. the vibration device according to claim 1 based on micro array structure is in direct contact heat dissipating method, it is characterised in that: Elastic micro array structure as thermal interfacial material has high-termal conductivity, i.e. thermal conductivity factor is higher than 10W/mK, the microarray Array element in structure is the nonmetallic of carbon nanotube, the metal nanometer line either good silicon of other thermal conductivity or silica Micro-nano structure.
3. the vibration device according to claim 2 based on micro array structure is in direct contact heat dissipating method, it is characterised in that: The size of array element in the micro array structure is micro/nano-scale, and the shape of array element is cylinder or cuboid.
4. the vibration device according to claim 1 based on micro array structure is in direct contact heat dissipating method, it is characterised in that: The substrate is that can carry out the heat safe Heat Conduction Material of micro array structure growth and processing, including silicon, silica or copper etc. Metal material.
5. the vibration device based on micro array structure according to claim 1 or 4 is in direct contact heat dissipating method, feature exists In:The shapes of substrates is planar or cylinder, annular shape, described planar including following any shape:Rectangle, disk Shape, circular ring shape, triangle or trapezoidal.
6. the vibration device according to claim 1 based on micro array structure is in direct contact heat dissipating method, it is characterised in that: Carbon nanotube microarray is grown on silicon chip or copper sheet substrate, and the contact under piezoelectric transformer plane vibration mode dissipates Heat;The piezoelectric transformer plane vibration mode include it is following any one or more:Strip vibration mode, radial vibration mould Formula, thickness vibration mode, radiation vibration mode.
7. the vibration device according to claim 1 based on micro array structure is in direct contact heat dissipating method, it is characterised in that: Laser ablation or lithography process copper nano-wire microarray in copper sheet substrate, and under piezoelectric transformer plane vibration mode Contact heat dissipation;The piezoelectric transformer plane vibration mode include it is following any one or more:Strip vibration mode, radial direction Vibration mode, thickness vibration mode, radiation vibration mode.
8. the vibration device according to claim 1 based on micro array structure is in direct contact heat dissipating method, it is characterised in that: In annulus or cylindric substrate inner wall growth carbon nanotube microarray, and for the contact under piezoelectric ceramic tube torsion modes Heat dissipation.
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