Three-dimension heat transmission device

Abstract

A three-dimensional heat transfer device includes a heat-conducting shell, at least one first tube, and at least one second tube. The heat-conducting shell has an airtight chamber. One end of the at least one first tube is connected to the heat-conducting shell and communicates with the airtight chamber. The at least one second tube is connected to the heat-conducting shell at least at two points and communicates with the airtight chamber.

Description

Technical Field

[0001] This invention relates to a heat transfer device, and more particularly to a three-dimensional heat transfer device. Prior Technology

[0002] The technical principle of a vapor chamber is similar to that of a heat pipe, but the heat conduction method differs. A heat pipe uses one-dimensional linear heat conduction, while heat in a vapor chamber is conducted over a two-dimensional surface, resulting in higher efficiency. Specifically, a vapor chamber mainly consists of a cavity and a capillary structure. The cavity contains a hollow chamber for filling with a working fluid. The capillary structure is arranged within the hollow chamber. The heated portion of the cavity is called the evaporation zone. The heat dissipation portion is called the condensation zone. The working fluid absorbs heat and vaporizes in the evaporation zone, rapidly expanding throughout the cavity. In the condensation zone, it releases heat and condenses into a liquid state. Then, the liquid working fluid returns to the evaporation zone through the capillary structure, forming a cooling cycle.

[0003] Generally, most vapor chambers and heat pipes operate independently, resulting in individual planar or linear heat transfer for each vapor chamber or heat pipe, rather than integrated three-dimensional heat transfer, thus limiting their cooling efficiency. Some manufacturers have integrated vapor chambers and heat pipes to create three-dimensional heat transfer devices. However, the heat transfer efficiency of current three-dimensional heat transfer devices remains insufficient due to limitations imposed by server height and overall system space, making the heat dissipation area projected by the original vapor chamber insufficient. Extending heat pipes to distant areas further limits capillary drive force due to increased distance. Therefore, improving the heat dissipation efficiency of three-dimensional heat transfer devices is one of the problems that researchers need to solve. Summary of the Invention

[0004] The present invention provides a three-dimensional heat transfer device to further improve the heat dissipation efficiency of the three-dimensional heat transfer device.

[0005] An embodiment of the present invention discloses a three-dimensional heat transfer device comprising a heat-conducting shell, at least one first tube, and at least one second tube. The heat-conducting shell has an airtight chamber. One end of the at least one first tube is connected to the heat-conducting shell and communicates with the airtight chamber. The at least one second tube is connected to the heat-conducting shell at least at two points and communicates with the airtight chamber.

[0006] According to the three-dimensional heat transfer device of the above embodiment, since the two opposite ends of the two second tubes are connected to the second shell of the heat-conducting shell and communicate with the airtight chamber, the heat dissipation area of ​​the three-dimensional heat transfer device can be additionally increased, and is not limited to the heat dissipation area formed by these first tubes. Furthermore, compared to a general three-dimensional heat transfer device that only has a single heat dissipation area, the heat dissipation area formed by these first tubes combined with the heat dissipation area formed by the two second tubes has lower thermal resistance and higher heat transfer capacity. In this way, the heat dissipation efficiency of the three-dimensional heat transfer device can be improved.

[0007] The above description of the content of this invention and the following description of the embodiments are used to demonstrate and explain the principles of this invention, and to provide a further explanation of the scope of the patent application of this invention. Simple Explanation of the Diagram

[0008] Figure 1 is a three-dimensional schematic diagram of the three-dimensional heat transfer device according to the first embodiment of the present invention. Figure 2 is an exploded view of the three-dimensional heat transfer device in Figure 1. Figure 3 is a top view of the three-dimensional heat transfer device shown in Figure 1. Figure 4 is a cross-sectional schematic diagram of the second tube of the three-dimensional heat transfer device in Figure 1. Figure 5 is a cross-sectional schematic diagram of the three-dimensional heat transfer device in Figure 1. Figure 6 is a partially enlarged cross-sectional view of the three-dimensional heat transfer device in Figure 1. Figure 7 is a three-dimensional cross-sectional view of the three-dimensional heat transfer device in Figure 1. Figure 8 is a partially enlarged cross-sectional view of the three-dimensional heat transfer device according to the second embodiment of the present invention. Figure 9 is a partially enlarged cross-sectional view of the three-dimensional heat transfer device according to the third embodiment of the present invention. Figure 10 is a three-dimensional schematic diagram of the three-dimensional heat transfer device according to the fourth embodiment of the present invention. Figure 11 is a cross-sectional schematic diagram of the three-dimensional heat transfer device according to the fifth embodiment of the present invention. Figure 12 is a cross-sectional schematic diagram of the three-dimensional heat transfer device according to the sixth embodiment of the present invention. Implementation

[0009] Please refer to Figures 1 to 3. Figure 1 is a perspective view of the three-dimensional heat transfer device according to the first embodiment of the present invention. Figure 2 is an exploded view of the three-dimensional heat transfer device of Figure 1. Figure 3 is a top view of the three-dimensional heat transfer device of Figure 1.

[0010] The three-dimensional heat transfer device 10 of this embodiment includes a heat-conducting shell 11, a plurality of first tubes 12, two second tubes 13, and two flow-blocking capillary structures 14. The heat-conducting shell 11 includes a first shell member 111 and a second shell member 112. The first shell member 111 is used for thermal coupling to a heat source (not shown). Thermal coupling refers to thermal contact or connection through other heat-conducting media. The second shell member 112 is installed on the first shell member 111, so that the first shell member 111 and the second shell member 112 together form an airtight chamber S. The airtight chamber S is used to contain cooling fluid (not shown).

[0011] One end of each of the first tubes 12 is connected to the opposite ends of the two second tubes 13 to the second shell 112 of the heat-conducting shell 11, and communicates with the airtight chamber S. Each second tube 13 has a cavity 131, and each second tube 13 includes a first end 132 and a second end 133. The first end 132 is used for gaseous cooling fluid that has been heated and evaporated into vapor to flow from the airtight chamber S to the cavity 131, and the second end 133 is used for liquid cooling fluid that has been cooled and condensed into liquid to flow back from the cavity 131 to the airtight chamber S. In addition, the middle sections of the two second tubes 13 are away from the heat-conducting shell 11. The middle sections of the first tubes 12 and the two second tubes 13 are used, for example, to be assembled with a plurality of fin assemblies (not shown).

[0012] Please refer to Figures 4 through 6. Figure 4 is a cross-sectional view of the second tube of the three-dimensional heat transfer device in Figure 1. Figure 5 is a cross-sectional view of the three-dimensional heat transfer device in Figure 1. Figure 6 is a partially enlarged cross-sectional view of the three-dimensional heat transfer device in Figure 1.

[0013] The pore size of the two flow-blocking capillary structures 14 is, for example, less than or equal to 100 micrometers. The two flow-blocking capillary structures 14 are located at one end of each of the two second tubes 13 and are used to restrict the flow of cooling fluid. For example, the two flow-blocking capillary structures 14 are located at the two second ends 133 of the two second tubes 13. The two flow-blocking capillary structures 14 occupy, for example, less than 50% of the volume of the two cavities 131, and the cross-sectional areas of the two flow-blocking capillary structures 14 are respectively matched to the cross-sectional area surrounded by the two second tubes 13. That is, the two flow-blocking capillary structures 14 are, for example, solid columnar and block the second ends 133 of the two second tubes 13, and the volume blocked by the two flow-blocking capillary structures 14 is, for example, less than 50% of the volume of the two cavities 131.

[0014] In this embodiment, since the two opposite ends of the two second tubes 13 are connected to the second shell 112 of the heat-conducting shell 11 and communicate with the airtight chamber S, and the middle sections of the two second tubes 13 are far from the heat-conducting shell 11 and are used for assembly with the fin assembly, the heat dissipation area of ​​the three-dimensional heat transfer device 10 can be additionally increased, and is not limited to the heat dissipation area formed by these first tubes 12. Furthermore, compared to a typical three-dimensional heat transfer device with only a single heat dissipation area, the heat dissipation area formed by these first tubes 12 combined with the heat dissipation area formed by the middle sections of the two second tubes 13 has lower thermal resistance and higher heat transfer capacity. In this way, the heat dissipation efficiency of the three-dimensional heat transfer device 10 can be improved.

[0015] In this embodiment, the three-dimensional heat transfer device 10 may further include a first capillary structure 15 and a second capillary structure 16. The pore diameter of the first capillary structure 15 and the pore diameter of the second capillary structure 16 are, for example, larger than the pore diameter of the flow-blocking capillary structure 14.

[0016] Specifically, the porosity of the first capillary structure 15 and the second capillary structure 16 is greater than the porosity of the flow-blocking capillary structure 14, and the difference between them is greater than or equal to 10%. For example, the porosity of the first capillary structure 15 and the second capillary structure 16 is greater than or equal to 40% and less than or equal to 75%. The porosity of the flow-blocking capillary structure 14 is less than or equal to 55%. In this way, gaseous cooling fluid can pass through the first capillary structure 15 and the second capillary structure 16, but not through the flow-blocking capillary structure 14.

[0017] A first capillary structure 15 is disposed on the first housing 111. A second capillary structure 16 is disposed on the second housing 112. By disposing of the first capillary structure 15 and the second capillary structure 16, the gaseous cooling fluid can release heat and condense in the second tube 13, and then flow back to the airtight chamber S through the first capillary structure 15 and the second capillary structure 16. A flow-blocking capillary structure 14 is connected to and flush with the second capillary structure 16.

[0018] In this embodiment, each of these first tubes 12 may also have a tube capillary structure 17. The pore size of the tube capillary structure 17 is, for example, larger than the pore size of the flow-blocking capillary structure 14. Since each of these first tubes 12 and each tube capillary structure 17 has the same structure, the following description will focus on one of the first tubes 12 and one tube capillary structure 17. The cross-sectional area of ​​the tube capillary structure 17 is, for example, smaller than the cross-sectional area surrounded by the first tubes 12. By providing the tube capillary structure 17, the gaseous cooling fluid can release heat and condense in the first tube 12, and then flow back to the airtight chamber S through the tube capillary structure 17.

[0019] In this embodiment, the two flow-blocking capillary structures 14, the first capillary structure 15, the second capillary structure 16, and the tube capillary structures 17 are selected, for example, from the group consisting of metal mesh, fibers, and powder sintered bodies. Furthermore, since the pore size of the flow-blocking capillary structure 14 is smaller than that of the first capillary structure 15, the second capillary structure 16, and the tube capillary structure 17, the cooling fluid primarily passes through the flow-blocking capillary structure 14 by the propulsion of vapor.

[0020] In this embodiment, there are multiple first tubes 12, but this is not a limitation. In other embodiments, the number of first tubes may be only a single one.

[0021] In this embodiment, there are two second tubes 13 and two flow-blocking capillary structures 14, but this is not a limitation. In other embodiments, the number of second tubes and the number of flow-blocking capillary structures may be only one or more.

[0022] In this embodiment, the two opposite ends of the two second tubes 13 are connected to the second shell 112 of the heat-conducting shell 11, but this is not a limitation. In other embodiments, the two second tubes may also be connected to the second shell of the heat-conducting shell at only one or more points.

[0023] Please refer to Figure 7. Figure 7 is a three-dimensional cross-sectional view of the three-dimensional heat transfer device of Figure 1. In this embodiment, since the two second tubes 13 are symmetrically arranged on the second shell 112, and the structures of each second tube 13 and each flow-blocking capillary structure 14 are identical, the following description will focus on one of the second tubes 13 and one flow-blocking capillary structure 14. Furthermore, in order to emphasize the key points of the present invention, the description of the first tube 12 will be omitted below.

[0024] First, the liquid cooling fluid in the airtight chamber S absorbs heat transferred from the heat source to the first shell 111 of the heat-conducting shell 11 and vaporizes into gaseous cooling fluid. This gaseous fluid then flows from the airtight chamber S to the cavity 131 through the first end 132 of the second tube 13 in direction A. Next, the gaseous cooling fluid condenses within the second tube 13 and is propelled to the second end 133 of the second tube 13 by the continuously flowing gaseous cooling fluid into the first end 132. Due to the capillary effect of the flow-blocking capillary structure 14, the liquid cooling fluid can flow back into the heat-conducting shell 11, while simultaneously preventing the gaseous cooling fluid from passing through the flow-blocking capillary structure 14. This prevents the gaseous cooling fluid from being insufficiently cooled within the second tube 13 and flowing back into the heat-conducting shell 11 via the second end 133. Next, the gaseous cooling fluid flowing into the second tube 13 from the first end 132 pushes the liquid cooling fluid that previously flowed to this point and condensed, causing the liquid cooling fluid to pass through the flow-blocking capillary structure 14 in direction C. Finally, the liquid cooling fluid flows back to the airtight chamber S, completing the cooling cycle.

[0025] In this embodiment, the flow-blocking capillary structure 14 is connected to and flush with the second capillary structure 16, but this is not a limitation. In other embodiments, please refer to FIG8. FIG8 is a partially enlarged cross-sectional schematic diagram of the three-dimensional heat transfer device according to a second embodiment of the present invention.

[0026] The three-dimensional heat transfer device 10A in this embodiment is similar to the three-dimensional heat transfer device 10 in the first embodiment. Therefore, the differences between this embodiment and the first embodiment will be described below, and the similarities will not be repeated. In this embodiment, the three-dimensional heat transfer device 10A includes a heat-conducting shell 11, two second tubes 13, and two flow-blocking capillary structures 14A. The heat-conducting shell 11 includes a first shell 111 and a second shell 112. The second shell 112 is installed on the first shell 111, so that the first shell 111 and the second shell 112 together form an airtight chamber S. The airtight chamber S is used to contain cooling fluid (not shown). The opposite ends of the two second tubes 13 are connected to the second shell 112 of the heat-conducting shell 11 and communicate with the airtight chamber S.

[0027] Each second tube 13 has a cavity 131, and each second tube 13 includes a first end 132 and a second end 133 opposite to each other. The first end 132 is used for gaseous cooling fluid that has been heated and evaporated into vapor to flow from the airtight chamber S to the cavity 131, and the second end 133 is used for liquid cooling fluid that has been cooled and condensed into liquid to flow back from the cavity 131 to the airtight chamber S. A flow-blocking capillary structure 14A is provided at the second end 133 of the second tube 13.

[0028] The three-dimensional heat transfer device 10A may further include a first capillary structure 15 and a second capillary structure 16A. The first capillary structure 15 is disposed on the first housing 111. The second capillary structure 16A is disposed on the second housing 112. By providing the first capillary structure 15 and the second capillary structure 16A, the gaseous cooling fluid can release heat from the heat source and condense, then flow back to the airtight chamber S through the first capillary structure 15 and the second capillary structure 16A. The flow-blocking capillary structure 14A is connected to and passes through the second capillary structure 16A.

[0029] In a first embodiment, the three-dimensional heat transfer device 10 includes a first capillary structure 15 and a second capillary structure 16, and the flow-blocking capillary structure 14 is connected to the second capillary structure 16, but this is not a limitation. In other embodiments, please refer to FIG9. FIG9 is a partially enlarged cross-sectional schematic diagram of the three-dimensional heat transfer device according to a third embodiment of the present invention.

[0030] The three-dimensional heat transfer device 10B of this embodiment is similar to the three-dimensional heat transfer device 10 of the first embodiment. Therefore, the differences between this embodiment and the first embodiment will be described below, and the similarities will not be repeated. In this embodiment, the three-dimensional heat transfer device 10B includes a heat-conducting shell 11, two second tubes 13B, and two flow-blocking capillary structures 14B. The heat-conducting shell 11 includes a first shell 111 and a second shell 112. The second shell 112 is installed on the first shell 111, so that the first shell 111 and the second shell 112 together form an airtight chamber S. The airtight chamber S is used to contain cooling fluid (not shown).

[0031] Each second tube 13 has a cavity 131, and each second tube 13 includes a first end 132 and a second end 133 opposite to each other. The first end 132 is used for gaseous cooling fluid that evaporates into vapor when heated to flow from the airtight chamber S to the cavity 131, and the second end 133 is used for liquid cooling fluid that condenses into liquid when cooled to flow back from the cavity 131 to the airtight chamber S.

[0032] The second end 133 of the second tube 13B is connected to the first shell 111 of the heat-conducting shell 11, and the first end 132 of the second tube 13B is connected to the second shell 112 of the heat-conducting shell 11, and communicates with the airtight chamber S. A flow-blocking capillary structure 14B is disposed in the second tube 13B and connected to one end of the first shell 111 of the heat-conducting shell 11.

[0033] The three-dimensional heat transfer device 10 may further include a first capillary structure 15B and a second capillary structure 16B. The first capillary structure 15B is disposed on the first housing 111. The second capillary structure 16B is disposed on the second housing 112. By providing the first capillary structure 15B and the second capillary structure 16B, the gaseous cooling fluid can release heat and condense in the second tube 13B, and then flow back to the airtight chamber S through the first capillary structure 15B and the second capillary structure 16B. The flow-blocking capillary structure 14B connects to the first capillary structure 15B. In this way, the path of the liquid cooling fluid returning to the heat source can be further shortened.

[0034] In this embodiment, the second end 133 of the two second tubes 13B is connected to the first shell 111 of the heat-conducting shell 11, and the first end 132 of the two second tubes 13B is connected to the second shell 112 of the heat-conducting shell 11, such that the flow-blocking capillary structure 14B is disposed in the second tube 13B at one end connected to the first shell 111 of the heat-conducting shell 11, but this is not a limitation. In other embodiments, the opposite ends of the two second tubes may also be connected to the second shell of the heat-conducting shell, such that the flow-blocking capillary structure is only partially disposed at one end of the second tube.

[0035] Please refer to Figure 10. Figure 10 is a perspective view of the three-dimensional heat transfer device according to the fourth embodiment of the present invention. The three-dimensional heat transfer device 10C of this embodiment is similar to the three-dimensional heat transfer device 10 of the first embodiment. Therefore, the differences between this embodiment and the first embodiment will be described below, and the similarities will not be repeated. In this embodiment, the three-dimensional heat transfer device 10C includes a plurality of fin groups 18. These fin groups 18 are respectively installed on the first tubes 12 and the two second tubes 13. In this way, the heat dissipation areas formed by the first tubes 12 and the heat dissipation areas formed by the middle sections of the two second tubes 13 can be further dissipated through these fin groups 18.

[0036] In the first embodiment, the three-dimensional heat transfer device 10 uses two flow-blocking capillary structures 14 to block the two second ends 133 respectively, but this is not a limitation. In other embodiments, please refer to FIG11. FIG11 is a cross-sectional schematic diagram of the three-dimensional heat transfer device according to the fifth embodiment of the present invention. The three-dimensional heat transfer device 10D of this embodiment is similar to the three-dimensional heat transfer device 10 of the first embodiment; therefore, the differences between this embodiment and the first embodiment will be described below, and the similarities will not be repeated.

[0037] In this embodiment, the three-dimensional heat transfer device 10D includes a heat-conducting shell 11, two second tubes 13, a first capillary structure 15, a second capillary structure 16D, and two third capillary structures 19. The heat-conducting shell 11 includes a first shell member 111 and a second shell member 112. The second shell member 112 is mounted on the first shell member 111, so that the first shell member 111 and the second shell member 112 together form an airtight chamber S. The airtight chamber S is used to contain cooling fluid. The opposite ends of the two second tubes 13 are connected to the heat-conducting shell 11.

[0038] Each second tube 13 has a cavity 131, and each second tube 13 includes a first end 132 and a second end 133 opposite to each other. The first end 132 is used for gaseous cooling fluid that evaporates into vapor when heated to flow from the airtight chamber S to the cavity 131, and the second end 133 is used for liquid cooling fluid that condenses into liquid when cooled to flow back from the cavity 131 to the airtight chamber S.

[0039] A first capillary structure 15 is disposed on the first housing 111. A second capillary structure 16D is disposed on the second housing 112 and closes the two second ends 133. In this way, the flow of cooling fluid can be restricted through the second capillary structure 16. The capillary efficiency of the two third capillary structures 19 is, for example, different from that of the flow-blocking capillary structure in the first embodiment, and they are respectively located at the two second ends 133 of the two second tubes 13, and the two third capillary structures 19 are, for example, hollow columnar. In addition, the third capillary structure 19 is connected to and flush with the second capillary structure 16D.

[0040] In the first embodiment, the three-dimensional heat transfer device 10 uses two flow-blocking capillary structures 14 to block the two second ends 133 respectively, but this is not a limitation. In other embodiments, please refer to FIG12. FIG12 is a cross-sectional schematic diagram of the three-dimensional heat transfer device according to the sixth embodiment of the present invention. The three-dimensional heat transfer device 10E of this embodiment is similar to the three-dimensional heat transfer device 10 of the first embodiment; therefore, the differences between this embodiment and the first embodiment will be described below, and the similarities will not be repeated.

[0041] In this embodiment, the three-dimensional heat transfer device 10E includes a heat-conducting shell 11, two second tubes 13, a first capillary structure 15, and a second capillary structure 16E. The heat-conducting shell 11 includes a first shell member 111 and a second shell member 112. The second shell member 112 is mounted on the first shell member 111, so that the first shell member 111 and the second shell member 112 together form an airtight chamber S. The airtight chamber S is used to contain cooling fluid. The opposite ends of the two second tubes 13 are connected to the heat-conducting shell 11.

[0042] Each second tube 13 has a cavity 131, and each second tube 13 includes a first end 132 and a second end 133 opposite to each other. The first end 132 is used for gaseous cooling fluid that evaporates into vapor when heated to flow from the airtight chamber S to the cavity 131, and the second end 133 is used for liquid cooling fluid that condenses into liquid when cooled to flow back from the cavity 131 to the airtight chamber S.

[0043] A first capillary structure 15 is disposed on the first housing 111. A second capillary structure 16E is disposed throughout the second housing 112 and closes the two second ends 133. In this way, the flow of cooling fluid can be restricted through the second capillary structure 16E.

[0044] In this embodiment, the second capillary structure 16E is disposed throughout the second housing 112 and closes the second ends 133 of the second tube 13, but is not limited thereto. In other embodiments, the second capillary structure may also be disposed only at the junction of the second housing and the second tube and close the second ends of the second tube.

[0045] According to the three-dimensional heat transfer device of the above embodiment, since the two opposite ends of the two second tubes are connected to the second shell of the heat-conducting shell and communicate with the airtight chamber, and the middle sections of the two second tubes are far from the heat-conducting shell and are used for assembly with the fin assembly, the heat dissipation area of ​​the three-dimensional heat transfer device can be additionally increased, and is not limited to the heat dissipation area formed by these first tubes. Furthermore, compared to a general three-dimensional heat transfer device that only has a single heat dissipation area, the heat dissipation area formed by these first tubes combined with the heat dissipation area formed by the middle sections of the two second tubes has lower thermal resistance and higher heat transfer capacity. In this way, the heat dissipation efficiency of the three-dimensional heat transfer device can be improved.

[0046] Although the present invention has been disclosed above with reference to the foregoing embodiments, it is not intended to limit the present invention. Anyone skilled in the art can make some modifications and refinements without departing from the spirit and scope of the present invention. Therefore, the scope of patent protection of the present invention shall be determined by the scope of the patent application attached to this specification.

[0047] 10, 10A~10E: Three-dimensional heat transfer device 11: Thermal conductive shell 111: First shell component 112: Second shell 12:First tube body 13,13B: Second tube body 131: Lumen 132: First end 133: Second end 14, 14A, 14B: Flow-blocking capillary structures 15,15B: First capillary structure 16, 16A, 16B, 16D, 16E: Second capillary structure 17: Capillary structure of the tube body 18: Fin group 19: Third capillary structure A, B, C: Direction S: Airtight chamber

Claims

1. A three-dimensional heat transfer device, comprising: a heat-conducting shell having an airtight chamber, the heat-conducting shell including a first shell member and a second shell member, the second shell member being mounted on the first shell member such that the first shell member and the second shell member together form the airtight chamber; at least one first tube body, one end of the at least one first tube body being connected to the second shell member and communicating with the airtight chamber; at least one second tube body, both opposite ends of the at least one second tube body being connected to the second shell member and communicating with the airtight chamber; at least one flow-blocking capillary structure located at one end of the at least one second tube body, the cross-sectional area of ​​the at least one flow-blocking capillary structure matching the cross-sectional area surrounded by the at least one second tube body; a first capillary structure disposed on the first shell member; and a second capillary structure disposed on the second shell member, wherein the at least one flow-blocking capillary structure is connected to the second capillary structure and the at least one flow-blocking capillary structure passes through the second capillary structure.

2. The three-dimensional heat transfer device as claimed in claim 1, wherein each of the at least one second tube has a cavity, and the at least one flow-blocking capillary structure occupies less than 50% of the volume of the at least one cavity.

3. The three-dimensional heat transfer device as claimed in claim 1, wherein the at least one first tube has a tube capillary structure, the cross-sectional area of ​​which is smaller than the cross-sectional area surrounded by the at least one first tube.

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