A flue gas reheater
Patent Information
- Application Number
- CN202522160193.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-13
- Publication Date
- 2026-09-11
- Estimated Expiration
- 2035-10-13
AI Technical Summary
[0006]本实用新型的目的在于提供一种烟气再热器,以解决上述背景技术中提出的现有的烟气再热器仍存在一些不足之处
[0024]该烟气再热器中,换热管采用 “一端嵌入蒸汽筒体、一端置于烟气筒体” 的穿透式布局,配合外壁增设的若干换热翅片,大幅增加了烟气与蒸汽之间的换热面积。与公开号为 CN216558428U 的传统结构相比,在相同体积下换热接触面积显著提升,使低温烟气与高温蒸汽的热交换速率明显加快,可将烟气快速加热至 80℃以上,有效消除 “白烟” 现象的同时,缩短了换热时间,避免了能量浪费。
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Figure CN224743527U_ABST
Abstract
Description
Technical Field
[0001] This utility model relates to the field of boiler technology, and more specifically, to a flue gas reheater. Background Technology
[0002] In the field of boiler technology, flue gas reheaters play a crucial role in the efficient and stable operation of the entire system. The background technology will be explained in detail below.
[0003] In current industrial production, especially in industries involving combustion processes such as thermal power generation and steel smelting, large amounts of high-temperature flue gas are generated. Direct emission of this flue gas not only wastes energy but also causes serious environmental pollution. Taking thermal power generation as an example, according to relevant statistics, a huge amount of energy is contained in the large quantities of high-temperature flue gas generated annually in my country's thermal power generation, which remains unutilized. To reduce energy consumption and environmental pollution, a series of treatments, such as desulfurization, are typically implemented for the flue gas.
[0004] In common desulfurization processes, wet desulfurization is widely used due to its high efficiency and mature technology. However, the temperature of the flue gas after wet desulfurization is significantly reduced, generally to around 50℃-60℃, and its moisture content is relatively high (15-18%). During the emission process, as the temperature of this low-temperature, high-humidity flue gas further decreases, the water vapor in it will gradually condense into mist, leading to the phenomenon of "white smoke" emanating from the chimney. This not only affects the company's image but may also cause concern among nearby residents. Simultaneously, the low-temperature flue gas will corrode the flue and chimney, shortening their service life and increasing maintenance costs. To solve these problems, the desulfurized flue gas needs to be reheated to raise its temperature to a certain level. Generally, the saturated wet flue gas entering the chimney needs to be heated to above 80℃ to eliminate the white smoke phenomenon and reduce corrosion of the flue and chimney.
[0005] Currently, various types of flue gas reheaters exist on the market. For example, patent document CN216558428U discloses a flue gas reheater structure with an expansion joint, which includes a front water chamber, a front tube sheet, a shell, a rear tube sheet, a rear water chamber, a steam inlet, a condensate outlet, a flue gas inlet, a flue gas outlet, and multiple heat exchange tubes. This structure achieves heat exchange through heat exchange tubes and convection, gradually increasing the flue gas temperature and gradually decreasing the steam temperature, ultimately reaching a flue gas temperature of 105℃, thus achieving the effect of bleaching the flue gas. However, existing flue gas reheaters still have some shortcomings. To improve heat exchange performance, some flue gas reheaters often require increasing the volume of the heat exchanger, which not only wastes a large amount of metal materials and increases costs, but also fails to fully utilize its heat exchange performance, resulting in long heat exchange times and unsatisfactory heat exchange effects. In addition, some flue gas reheaters suffer from problems such as corrosion and leakage during operation, seriously affecting their service life and operational stability. Therefore, developing a new, efficient, stable, and low-cost flue gas reheater is of great practical significance. Utility Model Content
[0006] The purpose of this invention is to provide a flue gas reheater to address some shortcomings of existing flue gas reheaters mentioned in the background section. To improve heat exchange performance, some flue gas reheaters often require increasing the volume of the heat exchanger, which not only wastes a large amount of metal material and increases costs, but also fails to fully utilize its heat exchange performance, resulting in long heat exchange times and unsatisfactory heat exchange effects.
[0007] To achieve the above objectives, this utility model provides a flue gas reheater, including a steam cylinder, a flue gas cylinder on the outer side of the steam cylinder, a steam outlet pipe seat connected to the bottom of the steam cylinder, a steam inlet pipe seat connected to the upper end of the steam cylinder, and a plurality of heat exchange tubes installed sequentially from top to bottom on the inner wall of the flue gas cylinder, one end of each heat exchange tube being located inside the steam cylinder and the other end being located inside the flue gas cylinder, and a plurality of heat exchange fins being provided on the outer wall.
[0008] This setup utilizes a nested structure of a steam cylinder and a flue gas cylinder. Steam enters the steam cylinder from the steam inlet pipe and transfers heat to the low-temperature flue gas located within the flue gas cylinder via heat exchange tubes. One end of the heat exchange tube absorbs heat from the steam within the steam cylinder, while the other end is within the flue gas cylinder, where heat is efficiently transferred to the flue gas through heat exchange fins on the outer wall. This achieves flue gas temperature increase based on the principles of heat conduction and convection heat transfer.
[0009] Preferably, a base plate is installed at the bottom of the flue gas cylinder, a support plate is installed on the outer side of the bottom of the flue gas cylinder, an upper sealing plate is installed at the top of the flue gas cylinder, a lifting lug is installed on the outer side of the top of the flue gas cylinder, and a lifting lug support is installed between the inner side of the lifting lug and the top of the flue gas cylinder.
[0010] This setup includes a base plate installed at the bottom of the flue gas cylinder, providing fundamental support for the entire equipment; a support plate reinforces the bottom structure, enhancing stability; an upper sealing plate seals the top of the flue gas cylinder to prevent flue gas leakage; and lifting lugs and their supports utilize mechanical support principles to facilitate the movement of the equipment during installation and handling using lifting equipment.
[0011] Preferably, a flue gas outlet is provided on one side of the lower part of the flue gas cylinder, and a flue gas inlet is provided on the top of the flue gas cylinder.
[0012] Based on the principle of flue gas flow, hot air usually flows upward. Therefore, a flue gas inlet is set at the top of the flue gas cylinder so that the incoming flue gas can flow from top to bottom and fully contact the heat exchange tubes for heat exchange. A flue gas outlet is set on one side at the bottom, which conforms to the flow direction of flue gas under the action of gravity and pressure difference, and facilitates the discharge of low-temperature flue gas after heat exchange.
[0013] Preferably, the upper and lower ends of the steam cylinder are fitted with elliptical end caps.
[0014] This design of the elliptical head is based on mechanical principles. Its curved structure effectively disperses the pressure generated by steam at the end of the cylinder, reducing stress concentration compared to a flat head. Simultaneously, the shape of the elliptical head helps the steam to form a more uniform flow state within the cylinder, reducing turbulent losses.
[0015] Preferably, the outer upper end of the steam cylinder is fixed to the inner wall of the flue gas cylinder by an upper bracket, and the outer lower end of the steam cylinder is fixed to the inner wall of the flue gas cylinder by a lower bracket, with a bottom bracket installed at the bottom of the lower bracket.
[0016] This setup involves fixing the upper and lower brackets to the inner wall of the flue gas cylinder from both ends, utilizing mechanical support principles to bear the weight of the steam cylinder as well as the vibrations and stresses generated during operation. The lower bracket further enhances the support stability of the lower bracket, preventing deformation due to long-term stress.
[0017] Preferably, a nameplate is installed on the outer wall of the flue gas cylinder.
[0018] As a carrier of equipment information, the nameplate, based on the principle of identification, displays important information such as the equipment model, specifications, technical parameters, and manufacturer in a visually intuitive way by installing a nameplate on the outer wall of the flue gas cylinder.
[0019] Preferably, a support pipe is vertically installed inside the steam cylinder, the outer wall of the support pipe is connected and fixed to one end of the heat exchange pipe, a blocking plate is installed on the top of the support pipe, and a connecting plate is installed between the outer side of the upper end of the support pipe and the inner wall of the steam cylinder.
[0020] This setup involves a vertically installed support pipe inside the steam cylinder, with its outer wall connected and fixed to one end of the heat exchange tube. This provides support for the heat exchange tube and prevents it from swaying or shifting under the impact of steam flow and flue gas. A blocking plate is installed at the top of the support pipe to prevent steam from entering the support pipe and affecting the heat exchange effect. The connecting plate between the upper outer side of the support pipe and the inner wall of the steam cylinder further enhances the stability of the overall structure, utilizing mechanical principles such as triangular stability for reinforcement.
[0021] Preferably, an inspection port is installed on the upper side of the flue gas cylinder.
[0022] This feature includes an inspection port on the upper side of the flue gas stack. Based on the principle of convenient equipment maintenance, when components such as heat exchange tubes inside the equipment need to be inspected, repaired, or replaced, staff can directly enter the equipment through the inspection port without disassembling a large number of equipment parts.
[0023] Compared with the prior art, the beneficial effects of this utility model are as follows:
[0024] In this flue gas reheater, the heat exchange tubes adopt a through-type layout with one end embedded in the steam cylinder and the other end placed in the flue gas cylinder. Combined with several heat exchange fins added to the outer wall, this significantly increases the heat exchange area between the flue gas and steam. Compared with the traditional structure disclosed in CN216558428U, the heat exchange contact area is significantly increased within the same volume, resulting in a markedly faster heat exchange rate between the low-temperature flue gas and the high-temperature steam. This allows the flue gas to be rapidly heated to above 80°C, effectively eliminating the "white smoke" phenomenon while shortening the heat exchange time and avoiding energy waste.
[0025] The steam cylinder is fixed to the inner wall of the flue gas cylinder by upper, lower, and bottom brackets, forming a double support structure. Combined with the support pipes' role in securing the heat exchange tubes, this significantly improves the overall stability of the structure under the impact of high-temperature flue gas. The elliptical head design reduces turbulent flow losses at the cylinder ends, lowers the risk of localized corrosion, and significantly extends the equipment's service life compared to traditional structures.
[0026] The inspection port located at the top of the flue gas stack allows for direct inspection and maintenance of the internal heat exchange tubes without disassembling the entire structure, significantly reducing maintenance time. The combination of top lifting lugs and supports facilitates equipment installation and transportation, while the load-bearing structure of the bottom support plate and base plate ensures safety during lifting and operation. The nameplate allows operators to quickly obtain equipment parameters, improving operational standardization.
[0027] The concentric design, with the steam cylinder nested within the flue gas cylinder, significantly saves installation space compared to traditional split layouts, making it particularly suitable for industrial boiler systems with limited space. The integrated design of the heat exchange fins and support tubes reduces metal material consumption, improving performance while lowering manufacturing costs, resulting in a superior overall cost-performance ratio compared to existing similar products. Attached Figure Description
[0028] Figure 1 This is a schematic diagram of the overall structure of this utility model;
[0029] Figure 2 This is a schematic diagram of the lower structure of this utility model;
[0030] Figure 3 This is a schematic diagram of the upper structure of this utility model;
[0031] Figure 4 This is a schematic diagram of the heat exchange tube in this utility model;
[0032] The meanings of the labels in the diagram are as follows:
[0033] 1. Base plate; 2. Support plate; 3. Flue gas cylinder; 4. Steam outlet pipe seat; 5. Flue gas outlet; 6. Elliptical end cap; 7. Base bracket; 8. Lower bracket; 9. Steam cylinder; 10. Nameplate; 12. Heat exchange tube; 13. Support tube; 14. Blocking plate; 15. Connecting plate; 16. Upper bracket; 17. Steam inlet pipe seat; 18. Inspection port; 19. Upper sealing plate; 20. Flue gas inlet; 21. Lifting lug support; 22. Lifting lug. Detailed Implementation
[0034] The technical solutions of the present utility model will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of the present utility model, and not all embodiments. Based on the embodiments of the present utility model, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present utility model.
[0035] This utility model provides a flue gas reheater, such as Figure 1 , Figure 2 , Figure 3 , Figure 4 As shown, it includes a steam cylinder 9, a flue gas cylinder 3 is provided on the outside of the steam cylinder 9, a steam outlet pipe seat 4 is connected to the bottom of the steam cylinder 9, a steam inlet pipe seat 17 is connected to the upper end of the steam cylinder 9, and a number of heat exchange tubes 12 are installed on the inner wall of the flue gas cylinder 3 from top to bottom. One end of the heat exchange tube 12 is located inside the steam cylinder 9, and the other end of the heat exchange tube 12 is located inside the flue gas cylinder 3, and a number of heat exchange fins are provided on the outer wall.
[0036] Utilizing the nested structure of the steam cylinder 9 and the flue gas cylinder 3, steam enters the steam cylinder 9 from the steam inlet pipe seat 17 and transfers heat to the low-temperature flue gas located inside the flue gas cylinder 3 via the heat exchange tube 12. One end of the heat exchange tube 12 absorbs heat from the steam inside the steam cylinder 9, while the other end is inside the flue gas cylinder 3, efficiently transferring heat to the flue gas through heat exchange fins on the outer wall. Based on the principles of heat conduction and convection heat transfer, the flue gas temperature is increased. This structural design makes the heat exchange process between steam and flue gas efficient and compact, significantly increasing the heat exchange area and accelerating the heat exchange rate. It can rapidly heat the low-temperature flue gas to above 80°C, effectively eliminating the phenomenon of "white smoke" emanating from the chimney, while also avoiding energy waste.
[0037] In this embodiment, as Figure 3 As shown, a base plate 1 is installed at the bottom of the flue gas cylinder 3, a support plate 2 is installed on the outer side of the bottom of the flue gas cylinder 3, an upper sealing plate 19 is installed on the top of the flue gas cylinder 3, a lifting lug 22 is installed on the outer side of the top of the flue gas cylinder 3, and a lifting lug support 21 is installed between the inner side of the lifting lug 22 and the top of the flue gas cylinder 3.
[0038] The base plate 1 is installed at the bottom of the flue gas cylinder 3, providing basic support for the entire equipment; the support plate 2 reinforces the bottom structure and enhances stability; the top sealing plate 19 seals the top of the flue gas cylinder 3 to prevent flue gas leakage; the combination of lifting lugs 22 and lifting lug supports 21 utilizes the principle of mechanical support to facilitate the movement of the equipment during installation and transportation using lifting equipment. These components work together to ensure the structural stability of the flue gas cylinder 3, enabling it to withstand lifting forces during equipment installation and transportation, ensuring equipment safety, and preventing damage due to structural problems during operation. Simultaneously, the excellent sealing prevents flue gas leakage and reduces the risk of environmental pollution.
[0039] Specifically, such as Figure 2 As shown, a flue gas outlet 5 is provided on one side of the lower part of the flue gas cylinder 3, and a flue gas inlet 20 is provided on the top of the flue gas cylinder 3.
[0040] Based on the principle of flue gas flow, hot air typically rises. Therefore, a flue gas inlet 20 is installed at the top of the flue gas cylinder 3, allowing the incoming flue gas to flow downwards and fully contact the heat exchange tubes 12 for heat exchange. A flue gas outlet 5 is installed on one side at the bottom, conforming to the flow direction of flue gas under gravity and pressure difference, facilitating the discharge of low-temperature flue gas after heat exchange. This reasonable inlet and outlet layout optimizes the flow path of flue gas within the cylinder, prolongs the contact time between the flue gas and the heat exchange tubes 12, improves heat exchange efficiency, and ensures the stable and efficient operation of the flue gas reheater.
[0041] Furthermore, such as Figure 2 , Figure 3 As shown, elliptical end caps 6 are installed at both the upper and lower ends of the steam cylinder 9.
[0042] The design of the elliptical head 6 is based on mechanical principles. Its curved structure effectively disperses the pressure generated by steam at the end of the steam cylinder 9, reducing stress concentration compared to a flat head. Simultaneously, the shape of the elliptical head 6 helps the steam to form a more uniform flow state within the steam cylinder 9, reducing turbulence losses. This lowers the risk of rupture at the end of the steam cylinder 9 due to stress concentration, improving the safety and reliability of the equipment. Reducing turbulence losses results in a more uniform energy distribution of the steam within the steam cylinder 9, which is beneficial for improving the heat exchange efficiency between the steam and the heat exchange tubes 12, indirectly enhancing the performance of the entire flue gas reheater.
[0043] Furthermore, such as Figure 3 As shown, the upper outer side of the steam cylinder 9 is fixed to the inner wall of the flue gas cylinder 3 by the upper bracket 16, and the lower outer side of the steam cylinder 9 is fixed to the inner wall of the flue gas cylinder 3 by the lower bracket 8. A bottom bracket 7 is installed at the bottom of the lower bracket 8.
[0044] The bracket 16 and the lower bracket 8 are fixed to the inner wall of the flue gas cylinder 3 from the upper and lower ends of the steam cylinder 9, respectively. Utilizing the principle of mechanical support, they bear the weight of the steam cylinder 9 as well as the vibrations and stresses generated during operation. The bottom bracket 7 further enhances the support stability of the lower bracket 8, preventing deformation due to long-term stress. This forms a stable double support structure, greatly enhancing the stability of the steam cylinder 9 within the flue gas cylinder 3. This allows it to maintain normal operation even under harsh conditions such as high temperature, high pressure, and flue gas impact, preventing the heat exchange effect from being affected by displacement or shaking of the steam cylinder 9, and extending the service life of the equipment.
[0045] Furthermore, such as Figure 2 As shown, a nameplate 10 is installed on the outer wall of the flue gas cylinder 3.
[0046] The nameplate 10 serves as a carrier of equipment information. Based on the principle of identification, it is installed on the outer wall of the flue gas stack 3 to visually display important information such as the equipment model, specifications, technical parameters, and manufacturer. This allows operators to quickly obtain relevant information during equipment installation, commissioning, maintenance, and daily operation, helping to operate the equipment correctly, reducing errors caused by a lack of understanding of equipment parameters, improving the safety and stability of equipment operation, and also facilitating equipment management and the organization of maintenance records.
[0047] Furthermore, such as Figure 2 , Figure 3 As shown, a support pipe 13 is vertically installed inside the steam cylinder 9. The outer wall of the support pipe 13 is connected and fixed to one end of the heat exchange pipe 12. A blocking plate 14 is installed on the top of the support pipe 13. A connecting plate 15 is installed between the outer side of the upper end of the support pipe 13 and the inner wall of the steam cylinder 9.
[0048] The support pipe 13 is vertically installed inside the steam cylinder 9, and its outer wall is fixedly connected to one end of the heat exchange pipe 12, providing support for the heat exchange pipe 12 and preventing it from shaking or shifting under the impact of steam flow and flue gas. A blocking plate 14 is installed on top of the support pipe 13 to prevent steam from entering the support pipe 13 and affecting the heat exchange effect. A connecting plate 15 installed between the upper outer side of the support pipe 13 and the inner wall of the steam cylinder 9 further enhances the stability of the overall structure, using mechanical principles such as triangular stability for reinforcement. This ensures the positional stability of the heat exchange pipe 12 during operation, enabling it to continuously and efficiently perform heat exchange. The stable structure helps improve the equipment's seismic resistance, reduces component wear and damage caused by vibration, extends the equipment's service life, and ensures normal steam flow within the steam cylinder 9, optimizing the heat exchange process.
[0049] Furthermore, such as Figure 2 , Figure 3 As shown, an inspection port 18 is installed on the upper side of the flue gas cylinder 3.
[0050] An inspection port 18 is installed on one side of the upper part of the flue gas stack 3. Based on the principle of convenient equipment maintenance, when components such as the heat exchange tubes 12 inside the equipment need to be inspected, repaired, or replaced, personnel can directly enter the equipment through the inspection port 18 without disassembling a large number of equipment parts. This greatly shortens the equipment maintenance time, improves maintenance efficiency, and reduces the impact of equipment downtime for maintenance on production. At the same time, it reduces the manpower and material costs of equipment maintenance, improves the maintainability of the equipment, and ensures the long-term stable operation of the equipment.
[0051] When the flue gas reheater of this utility model is in use, high-temperature steam first enters the steam cylinder 9 through the steam inlet pipe seat 17, and forms a stable flow field under the guidance of the elliptical head 6, which evenly fills the interior of the steam cylinder 9; at the same time, low-temperature flue gas of 50-60°C after wet desulfurization enters the flue gas cylinder 3 from the flue gas inlet 20, and flows from top to bottom along the interior of the cylinder under the action of gravity and pressure difference.
[0052] High-temperature steam inside the steam cylinder 9 contacts one end of the heat exchange tube 12, transferring heat to the tube 12 via thermal conduction. The heat is then conducted along the tube 12 to the other end inside the flue gas cylinder 3, where it undergoes convective heat exchange with the flowing low-temperature flue gas through the heat exchange fins on the outer wall, causing the flue gas temperature to gradually increase. During this process, the support tube 13 and connecting plate 15 ensure the stability of the heat exchange tube 12 under the impact of the flowing medium, while the blocking plate 14 prevents steam from entering the support tube 13 and affecting the heat exchange efficiency.
[0053] After heat exchange, the low-temperature steam condensate is discharged from the steam cylinder 9 through the steam outlet pipe seat 4 and can be recycled; the flue gas heated to above 80°C leaves the flue gas cylinder 3 through the flue gas outlet 5 and enters the subsequent flue and chimney, effectively avoiding the "white smoke" phenomenon and equipment corrosion.
[0054] During equipment operation, the upper bracket 16, lower bracket 8 and bottom bracket 7 maintain the relative stability of the steam cylinder 9 and the flue gas cylinder 3; the bottom plate 1, support plate 2 and upper sealing plate 19 ensure the overall structural stability and flue gas sealing; operators can obtain equipment parameters through the nameplate 10, and regularly inspect and maintain internal components through the inspection port 18; the lifting lugs 22 and lifting lug supports 21 facilitate equipment installation and transportation.
[0055] The foregoing has shown and described the basic principles, main features, and advantages of this utility model. Those skilled in the art should understand that this utility model is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the utility model. Various changes and modifications can be made to this utility model without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed utility model. The scope of protection of this utility model is defined by the appended claims and their equivalents.
Claims
1. A flue gas reheater comprising a steam drum (9), characterized in that: A flue gas cylinder (3) is provided on the outside of the steam cylinder (9). A steam outlet pipe seat (4) is connected to the bottom of the steam cylinder (9). A steam inlet pipe seat (17) is connected to the upper end of the steam cylinder (9). A number of heat exchange tubes (12) are installed on the inner wall of the flue gas cylinder (3) from top to bottom. One end of the heat exchange tube (12) is located inside the steam cylinder (9), and the other end of the heat exchange tube (12) is located inside the flue gas cylinder (3). A number of heat exchange fins are provided on the outer wall.
2. The flue gas reheater of claim 1, characterized in that: The bottom of the flue gas cylinder (3) is equipped with a base plate (1), a support plate (2) is installed on the outer side of the bottom of the flue gas cylinder (3), an upper sealing plate (19) is installed on the top of the flue gas cylinder (3), a lifting lug (22) is installed on the outer side of the top of the flue gas cylinder (3), and a lifting lug support (21) is installed between the inner side of the lifting lug (22) and the top of the flue gas cylinder (3).
3. The flue gas reheater of claim 1, wherein: A flue gas outlet (5) is provided on one side of the lower part of the flue gas cylinder (3), and a flue gas inlet (20) is provided on the top of the flue gas cylinder (3).
4. The flue gas reheater of claim 1, wherein: The upper and lower ends of the steam cylinder (9) are fitted with elliptical heads (6).
5. The flue gas reheater of claim 1, wherein: The upper outer side of the steam cylinder (9) is fixed to the inner wall of the flue gas cylinder (3) by the upper bracket (16), and the lower outer side of the steam cylinder (9) is fixed to the inner wall of the flue gas cylinder (3) by the lower bracket (8). A bottom bracket (7) is installed at the bottom of the lower bracket (8).
6. The flue gas reheater of claim 1, wherein: A nameplate (10) is installed on the outer wall of the flue gas cylinder (3).
7. The flue gas reheater of claim 1, wherein: The steam cylinder (9) is vertically installed inside a support pipe (13). The outer wall of the support pipe (13) is connected and fixed to one end of the heat exchange pipe (12). A blocking plate (14) is installed on the top of the support pipe (13). A connecting plate (15) is installed between the outer side of the upper end of the support pipe (13) and the inner wall of the steam cylinder (9).
8. The flue gas reheater of claim 1, wherein: An inspection port (18) is installed on the upper side of the flue gas cylinder (3).