EP1664655B1 - Changeur thermique - Google Patents

Changeur thermique Download PDF

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Publication number
EP1664655B1
EP1664655B1 EP04763801A EP04763801A EP1664655B1 EP 1664655 B1 EP1664655 B1 EP 1664655B1 EP 04763801 A EP04763801 A EP 04763801A EP 04763801 A EP04763801 A EP 04763801A EP 1664655 B1 EP1664655 B1 EP 1664655B1
Authority
EP
European Patent Office
Prior art keywords
fluid
heat exchanger
flow
corrugated
flat tubes
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Not-in-force
Application number
EP04763801A
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German (de)
English (en)
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EP1664655A1 (fr
Inventor
Gerrit WÖLK
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Mahle Behr GmbH and Co KG
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Behr GmbH and Co KG
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Application filed by Behr GmbH and Co KG filed Critical Behr GmbH and Co KG
Publication of EP1664655A1 publication Critical patent/EP1664655A1/fr
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Publication of EP1664655B1 publication Critical patent/EP1664655B1/fr
Not-in-force legal-status Critical Current
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Classifications

    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F28HEAT EXCHANGE IN GENERAL
    • F28FDETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
    • F28F1/00Tubular elements; Assemblies of tubular elements
    • F28F1/10Tubular elements and assemblies thereof with means for increasing heat-transfer area, e.g. with fins, with projections, with recesses
    • F28F1/12Tubular elements and assemblies thereof with means for increasing heat-transfer area, e.g. with fins, with projections, with recesses the means being only outside the tubular element
    • F28F1/126Tubular elements and assemblies thereof with means for increasing heat-transfer area, e.g. with fins, with projections, with recesses the means being only outside the tubular element consisting of zig-zag shaped fins
    • F28F1/128Fins with openings, e.g. louvered fins

Definitions

  • the invention relates to a heat exchanger, in particular for motor vehicles.
  • Such a heat exchanger can be designed, for example, as an integrated heat exchanger with a condenser of an air conditioning system and a coolant radiator for motor vehicles.
  • the heat exchanger usually has a number of juxtaposed, parallel to each other extending flat tubes in several rows. In these rows of flat tubes flow first fluids, in the above example, a refrigerant and a coolant.
  • the flat tubes are connected to manifolds and manifolds and exposed to the flow of a second fluid, such as ambient air, to effect heat transfer between the fluids. Between the individual, spaced-apart flat tubes flow paths for the second fluid are formed.
  • Another heat exchanger with cooling fins is for example from the US 4,676,304 known.
  • the cooling fins are substantially parallel to the flow direction of the second fluid (here: air).
  • the second fluid here: air
  • This problem is particularly significant when the heat exchanger in the direction of flow of the second fluid has small dimensions. In this case, a high mass flow rate of the second fluid does not necessarily cause a high heat transfer performance.
  • the available temperature difference between the first and the second fluid is used only to a relatively small extent.
  • the invention has for its object to provide a heat exchanger of the type mentioned with cooling fins, which are designed streamlined and at the same time reduce a thermal coupling between a plurality of first fluids.
  • a heat exchanger having the features of claim 1.
  • the heat exchanger of first fluids through flowable flat tubes, which are arranged in at least two rows, and the outside are acted upon by a second fluid and substantially transversely to the flow direction of Second fluid are arranged parallel to each other such that flow paths are formed for the second fluid, in which cooling fins are arranged, each extending between adjacent flat tubes.
  • the cooling fins are in this case formed as corrugated fins, wherein a plurality of corrugated fins are arranged one behind the other in the flow direction of the second fluid and these laterally, that are offset in the flow direction of the first fluid to each other.
  • a very high proportion of the second fluid flowing through the heat exchanger is used for heat transfer.
  • an overall higher mass flow of the second fluid flows through gills located in the area of the second fluid downstream side of a rib than without the offset between the corrugated fins. This may cause increased heat transfer performance in this area.
  • a temperature boundary layer which optionally forms on a pipe wall, influenced, so that under certain circumstances, a heat transfer from the pipe wall to the second fluid or vice versa is increased.
  • corrugated fins Due to the staggered arrangement of the corrugated fins is at the same time an undesirable heat transfer between different rows of tubes on the corrugated fins reduced, although the ribs are formed from a common band. This is in turn advantageous in production terms, since several successively arranged, formed from a common band, that is integral corrugated fins are easy to insert between the rows of tubes of the heat exchanger.
  • the corrugated ribs including the gills are in particular produced by rolling from a metal strip.
  • a streamlined design of the corrugated fins is preferably achieved in that their surfaces are substantially parallel to the flow direction of the second fluid, i. the surface normals of the corrugated fins are substantially at right angles to the flow direction of the second fluid.
  • the aerodynamic design of the corrugated fins is ensured by the lateral offset successively arranged corrugated fins that only a smaller proportion of the second fluid unused, i. without appreciable heat transfer, flows between the flat tubes than without such an offset.
  • This advantage is more pronounced the higher the rib spacing b between two ribs.
  • two or three similarly shaped corrugated ribs are offset from each other in succession.
  • the individual corrugated fins are preferably directly adjacent to each other, i. arranged without a distance in the flow direction of the second fluid. As a result, a large heat exchanger surface is given.
  • a spaced arrangement of the narrower in this case corrugated fins be provided.
  • the corrugated fins also have gills for guiding the second fluid.
  • gills for guiding the second fluid.
  • all the gills of a rib section enclosed between two flat tubes of a corrugated fin are inclined in the same direction with respect to the flow direction of the second fluid.
  • a similar inclination of the gills within a rib section has the advantage that, if appropriate, the flow can be directed to a downstream rib section.
  • the gills offset successively arranged rib portions are oppositely inclined, so that the heat exchanger through the flowing second fluid is given a longer flow path.
  • the gills of two adjacent gill panels can also be placed obliquely in the same direction, it may then be advantageous if the gills of the two adjacent gill panels upstream or downstream gills are inclined in opposite directions to the gills of the two adjacent gill panels.
  • Uniform coverage of the flow cross-section through which the second fluid flows is preferably achieved by displaced rib sections arranged one behind the other running parallel to one another.
  • the mutually offset rib sections are preferably perpendicular to the flat tubes. If the rib surfaces deviate slightly (up to about 6 degrees) from the parallelism, in which case they are still to be regarded as substantially parallel in the context of the invention, the thermodynamic advantages of the mutually offset ribs are scarcely impaired as a result. Likewise, the use of so-called V-ribs or even arbitrarily rounded ribs is conceivable.
  • the rib geometry according to the invention is particularly applicable to automotive heat exchangers such as coolant radiators, radiators, condensers and evaporators.
  • the depth Kiement LP LP in the range of 0.7 to 3 mm at a gill angle of 20 to 30 degrees performance, because thereby the flow angle, i. the deflection of the second fluid is increased from one channel to the adjacent, which in turn results in a longer flow path for the second fluid.
  • the rib height for such a system is advantageously in the range of 4 to 12 mm.
  • the rib density for this system is advantageously in the range of 40 to 85 Ri / dm, which corresponds to a rib spacing or a rib pitch of 1.18 to 2.5 mm.
  • the Fig. 1 a, 1 b and 2a, 2b show a detail of a heat exchanger 1 with parallel arranged flat tubes 2, which are flowed through by a first fluid FL1a in a first flow direction S1.
  • the flat tubes 2 are equipped with flow guide 2a and connected to (not shown) manifolds or manifolds.
  • the fluid FL1a is for example a cooling liquid or a refrigerant condensing in the heat exchanger 1.
  • Corrugated fins 3 arranged as cooling fins. Embodiments with a higher number of corrugated fins 3 are also feasible.
  • the corrugated fins 3 are meander-shaped bent from a metal sheet, with each one adjacent to a flat tube 2 rib section 4a with a two adjacent flat tubes 2 connecting rib section 4b alternates.
  • the voltage applied to the flat tubes 2 rib portions 4a are thermally conductively connected to the flat tubes 2, in particular soldered.
  • the two adjacent flat tubes 2 connecting rib sections 4b are perpendicular to the flat tubes 2 and form flow paths for a second fluid FL2, for example, air, which flows through the heat exchanger 1 in the flow direction S2.
  • the second fluid FL2 flows substantially parallel to the surface 5 of the corrugated fins 3, ie, the second fluid FL2 initially encounters only the narrow end faces 6 of the corrugated fins 3 when flowing into the heat exchanger 1.
  • the second fluid FL2 can thereby heat exchanger 1 at high speed and flow through correspondingly high mass flow rate.
  • Two corrugated fins 3 arranged one behind the other between two flat tubes 2 are offset from one another by half the width b between adjacent fin sections 4b.
  • an offset of b / 3 can also be selected, wherein other values for the offset are also conceivable.
  • Two or three adjacent corrugated fins 3, which extend across the depth T of the heat exchanger 1, are produced by rolling from a belt 8.
  • the band 8 is in the range of the respective offset between the two ( Fig. 1a, 1b . Fig. 3 ) or three ( Fig. 2a, 2b . Fig. 4 )
  • Corrugated ribs 3 cut and cut the gills 7 in the corrugated fins 3.
  • Offset or higher-order offset ( Fig. 5e, 5f, 5g ) of the corrugated fins 3 is alternatively produced by the same type of separate corrugated fins 3 are arranged with an offset between 0.1 mm and b / 2, where b is the distance between two adjacent flat tubes 2.
  • FIG. 5d is disturbed by the downstream of the flow direction S2 corrugated fin 3, so that an increase in the temperature gradient is generated, which causes an increase in the heat transfer.
  • a heat exchanger 1 with a shallow depth T of, for example, 12 to 20 mm, a highly effective heat transfer between the second fluid FL2 and the first fluid FL1 a is given.
  • Fig. 5 shows corrugated fins 10a, b .., l, each with a plurality of gill fields in cross-sectional view.
  • cooling fins with flow-guiding lamellae (gills) in the individual fins is usually a rib between two tubes in the main flow direction of the second fluid exclusively in a plane without offset ( Fig. 5a, 5b ).
  • These cooling fins have at least two so-called gill panels 11, 12 and 13, 14, which are separated by a web of different design.
  • the orientation of the flow-conducting lamellae (gills) of adjacent gill fields is usually in opposite directions.
  • corrugated fins can also two, three or more similarly shaped corrugated fins (cooling fins) offset from each other to be arranged one behind the other, ie, the one corrugated fin with flow-conducting fins (gills) can be offset in several planes to each other.
  • the number of corrugated fins, which are arranged one behind the other viewed in the direction of flow of the second fluid, depending on the depth of the heat exchanger and / or the depth of the corrugated fins are selected.
  • 2, 3 or more rows can be used; for example, 2, 3, 4 or more rows can be used for a depth of up to 24 mm; for example, 2, 3 can be used for a depth of up to 30 mm , 4, 5 or more rows are used, with a construction depth of up to 36 mm, for example, 2, 3, 4, 5, 6 or more rows can be used, with a construction depth of up to 42 mm, for example, 2, 3, 4, 5, 6, 7 or more rows can be used, with a depth up to 48 mm, for example, 2, 3, 4, 5, 6, 7, 8 or more rows can be used, with a depth
  • 2, 3, 4, 5, 6, 7, 8, 9 or more rows can be used up to 54 mm, for example 2, 3, 4, 5, 6, 7, 8, 9, for a construction depth of up to 60 mm, 10 or more rows are used, with a depth up to 66 mm, for example, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or more rows can be used.
  • An embodiment for 2 rows 15 and 16 shows Fig. 5c in a cross-sectional view.
  • FIG. 5d An embodiment for 3 rows 17, 18 and 19 shows Fig. 5d in a cross-sectional view.
  • An embodiment for 4 rows 20, 21, 22 and 23 shows Fig. 5e in a cross-sectional view.
  • An embodiment for 5 rows 24, 25, 26, 27 and 28 shows Fig. 5f in a cross-sectional view.
  • An embodiment for 5 rows 29, 30, 31, 32 and 33 shows Fig. 5g in a cross-sectional view.
  • An embodiment for 5 rows 34, 35, 36, 37 and 38 shows Fig. 5h in a cross-sectional view.
  • More than two mutually offset rows can preferably be distributed over a total of two mutually offset planes as in the embodiments in the Figures 5d, 5e and 5g , But they can also be distributed on three or more different levels as in the embodiments in the Figures 5f and 5h , where the distances between each two levels may be the same or different.
  • the corrugated rib 10i or 10j has no gill. This embodiment also causes an influence of the temperature boundary layer on the tube walls and / or an improved flow through the lamellae.
  • the gill panels 45, 46, 47 of the corrugated fin 10k may be different in size ( Fig. 5k ).
  • an assignment of the gill panels 45, 46 of a first row of tubes and the gill panel 47 of a second row of tubes advantageous because the displacement 49 between the gill panels 46 and 47, a thermal connection between the rows of tubes is suppressed.
  • a combination of different sized gill fields 65, 66, 67, 68, 69 in different planes is possible as in the corrugated fin 10l ( Fig. 5l ).
  • the number of gills per row is for example between 2 and 30 gills depending on the number of rows and the depth of the heat exchanger.
  • the number of gills per gill field from an engineering point of view in odd number of rows that is not identical at 3, 5, 7, 9 or 11 rows.
  • the number of gills per gill panel can be identical, but this is not necessary.
  • a corrugated fin in a row i. E. without offset, consisting of a row with two gill panels, which are separated by a ridge in the form of a roof, considered (prior art).
  • a corrugated fin with 2 rows and a corrugated fin with 3 rows is considered.
  • the simulation determines the mass flow through the individual fin openings as well as the radiation power from the pipe to the cooling air.
  • Fig. 6 shows the flow field of the air at an air inlet velocity v air of 3 m / s in a heat exchanger 51 with corrugated fins 52, 53 under the boundary conditions described above in the area between two gill fields 54, 55 and 56, 57.
  • the webs 58 and 59 between two Gill fields here have a roof shape.
  • the arrows 60 show the main flow path of the air particles, which flow through the last fin opening 61 in front of the web 59, then undergo a flow deflection and flow through the fin openings 62, 63 in the adjacent gill field 57.
  • the figure shows that only the second slat opening 62 of the gill field 57 is again flowed through by a larger number of air particles, whereby only the speed field through the third slat opening 63 corresponds approximately to the Geschwindkeitstruck in the previous gill field 56 again.
  • Fig. 7 shows the flow field of the air at an air inlet velocity v air of 3 m / s in a heat exchanger 71 with corrugated fins 72, 73 under the The boundary conditions described above in the region of a displacement point 74 or 75 between two gill arrays 76, 77 and 78, 79.
  • the arrows 80 show the main flow path of the air particles before the offset 75, on the one hand through the last slat opening 81 before the offset and on the other by the Displacement opening 75.
  • the air particles undergo a flow deflection after the flow through the offset opening 75, wherein the air particles which flow through the offset opening, then flow mainly through the first and second fin opening 82, 83 of the adjacent gill field 79.
  • FIG. 8 shows the percentage air mass flow in the two corrugated fin configurations with two or three rows (one or two offset points) always above 9%, whereas in corrugated fins in a plane / row of air mass flow at the two fin openings following the land area below 8% with a minimum of about 4% drops. If the air mass flow in the corrugated rib consisting of a plane in the Lammellenö réelle before the land area of about 12% to about 10%, then decreases in the corrugated rib consisting of two Plains / rows here the mass flow through the last slat opening in front of the offset point of about 12 to about 13%.
  • FIG. 9 shows the percentage air mass flow in the two corrugated fin configurations with two or three rows (one or two offset points) always above 12%, whereas in corrugated ribs in a plane / row of air mass flow at the two lamellar openings subsequent to the land area under 11% with a minimum of about 4.5%. If the air mass flow at the corrugated rib consisting of a plane in the Lammellenö réelle before the web area of about 16.5% drops to about 15%; Thus, in the corrugated rib consisting of two levels / rows here increases the mass flow through the last slat opening in front of the offset point of about 16.5 to about 18%.
  • the Fig. 10a, b and 11a, b each show a detail of a heat exchanger 1 according to the invention with in two rows 1a, b arranged parallel to each other flat tubes 2, which are flowed through by first fluids FL1a, b in a first flow direction S1.
  • the flat tubes 2 are connected to (not shown) manifolds or manifolds.
  • the fluids FL1a, b are, for example, a cooling liquid and a refrigerant condensing in the heat exchanger 1. It may as well be two identical fluids within a two- or more-row heat exchanger 1.
  • Corrugated fins 3 arranged as cooling fins. Embodiments with a higher number of corrugated fins 3 are also feasible.
  • the corrugated fins 3 are meander-shaped bent from a metal sheet, with each one adjacent to a flat tube 2 rib section 4a with a two adjacent flat tubes 2 connecting rib section 4b alternates.
  • the voltage applied to the flat tubes 2 rib portions 4a are thermally conductively connected to the flat tubes 2, in particular soldered.
  • the two adjacent flat tubes 2 connecting rib sections 4b are perpendicular to the flat tubes 2 and form flow paths for a second fluid FL2, for example, air, which flows through the heat exchanger 1 in the flow direction S2.
  • the second fluid FL2 flows substantially parallel to the surface of the corrugated fins 3, ie, the second fluid FL2 strikes when entering the heat exchanger 1 initially only on the narrow end faces 6 of the corrugated fins 3.
  • the second fluid FL2 can thereby the heat exchanger 1 at high speed and flow through correspondingly high mass flow rate.
  • Gills 7 are formed out of the rib sections 4b and extend transversely to the flow direction S2 of the second fluid FL2 and transversely to the flow direction S1 of the first fluids FL1a, b.
  • the gills 7 Within a rib section 4b, on the one hand, a particularly good heat transfer between the second fluid FL2 and this rib section 4b, on the other hand, a targeted conduction of the second fluid FL2 to the rib section 4b arranged obliquely behind in the flow direction S2. In this way, the mass flow of the second fluid FL2 flowing through the heat exchanger 1 is almost completely utilized with high utilization of the temperature difference between the first fluids FL1a, b and the second fluid FL2 for heat transfer.
  • the corrugated fins 3 are offset from each other. Because of the one-piece design, the corrugated fins 3 of different rows of tubes are connected to one another via narrow webs 9a in the region of the rib sections 4a resting against the flat tubes 2. Since these webs 9a represent the only heat-conducting connection between the rows of tubes 1a, b, heat transfer from one row of tubes to the other is effectively suppressed.

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  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Geometry (AREA)
  • Thermal Sciences (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Heat-Exchange Devices With Radiators And Conduit Assemblies (AREA)
  • Power Steering Mechanism (AREA)
  • Compression-Type Refrigeration Machines With Reversible Cycles (AREA)
  • Separation By Low-Temperature Treatments (AREA)

Claims (9)

  1. Echangeur de chaleur, en particulier pour des véhicules automobiles, comprenant des tubes plats (2) qui peuvent être traversés intérieurement par des premiers fluides (FL1a, FL1b), tubes plats qui peuvent être sollicités extérieurement par un deuxième fluide (FL2) et qui sont disposés sensiblement de façon transversale par rapport à la direction d'écoulement (S2) du deuxième fluide (FL2) et parallèlement entre eux dans au moins deux rangées, où au moins une rangée de tubes est affectée à chaque premier fluide, où les tubes plats d'une rangée de tubes sont espacés les uns des autres et forment ici, pour le deuxième fluide (FL2), des trajets d'écoulement traversant l'échangeur de chaleur, où des ailettes de refroidissement sont disposées dans les trajets d'écoulement, ailettes de refroidissement qui s'étendent à chaque fois entre des tubes plats voisins (2) où, comme ailettes de refroidissement, il est prévu plusieurs ailettes ondulées (3) disposées les unes derrière les autres dans la direction d'écoulement (S2) du deuxième fluide (FL2), ailettes ondulées qui, dans une zone intermédiaire (9), sont décalées latéralement les unes par rapport aux autres, entre les rangées de tubes, et où plusieurs ailettes ondulées (3) disposées les unes derrière les autres sont formées par une bande commune (8), où les ailettes ondulées (3) disposées les unes derrière les autres présentent des ouïes (7) servant à la direction du deuxième fluide (FL2),
    caractérisé en ce que les ouïes (7) de deux parties d'ailettes (4b) disposées l'une derrière l'autre, de façon décalée, sont placées de manière oblique et en sens inverse.
  2. Echangeur de chaleur selon la revendication 1,
    caractérisé en ce que les surfaces (5) des ailettes ondulées (3) sont disposées sensiblement de façon parallèle à la direction d'écoulement (S2) du deuxième fluide (FL2).
  3. Echangeur de chaleur selon la revendication 1 ou 2,
    caractérisé en ce que plusieurs ailettes ondulées (3) disposées de façon décalée les unes par rapport aux autres sont formées de façon similaire.
  4. Echangeur de chaleur selon l'une quelconque des revendications précédentes, caractérisé en ce que toutes les ouïes (7) d'une partie d'ailette (4b) délimitée par deux tubes plats (2) sont placées de manière oblique et dans le même sens par rapport à la direction d'écoulement (S2) du deuxième fluide (FL2).
  5. Echangeur de chaleur selon l'une quelconque des revendications 1 à 4, caractérisé en ce que deux parties d'ailettes (4b) disposées l'une derrière l'autre, de façon décalée, sont sensiblement parallèles entre elles.
  6. Echangeur de chaleur selon la revendication 5,
    caractérisé en ce que les parties d'ailettes (4b) sont disposées sensiblement de façon perpendiculaire aux tubes plats (2).
  7. Echangeur de chaleur selon l'une quelconque des revendications 1 à 6, caractérisé en ce que les ailettes ondulées (3) possèdent, dans la principale direction d'écoulement du deuxième fluide, une dimension identique ou semblable.
  8. Echangeur de chaleur selon l'une quelconque des revendications 1 à 7, caractérisé en ce que différentes rangées de tubes sont traversées par différents fluides.
  9. Echangeur de chaleur selon l'une quelconque des revendications 1 à 8, caractérisé en ce que différentes rangées de tubes sont traversées par un fluide.
EP04763801A 2003-09-11 2004-08-04 Changeur thermique Not-in-force EP1664655B1 (fr)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
DE10342241A DE10342241A1 (de) 2003-09-11 2003-09-11 Wärmetauscher
PCT/EP2004/008754 WO2005028987A1 (fr) 2003-09-11 2004-08-04 Échangeur thermique

Publications (2)

Publication Number Publication Date
EP1664655A1 EP1664655A1 (fr) 2006-06-07
EP1664655B1 true EP1664655B1 (fr) 2008-10-29

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Application Number Title Priority Date Filing Date
EP04763801A Not-in-force EP1664655B1 (fr) 2003-09-11 2004-08-04 Changeur thermique

Country Status (8)

Country Link
US (1) US20070267187A1 (fr)
EP (1) EP1664655B1 (fr)
JP (1) JP2007505282A (fr)
CN (1) CN1849493A (fr)
AT (1) ATE412865T1 (fr)
BR (1) BRPI0414273A (fr)
DE (2) DE10342241A1 (fr)
WO (1) WO2005028987A1 (fr)

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CN106643263B (zh) * 2015-07-29 2019-02-15 丹佛斯微通道换热器(嘉兴)有限公司 用于换热器的翅片组件和具有该翅片组件的换热器
CN106767100A (zh) * 2017-01-17 2017-05-31 重庆超力高科技股份有限公司 换热器用翅片以及换热器
JP2018132247A (ja) * 2017-02-15 2018-08-23 富士電機株式会社 自動販売機
EP3399271B1 (fr) * 2017-05-02 2021-08-18 HS Marston Aerospace Limited Échangeur de chaleur
KR102400223B1 (ko) * 2017-12-21 2022-05-23 한온시스템 주식회사 열교환기
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Publication number Publication date
CN1849493A (zh) 2006-10-18
WO2005028987A1 (fr) 2005-03-31
DE10342241A1 (de) 2005-04-07
JP2007505282A (ja) 2007-03-08
BRPI0414273A (pt) 2006-11-07
ATE412865T1 (de) 2008-11-15
EP1664655A1 (fr) 2006-06-07
DE502004008363D1 (de) 2008-12-11
US20070267187A1 (en) 2007-11-22

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