CN111415915A - Heat radiation structure of micro-channel radiator - Google Patents

Heat radiation structure of micro-channel radiator Download PDF

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Publication number
CN111415915A
CN111415915A CN202010364369.6A CN202010364369A CN111415915A CN 111415915 A CN111415915 A CN 111415915A CN 202010364369 A CN202010364369 A CN 202010364369A CN 111415915 A CN111415915 A CN 111415915A
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rib plate
plate column
working medium
heat exchange
channel
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CN111415915B (en
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李云
陈曦
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Xian Jiaotong University
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Xian Jiaotong University
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    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01LSEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
    • H01L23/00Details of semiconductor or other solid state devices
    • H01L23/34Arrangements for cooling, heating, ventilating or temperature compensation ; Temperature sensing arrangements
    • H01L23/46Arrangements for cooling, heating, ventilating or temperature compensation ; Temperature sensing arrangements involving the transfer of heat by flowing fluids
    • H01L23/473Arrangements for cooling, heating, ventilating or temperature compensation ; Temperature sensing arrangements involving the transfer of heat by flowing fluids by flowing liquids
    • HELECTRICITY
    • H01ELECTRIC ELEMENTS
    • H01LSEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
    • H01L23/00Details of semiconductor or other solid state devices
    • H01L23/34Arrangements for cooling, heating, ventilating or temperature compensation ; Temperature sensing arrangements
    • H01L23/36Selection of materials, or shaping, to facilitate cooling or heating, e.g. heatsinks
    • H01L23/367Cooling facilitated by shape of device
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02DCLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D10/00Energy efficient computing, e.g. low power processors, power management or thermal management

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Condensed Matter Physics & Semiconductors (AREA)
  • General Physics & Mathematics (AREA)
  • Computer Hardware Design (AREA)
  • Microelectronics & Electronic Packaging (AREA)
  • Power Engineering (AREA)
  • Chemical & Material Sciences (AREA)
  • Materials Engineering (AREA)
  • Cooling Or The Like Of Semiconductors Or Solid State Devices (AREA)
  • Cooling Or The Like Of Electrical Apparatus (AREA)

Abstract

The invention discloses a heat radiation structure of a microchannel radiator, which is characterized in that a plurality of rib plate column units with bottom surfaces being centrosymmetric graphs and two diagonal angle bisectors being collinear and passing through a symmetric center are arrayed on the same substrate plane, a microchannel formed by a plurality of rib plate column units forms a main flow channel of a heat exchange working medium between two adjacent rib plate columns in the Y-axis direction, the fluid meets the vertex angle of a downstream staggered rib plate column unit at the tail end of the main flow channel of the heat exchange working medium, is shunted by the vertex angle and is guided into an inclined secondary channel of the heat exchange working medium, the inclined secondary channel of the heat exchange working medium is used for uniformly shunting the main flow channel of the heat exchange working medium, the stagnation effect of the flow can be effectively reduced, the fluid can be rapidly diffused in the main flow channel of the heat exchange working medium, the flow resistance is reduced, the pressure loss is reduced, the pressure drop is reduced, the rib plate columns in the staggered array can be better and directly contacted with, the heat resistance of convection heat transfer is reduced, thereby improving the whole heat transfer effect.

Description

Heat radiation structure of micro-channel radiator
Technical Field
The invention belongs to the field of heat dissipation of micro-channel radiators, and particularly relates to a heat dissipation structure of a micro-channel radiator.
Background
The development level of high-performance electronic components is improved, the power of the high-performance electronic components is increased, the size of the high-performance electronic components is decreased, the integration level is increased, the power density is increased, and the thermal management of the high-performance electronic components is very important. The power density of the high-performance ultra-large scale integrated circuit can reach 106W/m2. Along with the rise of temperature, the working efficiency, reliability and service life of the electronic deviceAnd rapidly decreases. Excessive temperature (>85 ℃) directly leads to the chip not working normally and burning out. The micro-channel radiator is an effective means for radiating electronic devices developed in recent years, and due to the tiny size, the hydraulic diameter of the channel is smaller than 1mm, the micro-channel radiator has the characteristics of large specific surface area and large comprehensive heat transfer coefficient, and can control the temperature of the high-power density electronic device within a lower temperature range. In order to adapt to super-high power density (-10)6W/m2) In order to further enhance heat exchange, there are some researchers and researchers who design protruding fins or curved channels on the wall surface of the micro-channel, so as to increase the surface area, disturb fluid flow, and increase the convection heat exchange coefficient. These fins, which serve to increase the surface area and disturb the fluid, create additional flow resistance and, in turn, reduce the overall efficiency. For example, in a pin fin micro heat exchanger (the pin fin is in a circular, square or triangular shape, etc.) arranged in parallel or staggered mode, when a flowing space of a heat exchange working medium passes through the pin fin, the flowing sectional area is contracted, and the flowing sectional area is expanded behind the pin fin, fluid flows in the periodically contracted space to form a large amount of disturbance, so that the flowing resistance is greatly increased, although the heat exchange is enhanced to a certain degree, the resistance characteristic of a conventional straight channel is lower, the pump power can be completely improved to be consistent with that of the pin fin micro heat exchanger by improving the pump work, so that the flow of the heat exchange working medium is increased, and the heat exchange is enhanced. Thus, the pin fin micro heat exchanger or other technology micro heat exchangers have a limit to enhanced heat transfer compared to a substantially straight micro channel due to excessive resistance increase. Meanwhile, the excessively high resistance requires a pump with a higher lift in the system, which increases the initial cost and fails to achieve the expected heat dissipation effect.
Disclosure of Invention
The invention aims to provide a micro-channel radiator heat dissipation structure to overcome the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a heat radiation structure of a micro-channel radiator is characterized in that a plane on the other side of a substrate is attached to a heat radiation surface of an electronic device and comprises a plurality of rib plate column units arrayed on the same plane of the substrate, each rib plate column unit is a straight hexagonal prism, the bottom surface of each straight hexagonal prism is a centrosymmetric graph, the angular bisectors of two opposite angles on the bottom surface are collinear and cross a symmetric center, the angular bisectors of the two opposite angles are central lines in the length direction of the bottom surface, the central line direction of the bottom surface, which is perpendicular to the length direction of each rib plate column unit, is the width direction of the bottom surface, the central line in the length direction of; the rib plate column units are arrayed at equal intervals along the Y axis to form a rib plate column unit row, the interval distance between every two adjacent rib plate column units along the Y axis is the same as the width of the rib plate column units, the central line of the rib plate column units in the rib plate column unit row in the length direction is parallel to the X axis, and the diagonal vertex connecting line of the rib plate column units at the same end is vertical to the X axis; the rib plate column unit rows are arrayed at intervals along the X axis, and the rib plate column units in the two adjacent rib plate column unit rows are arranged at equal intervals in the Y axis direction.
Furthermore, a main flow channel of the heat exchange working medium is formed between two adjacent rib plate column units in the same row of rib plate column units, and the hydraulic diameter D of the main flow channel of the heat exchange working mediumhIs 50-500 um.
Furthermore, a heat exchange working medium oblique secondary flow channel is formed between two rib plate column units which are adjacent in the X direction.
Further, the height-diameter ratio H of the rib plate column unitc/DhThe length-diameter ratio of the alloy is 1.5-3, and the length-diameter ratio can be L/Dh=2~4,HcIs the unit height of the rib plate column, DhL is the length of the ribbed plate column unit, which is the hydraulic diameter of the main flow channel of the heat exchange working medium.
Further, the angle bisectors are collinear and the angle of the diagonal passing through the center of symmetry is less than or equal to 45 °.
Furthermore, a hot working medium flowing groove is formed in the substrate, and the rib plate columns are arrayed in the plane of the hot working medium flowing groove.
Furthermore, a cover plate is fixed on one side of the base plate, which is provided with the hot working medium flowing groove, and the cover plate and the base plate are packaged and fixed; the cover plate is provided with a hot working medium inlet and a hot working medium outlet which are connected with an external pipeline.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention relates to a heat radiation structure of a microchannel radiator, which is characterized in that a plurality of rib plate column units are arrayed on the same substrate plane, the bottom surfaces of the rib plate column units are in a central symmetrical pattern, the angular bisectors of two opposite angles on the bottom surfaces are collinear and pass through the symmetrical center, a microchannel formed by a plurality of rib plate column units forms a heat exchange working medium main flow channel between two adjacent rib plate columns in the Y-axis direction, the heat exchange working medium main flow channel and the vertex angle of the rib plate column unit form a heat exchange working medium oblique secondary flow channel, fluid meets the vertex angle of the rib plate column unit staggered at the downstream at the tail end of the heat exchange working medium main flow channel, is divided by the vertex angle and is guided into the heat exchange working medium oblique secondary channel, the heat exchange working medium oblique secondary channel is used for carrying out uniform division and division on the heat exchange working medium main flow channel, the flow stagnation effect, the ribbed plate column units in staggered arrays are better and directly contacted with a cooler working medium in a main flow area to generate heat exchange, so that the heat resistance of convective heat transfer is reduced, and the overall heat transfer effect is improved.
Further, the height-diameter ratio H of the rib plate column unitc/DhThe length-diameter ratio of the alloy is 1.5-3, and the length-diameter ratio can be L/D h2 ~ 4, the fluid resistance is little when the oblique secondary passage of heat transfer working medium shunts, and the dispersion is even.
Drawings
Fig. 1 is a schematic structural diagram of an array of rib pillar units in an embodiment of the present invention.
Fig. 2 is a cross-sectional view of a rib post unit in an embodiment of the present invention.
Fig. 3 is a top view of a rib post unit in an embodiment of the present invention.
FIG. 4 is a schematic diagram of a heat exchange working medium channel structure in the embodiment of the present invention.
Fig. 5 is a top cross-sectional view of an array of rib post units in an embodiment of the invention.
Fig. 6 is a schematic diagram of a substrate package structure according to an embodiment of the invention.
Wherein, 1, a cover plate; 2. a substrate; 3. a heat exchange working medium inlet; 4. a heat exchange working medium outlet; 5. a rib post unit.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
as shown in fig. 1, the heat dissipation structure of a micro-channel heat sink of the present invention includes a plurality of rib plate column units 5 arrayed on the same plane of a substrate 2, a plane on the other side of the substrate 2 is attached to a heat dissipation surface of an electronic device, the rib plate column units 5 are straight hexagonal prisms, bottom surfaces of the straight hexagonal prisms are centrosymmetric patterns, angular bisectors of two opposite angles on the bottom surfaces are collinear and cross a symmetric center, the angular bisectors of the two opposite angles are central lines in a length direction of the bottom surfaces, that is, the central lines in the length direction of the rib plate column units 5, a direction of the bottom surface perpendicular to the central line in the length direction of the rib plate column units 5 is a width direction of the bottom surface, the central; the rib plate column units 5 are arrayed at equal intervals along the Y axis to form a rib plate column unit row, the interval distance between every two adjacent rib plate column units 5 along the Y axis is the same as the width of the rib plate column unit 5, the middle line of the rib plate column units 5 in the rib plate column unit row in the length direction is parallel to the X axis, and the connecting line of the diagonal vertexes of the rib plate column units 5 at the same end is vertical to the X axis; the rib plate column unit rows are arrayed at zero intervals along the X axis, namely the interval distance between adjacent rib plate column unit rows along the X axis is zero; the rib plate column units 5 in two adjacent rib plate column unit rows are arranged at equal intervals in the Y-axis direction, namely the middle line of the rib plate column unit 5 in one rib plate column unit row is collinear with the middle line of the middle lines of the rib plate column units 5 in the two adjacent rib plate column unit rows;
specifically, as shown in fig. 2 and 3, the bottom surface of the straight hexagonal prism is formed by splicing two congruent isosceles trapezoid long bottom edges, the two congruent isosceles trapezoid long bottom edges are the central line in the length direction of the bottom surface of the straight hexagonal prism, the height of the two congruent isosceles trapezoids and the width of the bottom surface of the straight hexagonal prism are the width of the rib plate column unit 5, and the length of the isosceles trapezoid long bottom edge is the length of the bottom surface of the straight hexagonal prism and is the length of the rib plate column unit 5; the length direction of the long bottom side of the isosceles trapezoid is taken as the X direction, the height direction of the isosceles trapezoid is taken as the Y direction, and the height of the ribbed slab column unit 5 is taken as the Z direction; the rib plate column units 5 are arrayed at equal intervals in the Y direction to form a rib plate column unit row, the central line of the length direction of the bottom surface of each rib plate column unit 5 in the rib plate column unit row is parallel to the X axis, and vertex angles at two ends of each rib plate column unit 5 in the rib plate column unit row are aligned; the rib plate column unit rows are staggered in the X direction at zero intervals, namely the end faces of the adjacent ends of the two adjacent rib plate column unit rows are in the same plane, and in the X direction, the central line of the length direction of the bottom surface of each rib plate column unit 5 is collinear with the central line of the length direction of the bottom surface of each two adjacent rib plate column units 5 in the adjacent rib plate column unit row.
The interval width of the adjacent rib post units 5 in the Y direction is the same as the width of the rib post unit 5.
As shown in fig. 4 and 5, a main flow channel of the heat exchange working medium is formed between two adjacent rib plate column units 5 in the same rib plate column unit row, and the hydraulic diameter D of the main flow channel of the heat exchange working mediumhThe diameter of the heat exchange working medium is 50-500 mu m, the hydraulic diameter of a main flow channel of the heat working medium is selected according to radiators of different types, and an oblique secondary flow channel of the heat exchange working medium is formed between two rib plate column units 5 adjacent to each other in the X direction. As shown in FIG. 2, the substrate 2 has a thickness HsThe height of the rib plate column unit 5 is HcThe total height of the base plate 2 and the ribbed plate column unit 5 is H; i.e. the original machined plate height. The rib plate column units 5 and the substrate 2 can be integrally formed in 3D, in three-dimensional drawing software, the rib plate column units 5 are formed by drawing a cross-sectional structure of one rib plate column unit 5, scanning the cross-sectional structure in the Z direction, and the rib plate column units 5 are arrayed in the X direction and the Y direction to form a heat sink heat dissipation structure. Or etching a main flow channel and an oblique secondary flow channel on the substrate by adopting an ion etching method, and simultaneously forming the structure of the rib plate column unit 5.
As shown in fig. 2 and 3, one of the rib plate column units 5 has a length of L and a width of WrHeight of Hc(ii) a Two angles (namely, the diagonal angles with the angle bisectors collinear and passing through the symmetrical center) of the rib plate column unit 5 at two ends along the length direction are divided into a front edge angle and a rear edge angle, and the front edge angle and the rear edge angle are theta; a main flow channel of the heat exchange working medium is formed between two adjacent ribbed plate columns in the Y direction, an oblique secondary flow channel of the heat exchange working medium is formed between two adjacent ribbed plate columns in the X direction, and the vertex (the vertex of the front edge or the vertex of the rear edge) of the end part in the length direction of the ribbed plate column unit 5 is positioned at the main flow channelGaps of the rib plate column units 5 arrayed in the Y direction form regular and ordered heat exchange working medium channels in the middle of the flow channels, and heat exchange working media can flow in order in the regular and ordered heat exchange working medium channels. The width of the main flow channel is WcAnd is the same as the width Wr of the rib post unit 5. Height-diameter ratio H of rib plate column unit 5c/DhThe length-diameter ratio of the alloy is 1.5-3, and the length-diameter ratio can be L/DhThe leading edge angle and the trailing edge angle theta are less than or equal to 45 degrees.
As shown in fig. 6, the other side of the region of the substrate where the rib post unit 5 is disposed completely covers the heat dissipation surface of the electronic device, so as to achieve the maximum heat dissipation effect. A hot working medium flowing groove is formed in the base plate 2, the rib plate column units 5 are arrayed in the plane of the hot working medium flowing groove, a cover plate 1 is fixed on one side of the base plate 2, where the hot working medium flowing groove is formed, and the cover plate 1 and the base plate 2 are fixedly packaged; the cover plate 1 is provided with a hot working medium inlet 3 and a hot working medium outlet 4, and the hot working medium inlet 3 and the hot working medium outlet 4 are connected with an external pipeline; the heat exchange working medium enters the hot working medium flowing groove of the base plate 2 through the hot working medium inlet 3 and flows into the microchannel formed by the ribbed plate column unit 5, the heat conduction efficiency between the substrate 2 and the heat dissipation surface of the electronic device is improved by utilizing the slotted thin surface side of the substrate 2, the heat generated by the electronic device is absorbed, the heat exchange is carried out between the surface of the ribbed plate column unit 5 and a hot working medium, in the microchannel formed by the ribbed plate columns, fluid meets the front edge vertex angle of the ribbed plate column unit 5 staggered at the downstream at the tail end of the main flow channel, is shunted by the front edge vertex angle and is guided into the oblique secondary channel, the triangular front edge of the front edge vertex angle can effectively reduce the flow stagnation effect, two sides of the triangle can play a good role in diversion, flow separation is avoided, flow resistance is reduced, the heat exchange working medium flowing out of the oblique secondary flow channel and the fluid of the adjacent oblique secondary flow channel are mixed and flow into the next main flow channel, the operation is repeated, and the heat exchange is finished and the fluid finally leaves the micro radiator. The overall geometry and size of the substrate package can be determined according to the size of the electronic device and the overall package requirement; the cooling device is mainly suitable for cooling the strip-shaped or square heating surface with a plane; the heat exchange working medium can be selected from deionized water, acetone, methanol, refrigerant (such as FC-72) and other insulating fluids.
Example (b):
for an area of 10mm × 10mm, workRate density of 106w/m2The total length of the channel region is 10mm, the length L of a single rib plate column is 0.5mm, the leading edge angle and the trailing edge angle theta of two ends of the rib plate column are 45 degrees, and the width W of the rib plate columnrAnd the width W of the main flow channelcAll are 0.15mm, the thickness Hs of the base plate is 0.1mm, and the height of the rib plate column is 0.3 mm. The hydraulic diameter of the formed channel is 200um, the characteristic length of the hydraulic radius of the channel is taken as Re being 500, namely the average flow speed in the channel is 2.512 m/s. The heat exchange working medium is deionized water, and the inlet temperature is 300K. Through numerical simulation, the average Nu of the micro-channel based on the heat exchange area is 21.5, the total pressure drop is 42kPa, the pressure drop in the channel per unit length is 4.2kPa/mm, and the highest temperature of the substrate is only 38 ℃. The hexagonal rib plate column can play a good role in guiding flow, and can reduce excessive disturbance in the flow of the conventional staggered circular or square pin rib micro radiator, thereby reducing pressure loss and pressure drop. The rib plate columns in staggered arrays can be in better direct contact with a cold working medium in a main flow area to generate heat exchange, and the heat resistance of convective heat transfer is reduced, so that the overall heat transfer effect is improved.

Claims (6)

1. A micro-channel radiator heat dissipation structure is characterized by comprising a plurality of rib plate column units (5) arrayed on the same side plane of a substrate (2), wherein the other side plane of the substrate (2) is attached to a heat dissipation surface of an electronic device, the rib plate column units (5) are straight hexagonal prisms, the bottom surfaces of the straight hexagonal prisms are centrosymmetric patterns, the angular bisectors of two opposite angles on the bottom surfaces are collinear and cross a symmetric center, the angular bisectors of the two opposite angles are central lines in the length direction of the bottom surfaces, the direction of the bottom surfaces, which is perpendicular to the central line direction in the length direction of the rib plate column units (5), is the width direction of the bottom surfaces, the central line in the length direction of the bottom surfaces is an X; the rib plate column units (5) are arrayed at equal intervals along the Y axis to form a rib plate column unit row, the interval distance between every two adjacent rib plate column units (5) along the Y axis is the same as the width of the rib plate column unit (5), the central line of the rib plate column unit (5) in the rib plate column unit row in the length direction is parallel to the X axis, and the diagonal vertex connecting line of the rib plate column unit (5) at the same end is vertical to the X axis; the rib plate column units are arrayed in a zero-interval mode along an X axis, rib plate column units (5) in two adjacent rib plate column unit rows are arranged at equal intervals in a Y axis direction, a heat exchange working medium main flow channel is formed between two adjacent rib plate column units (5) in the same rib plate column unit row, and a heat exchange working medium oblique secondary flow channel is formed between two adjacent rib plate column units (5) in the X direction.
2. The heat dissipating structure of a microchannel heat sink as recited in claim 1, wherein the main flow channel of the heat exchange medium has a hydraulic diameter DhIs 50-500 um.
3. The heat dissipating structure of a micro-channel heat sink as claimed in claim 2, wherein the height to diameter ratio H of the rib pillar unitsc/DhThe length-diameter ratio of the alloy is 1.5-3, and the length-diameter ratio can be L/Dh=2~4,HcIs the rib post unit height, L is the length of the rib post unit.
4. The heat dissipating structure of a microchannel heat sink of claim 1, wherein the bisectors of the angles are collinear and the angle across the diagonal of the center of symmetry is equal to or less than 45 °.
5. The heat dissipation structure of a micro-channel heat sink as recited in claim 1, wherein the substrate (2) is formed with a thermal working fluid flow groove, and the rib plate columns are arrayed in a plane of the thermal working fluid flow groove.
6. The heat dissipation structure of a micro-channel heat sink according to claim 1, wherein a cover plate (1) is fixed on one side of the substrate (2) where the hot working medium flowing groove is formed, and the cover plate (1) and the substrate (2) are fixed in a sealing manner; the cover plate (1) is provided with a hot working medium inlet (3) and a hot working medium outlet (4), and the hot working medium inlet (3) and the hot working medium outlet (4) are connected with an external pipeline.
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Cited By (6)

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CN112888264A (en) * 2021-02-02 2021-06-01 西安交通大学 Double-deck microchannel heat abstractor based on gas-liquid separation
CN113380283A (en) * 2021-06-09 2021-09-10 西安交通大学 M2 solid state disk heat dissipation subsides
CN113543600A (en) * 2021-07-21 2021-10-22 中国石油大学(华东) Incomplete filling staggered micro-channel heat exchanger
CN114390869A (en) * 2022-01-17 2022-04-22 广州大学 One-way heat transfer heat pipe with Y-shaped diversion table liquid absorption core and processing method thereof
CN115332939A (en) * 2022-10-13 2022-11-11 合肥圣达电子科技实业有限公司 High-power fiber laser packaging shell with heat dissipation channel
CN117133733A (en) * 2023-10-26 2023-11-28 国网经济技术研究院有限公司 Water-cooling radiator with high heat dissipation performance and design method thereof

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Publication number Priority date Publication date Assignee Title
CN112888264A (en) * 2021-02-02 2021-06-01 西安交通大学 Double-deck microchannel heat abstractor based on gas-liquid separation
CN113380283A (en) * 2021-06-09 2021-09-10 西安交通大学 M2 solid state disk heat dissipation subsides
CN113543600A (en) * 2021-07-21 2021-10-22 中国石油大学(华东) Incomplete filling staggered micro-channel heat exchanger
CN114390869A (en) * 2022-01-17 2022-04-22 广州大学 One-way heat transfer heat pipe with Y-shaped diversion table liquid absorption core and processing method thereof
CN114390869B (en) * 2022-01-17 2023-09-08 广州大学 Unidirectional heat transfer pipe with Y-shaped diversion table liquid suction core and processing method thereof
CN115332939A (en) * 2022-10-13 2022-11-11 合肥圣达电子科技实业有限公司 High-power fiber laser packaging shell with heat dissipation channel
CN117133733A (en) * 2023-10-26 2023-11-28 国网经济技术研究院有限公司 Water-cooling radiator with high heat dissipation performance and design method thereof

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