Heating device

By placing the primary and secondary thermostats at the inlet and outlet of the heating device respectively, and utilizing the temperature gradient formed by the water flow, the problem of excessively high trigger temperature of the thermostat in traditional heating devices is solved, achieving cost savings and improved safety.

CN223896262UActive Publication Date: 2026-02-10KUNSHAN TYREK INTELLIGENT TECH CO LTD
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Patent Information

Application Number
CN202522825811.1
Authority / Receiving Office
CN · China
Patent Type
Utility models(China)
Current Assignee / Owner
Filing Date
2025-12-31
Publication Date
2026-02-10
Estimated Expiration
2035-12-31

AI Technical Summary

Technical Problem

In traditional heating devices, the dual-temperature controller layout leads to excessively high trigger temperatures for the primary protection temperature controller, increasing manufacturing costs and safety hazards, while the secondary protection is prone to malfunction.

Method used

The primary thermostat is placed at the water inlet, and the secondary thermostat is placed at the water outlet. The temperature gradient formed by the water flow is used to reduce the trigger temperature of the thermostat, thereby achieving graded protection.

Benefits of technology

It reduces the temperature resistance requirements of structural components, saves costs, and improves safety by using rapid-response primary protection to avoid malfunctions of secondary protection.

✦ Generated by Eureka AI based on patent content.

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Abstract

The utility model discloses a heating device which comprises a heating assembly, a first temperature controller and a second temperature controller. The heating assembly comprises an outer pipe and a heating pipe penetrating through the outer pipe. A water inlet and a water outlet are formed in the two ends of the outer pipe. A first mounting platform and a second mounting platform are arranged between the water inlet and the water outlet on the outer pipe, the first mounting platform is close to the water inlet, and the second mounting platform is close to the water outlet. The first temperature controller is arranged on the first mounting platform and has a first trigger temperature; the second temperature controller is arranged on the second installation platform and has a second trigger temperature higher than the first trigger temperature. The first-stage temperature controller and the second-stage temperature controller are arranged at the water inlet end and the water outlet end of the heating device correspondingly, the temperature gradient naturally formed by water flow is utilized, the trigger temperature of the double temperature controllers is reduced on the premise that the safe temperature difference is ensured, and therefore grading rapid protection is achieved, the trigger temperature of the second-stage temperature controller is reduced, and the service life of the water heater is prolonged. The requirement for heat resistance of the whole machine is lowered, safety and reliability are improved, and cost is saved.
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Description

Technical Field

[0001] This application belongs to the technical field of electric heating equipment, and particularly relates to a water heating device. Background Technology

[0002] In household and commercial liquid heating equipment such as instant or storage-type electric water heaters, water dispensers, and coffee machines, the water heater is the core heating component, and its safety and reliability directly affect the overall safety of the machine. To prevent overheating of the heater due to abnormal water flow, control circuit failure, or dry burning, which could lead to structural deformation, smoke, or even fire, relevant safety standards (such as the IEC 60335 series standards) clearly require such heating devices to be equipped with a dual temperature protection mechanism, i.e., graded protection. This mechanism is usually implemented by connecting an automatic reset thermostat (primary protection) and a manual reset thermostat (secondary protection) in series in the power circuit: the primary thermostat has a lower trigger temperature (KTz), which can cut off the power supply at the initial stage of abnormal temperature rise and automatically reset after the temperature drops back to a safe range; the secondary thermostat has a higher trigger temperature (KTs), which requires manual intervention to reset once triggered, providing ultimate safety assurance when the primary protection fails. To ensure the effectiveness of graded protection, the standard also stipulates that a sufficient temperature difference must be maintained between KTs and KTz (i.e., KTs−KTz≥ΔTmin) to avoid falsely triggering of secondary protection when primary protection is working normally.

[0003] However, in such traditional heaters, both thermostats are installed in the middle area of ​​the heating element, with the automatic reset thermostat located on the outlet side. Because the outlet temperature is significantly higher than the inlet temperature during heating, while the temperature in the middle section where the thermostat is located is higher than the inlet temperature but lower than the outlet temperature, this layout results in a higher ambient temperature for the automatic reset thermostat. To prevent it from malfunctioning due to localized high temperatures during normal operation, designers have to increase the KTz setting. Limited by the minimum temperature difference ΔTmin requirement, increasing KTz directly leads to a corresponding increase in KTs. This not only forces the use of higher-temperature-resistant structural materials (such as high-temperature engineering plastics or flame-retardant components), significantly increasing manufacturing costs, but also makes the entire heater more prone to reaching the material's thermal deformation or decomposition temperature under extreme conditions, increasing safety hazards. Especially in uncontrolled heating scenarios such as dry burning, if the primary thermostat fails, and the secondary thermostat triggers at an excessively high temperature, the heating duration is prolonged, leading to a large accumulation of heat and a rapid rise in overall temperature, resulting in a higher risk of fire. Utility Model Content

[0004] The main objective of this application is to provide a heating device that, by setting a primary thermostat and a secondary thermostat at the water inlet and outlet of the heating device respectively, utilizes the temperature gradient naturally formed by the water flow to reduce the trigger temperature of the dual thermostats while ensuring a certain temperature difference. This achieves the technical effects of graded rapid protection, reducing the overall temperature resistance requirements of the device, and saving costs.

[0005] This application achieves the above-mentioned objective through the following technical solution: A heating device includes a heating component, a first thermostat, and a second thermostat. The heating component includes an outer tube and a heating tube penetrating the interior of the outer tube. An inlet and an outlet are respectively provided near both ends of the outer tube. A first mounting platform and a second mounting platform are provided on the section of the outer tube between the inlet and the outlet. The first mounting platform is located near the inlet, and the second mounting platform is located near the outlet. The first thermostat has a first trigger temperature, and the second thermostat has a second trigger temperature, which is greater than the first trigger temperature. The first thermostat is mounted on the first mounting platform, and the second thermostat is mounted on the second mounting platform.

[0006] Furthermore, a closed flow channel is formed between the outer tube and the heating tube, and the water inlet and the water outlet are connected to the flow channel.

[0007] Furthermore, the cross-sectional structure of both the first mounting platform and the second mounting platform includes a platform portion and an arc portion that are opposite each other, as well as a first protrusion and a second protrusion connecting the platform portion and the arc portion; the first temperature controller and the second temperature controller are mounted on the platform portion.

[0008] Furthermore, the platform portion is fitted to the outer peripheral surface of the heating tube.

[0009] Furthermore, an opening is formed between the inner wall of the first protrusion and the inner wall of the second protrusion and the inner wall of the heating tube to facilitate water flow.

[0010] Furthermore, the two ends of the heating tube extend beyond the corresponding two ends of the outer tube, and terminal A and terminal B are provided at the extended ends; terminal A and terminal B are respectively electrically connected to the neutral wire and the live wire of the power supply to form an electrical circuit, and the first thermostat and the second thermostat are connected in series in the electrical circuit.

[0011] Furthermore, the first temperature controller is an automatic reset temperature controller, and the second temperature controller is a manual reset temperature controller or a thermal fuse.

[0012] Furthermore, the temperature sensing surfaces of the first and second temperature controllers are fitted together with the outer wall of the heating tube.

[0013] Furthermore, a thermally conductive silicone grease or a metal gasket is provided between the temperature-sensing surface and the first mounting platform or the second mounting platform.

[0014] Furthermore, both the first thermostat and the second thermostat are fitted with clamps around the periphery of the first mounting platform and the second mounting platform, respectively.

[0015] Compared with the prior art, the beneficial effects of the heating device of this application are as follows: by arranging the primary thermostat in the low-temperature zone at the water inlet and the secondary thermostat in the high-temperature zone at the water outlet, the axial temperature gradient formed by the water flow is cleverly utilized, so that the primary protection can work reliably at a lower trigger temperature, and the setting temperature of the secondary protection can also be reduced. Thus, while meeting the safety specifications, the overall requirements for the temperature resistance of structural components are reduced, saving costs. When faults such as dry burning occur, because the trigger temperature of the primary thermostat is selected to be lower, the primary protection can respond more quickly and cut off the circuit, effectively suppressing the temperature rise of the whole machine, avoiding false tripping of the secondary protection, and realizing reliable graded overheat protection. Attached Figure Description

[0016] Figure 1 This is a three-dimensional structural diagram of an embodiment of this application;

[0017] Figure 2 This is a cross-sectional structural diagram of an embodiment of this application;

[0018] Figure 3 This is a schematic diagram of the vertical cross-sectional structure of the outer tube at the first mounting platform in an embodiment of this application;

[0019] Figure 4 This is a schematic diagram of the vertical cross-sectional structure at the second mounting platform according to an embodiment of this application;

[0020] Figure 5 This is a schematic diagram of the heating temperature when water flows normally inside the outer pipe in an embodiment of this application;

[0021] Figure 6 This is a schematic diagram of the abnormal heating temperature when the water inside the outer pipe is not flowing or there is no water in an embodiment of this application.

[0022] The numbers in the diagram represent:

[0023] 100 - Heating device;

[0024] 1-Heating component, 11-Outer tube, 111-First mounting platform, 1111-Platform section, 1112-Arc section, 1113-First protrusion, 1114-Second protrusion, 1115-Port, 112-Second mounting platform, 12-Heating tube, 121A, 121B-Terminals, 13-Flow channel, 14-Inlet, 15-Outlet;

[0025] 2-First thermostat; 3-Second thermostat; 4-Holding; 5-Screw; 6-Grounding plug. Detailed Implementation

[0026] Example 1:

[0027] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0028] In the description of this application, it should be understood that if terms such as "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential" appear, these terms indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0029] Furthermore, where the terms "first" and "second" appear, these terms are for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, where the term "multiple" appears, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0030] In this application, unless otherwise expressly specified and limited, the terms "installation," "connection," "joining," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise expressly limited. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0031] In this application, unless otherwise expressly specified and limited, the use of descriptions such as "above" or "below" the second feature indicates that the first and second features are in direct contact or indirect contact via an intermediate medium. Furthermore, "above," "on top of," and "over" the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. Similarly, "below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0032] It should be noted that if an element is referred to as being "fixed to" or "set on" another element, it can be directly on the other element or there may be an intervening element. If an element is considered to be "connected to" another element, it can be directly connected to the other element or there may be an intervening element. If so, the terms "vertical," "horizontal," "upper," "lower," "left," "right," and similar expressions used in this application are for illustrative purposes only and do not represent the only possible implementation.

[0033] Please refer to Figures 1-6 This embodiment is a heating device 100, which includes a heating component 1, a first thermostat 2 and a second thermostat 3.

[0034] The heating assembly 1 includes an outer tube 11 and a heating tube 12 penetrating the interior of the outer tube 11, with a closed flow channel 13 formed between the outer tube 11 and the heating tube 12. The outer tube 11 has an inlet 14 and an outlet 15 near both ends, respectively, communicating with the flow channel 13. The heating tube 12 extends beyond the corresponding ends of the outer tube 11, and terminals 121A and 121B are provided at the extended ends. The connection interfaces between the two ends of the outer tube 11 and the heating tube 12 are sealed using methods such as welding, sealing rings, or sealant.

[0035] In this embodiment, a first mounting platform 111 and a second mounting platform 112, which have been subjected to compression deformation, are provided on the section between the inlet 14 and the outlet 15 on the outer pipe 11. The first mounting platform 111 is located near the inlet 14, and the second mounting platform 112 is located near the outlet 15. The cross-sectional structure of the first mounting platform 111 and the second mounting platform 112 both include a platform portion 1111, an arc portion 1112, and a first protrusion 1113 and a second protrusion 1114 connecting the platform portion 1111 and the arc portion 1112.

[0036] In this embodiment, the platform portion 1111 is in close contact with the outer peripheral surface of the heating tube 12, ensuring a good thermal conductivity interface between the temperature sensing surface of the thermostat and the heating tube 12, thereby reducing thermal resistance and improving temperature sensing accuracy. The platform portion 1111 is used to install the first thermostat 2 or the second thermostat 3. A through-hole 1115 is formed between the inner wall of the first protrusion 1113 and the inner wall of the second protrusion 1114 and the inner wall of the heating tube 12 to facilitate water flow.

[0037] In this embodiment, the first temperature controller 2 is an automatic reset temperature controller, which is installed on the platform portion 1111 of the first mounting platform 111; the second temperature controller 3 is a manual reset temperature controller, which is installed on the platform portion 1111 of the second mounting platform 112. The temperature sensing surfaces of both the first temperature controller 2 and the second temperature controller 3 are in direct contact with the outer wall of the heating tube 12.

[0038] The first temperature controller 2 is an automatic reset temperature controller, referred to as a first-level protection in the heating device 100. It has a first trigger temperature and is connected in series in the electrical circuit. The first trigger temperature KTz is generally low. When the temperature of the outer tube 11 exceeds the first trigger temperature, the contacts inside the automatic reset temperature controller open, cutting off the circuit and causing the heating tube 12 to stop heating, thus playing a protective role. When the temperature of the outer tube 11 drops to a certain value below the first trigger temperature, the automatic reset temperature controller resumes conduction.

[0039] The second thermostat 3 is a manually reset thermostat or a thermal fuse, referred to as secondary protection in the heating device 100. It is connected in series with the first thermostat 2 in the electrical circuit, typically with one thermostat connected in series with each of the neutral and live wires. It has a second trigger temperature KTs, which is generally higher than the first trigger temperature KTz. When the temperature of the outer tube 11 exceeds the second trigger temperature KTs, the internal contacts of the second thermostat 3 open, cutting off the circuit and stopping the heating tube 12 from heating, thus providing protection. No matter how much the temperature of the outer tube 11 drops, it will not automatically restore conductivity; manual intervention is required to restore circuit conductivity.

[0040] In this embodiment, the terminals 121A and 121B at both ends of the heating tube 12 are electrically connected to the neutral wire and the live wire of the power supply, respectively (for example, terminal 121A is connected to the neutral wire and terminal 121B is connected to the live wire) to form an electrical circuit. The first thermostat 2 and the second thermostat 3 are connected in series in the electrical circuit. For example, the first thermostat 2 is connected in series on the neutral wire and the second thermostat 3 is connected in series on the live wire, or they are connected in reverse, depending on the actual wiring method, but the two are always connected in series.

[0041] In this embodiment, the first thermostat 2 and the second thermostat 3 have the same installation structure, and both are fastened to the periphery of the first installation platform 111 and the second installation platform 112 by means of a clamp 4 and screws 5.

[0042] In this embodiment, a grounding plug 6 is also attached to the outer peripheral surface of the outer tube 11 for grounding protection to prevent accidental electric shock.

[0043] As the water continuously absorbs the heat released by the heating pipe 12, a temperature gradient naturally forms along the axial direction of the heating pipe 12: the inlet end maintains a lower temperature due to the replenishment of cold water, while the outlet end has a higher temperature due to accumulated heat absorption. A schematic diagram of the heating temperature when water normally flows through the heating device 100 is shown below. Figure 5 As shown. Therefore, the actual temperature at the first installation platform 111 installed at the water inlet is significantly lower than the temperature at the second installation platform 112. Under these conditions, the temperature sensed by the first thermostat 2 is much lower than its trigger temperature KTz (e.g., set to 70℃), and it will not trigger a disconnection action; while the second thermostat 3, although in a higher temperature range, will not malfunction because KTs (e.g., set to 185℃) is higher than KTz and meets the graded protection requirement of KTs−KTz≥110℃. This layout allows the first-level protection thermostat to operate stably at a lower trigger temperature, avoiding the problem in traditional centralized installation methods where KTz has to be increased due to high-temperature environments.

[0044] When abnormal operating conditions such as dry burning, no water flow, or severely insufficient water flow occur, for example, due to water pump failure, inlet valve closure, or control system malfunction causing the heating element to remain powered, the heat generated by the heating element 12 cannot be effectively carried away by the water flow, causing the element temperature to rise rapidly. The abnormal heating temperature diagram when the water in the heating device 100 is not flowing or is empty is shown below. Figure 6As shown. At this time, no cooling water flows through the inlet 14. Since the first thermostat 2 is directly attached to the outer wall of the heating tube 12, its temperature sensing element can quickly respond to temperature changes. When the local temperature of the heating tube 12 reaches KTz (e.g., 70℃), the bimetallic strip inside the first thermostat 2 deforms due to heat, pushing the contacts to open, cutting off the main circuit power supply, and stopping heating. Since the power outage occurs in the early stage of temperature rise, the overall temperature rise is limited, especially since the outlet area has not accumulated enough heat, and the temperature at the second mounting platform 112 is still below KTs (e.g., 185℃). Therefore, the second thermostat 3 is not triggered and remains closed. This achieves the hierarchical protection logic of "first-level protection takes priority and second-level protection does not trigger falsely".

[0045] If the first thermostat 2 fails due to contact adhesion, mechanical jamming, or electrical short circuit caused by prolonged use, and cannot properly disconnect the circuit, the heating element 12 will continue to heat up. As heat is conducted and radiated along the axial direction, the outlet water temperature gradually increases. When the temperature at the second mounting platform 112 reaches KTs (e.g., 185℃), the internal mechanism of the second thermostat 3 activates, the contacts open, and the power supply is completely cut off. Because this thermostat is a manual reset type, it cannot automatically resume conduction even if the temperature subsequently drops. The user must press its external reset lever to reconnect the circuit, thus preventing the equipment from restarting without troubleshooting and providing a reliable backup protection mechanism.

[0046] This application conducted temperature controller trigger temperature selection and comparative testing for heating tubes of specific specifications, and the data is shown in Table 1.

[0047] Table 1

[0048]

[0049] As shown in the comparative test in Table 1 above, the overall solution using the heating device structure described in this embodiment, combined with a first-stage and second-stage temperature controller with lower trigger temperatures, significantly shortens the protection response time when the heater or its control circuit malfunctions and dry-burns, compared to the traditional solution. This results in a significant reduction in the peak temperature of the heater and surrounding components, effectively lowering the overall heat resistance requirements and improving safety and reliability.

[0050] In certain high-safety applications, the second thermostat 3 can be replaced with a thermal fuse. This thermal fuse is also mounted on the second mounting platform 112 and connected in series with the main circuit. When the temperature reaches its melting threshold (typically slightly below KTs, such as 165℃), the internal alloy wire melts, permanently disconnecting the circuit and preventing reset. This solution is suitable for critical applications where manual reset is not permitted, such as commercial water dispensers and medical water equipment, further enhancing the safety level.

[0051] To ensure efficient heat transfer between the thermostat and the heating element 12, this embodiment applies thermally conductive silicone grease or adds copper metal gaskets between the temperature-sensing bases of the first thermostat 2 and the second thermostat 3 and their corresponding mounting platforms to fill microscopic gaps and reduce contact thermal resistance. Simultaneously, the electrical leads of the thermostats are led out through pre-set sealed wiring holes on the outer tube. These wiring holes are embedded with fluororubber or silicone sealing rings that are resistant to temperatures above 200°C, ensuring electrical insulation performance and preventing moisture ingress that could cause short circuits or corrosion.

[0052] In summary, this application, by arranging the first thermostat 2 on the first mounting platform 111 at the water inlet and the second thermostat 3 on the second mounting platform 112 at the water outlet, fully utilizes the natural temperature gradient formed by the water flow direction, placing the primary protection device in the low-temperature zone. This allows its trigger temperature KTz to be set even lower, avoiding malfunctions during normal operation and reducing the secondary protection trigger temperature KTs while meeting the temperature difference requirements of safety regulations. This not only reduces the temperature resistance requirements for non-metallic structural components (such as plastic brackets, sealing rings, and terminal sheaths)—allowing the use of conventional engineering plastics with a UL94V-0 rating and a temperature resistance of 105℃ instead of special flame-retardant materials with a temperature resistance of over 130℃—significantly saving costs; simultaneously, under extreme faults such as dry burning, the rapid response of the primary protection effectively suppresses the highest temperature of the entire unit, preventing the water outlet temperature from reaching KTs and thus eliminating the need for secondary protection, verifying the effectiveness of graded protection and avoiding unnecessary shutdowns or manual resets. This solution does not require the addition of electronic control modules or complex logic judgments. It achieves reliable graded overheat protection that meets international safety standards through physical layout optimization alone, while also being simple in structure, economical in manufacturing, and safe in use.

[0053] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0054] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A heating device, comprising a heating assembly, a first thermostat, and a second thermostat, wherein the heating assembly includes an outer tube and a heating tube penetrating the interior of the outer tube, and an inlet and an outlet are respectively provided near both ends of the outer tube; characterized in that, The outer pipe is provided with a first installation platform and a second installation platform in the section between the inlet and the outlet; the first installation platform is located near the inlet, and the second installation platform is located near the outlet; the first thermostat has a first trigger temperature, and the second thermostat has a second trigger temperature, the second trigger temperature being greater than the first trigger temperature; the first thermostat is located on the first installation platform, and the second thermostat is located on the second installation platform.

2. The heating device as described in claim 1, characterized in that, A closed flow channel is formed between the outer tube and the heating tube, and the water inlet and the water outlet are connected to the flow channel.

3. The heating device as described in claim 1, characterized in that, Both the first mounting platform and the second mounting platform have cross-sectional structures including a platform portion and an arc portion that are opposite each other, as well as a first protrusion and a second protrusion connecting the platform portion and the arc portion; the first temperature controller and the second temperature controller are mounted on the platform portion.

4. The heating device as described in claim 3, characterized in that, The platform portion is fitted to the outer peripheral surface of the heating tube.

5. The heating device as described in claim 3, characterized in that, The inner walls of the first protrusion and the second protrusion are each provided with an opening to facilitate water flow between them and the inner wall of the heating tube.

6. The heating device as described in claim 1, characterized in that, The heating tube extends beyond the corresponding ends of the outer tube at both ends, and terminal A and terminal B are provided at the extended ends; terminal A and terminal B are respectively electrically connected to the neutral wire and the live wire of the power supply to form an electrical circuit, and the first thermostat and the second thermostat are connected in series in the electrical circuit.

7. The heating device as described in claim 1, characterized in that, The first temperature controller is an automatic reset temperature controller, and the second temperature controller is a manual reset temperature controller or a thermal fuse.

8. The heating device as claimed in claim 1, characterized in that, The sensing surfaces of the first and second temperature controllers are fitted together with the outer wall of the heating tube.

9. The heating device as described in claim 8, characterized in that, Thermal grease or a metal pad is provided between the temperature sensing surface and the first or second mounting platform.

10. The heating device as claimed in claim 1, characterized in that, Both the first and second temperature controllers are fitted with clamps around the periphery of the first and second mounting platforms, respectively.