Method for measuring and calculating heat conductivity coefficient of insulating heat-conducting filler adaptive to cylindrical electric heating element
By constructing a simplified heat conduction model and calculating steady-state heat conduction formulas, the problems of disassembly and high cost in the calculation of thermal conductivity of electric heating elements in the prior art are solved, realizing fast and accurate thermal conductivity calculation and supporting the thermal design optimization of electric heating elements.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHENJIANG DONGFANG ELECTRIC HEATER
- Filing Date
- 2026-01-26
- Publication Date
- 2026-05-08
AI Technical Summary
Existing methods for calculating the thermal conductivity of insulating thermally conductive fillers suffer from problems such as disassembling heating elements, long testing cycles, high costs, and limited data reference value, making them unsuitable for the rapid design needs of extreme industrial scenarios such as aerospace and ultra-high temperature gas heating.
A method for calculating the thermal conductivity of insulating thermally conductive filler adapted to cylindrical electric heating elements is provided. By constructing a simplified heat conduction model, collecting relevant parameters, and using the steady-state heat conduction formula to calculate the thermal conductivity, the method avoids disassembly and the use of high-precision equipment.
It enables rapid, accurate, and low-cost thermal conductivity calculation, is applicable to various industrial scenarios, meets engineering accuracy requirements, and supports thermal design optimization of heating elements.
Smart Images
Figure CN121997594A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of electric heating element design technology, specifically relating to a method for calculating the thermal conductivity of insulating thermally conductive filler adapted to cylindrical electric heating elements. Background Technology
[0002] In extreme industrial scenarios such as aerospace and ultra-high temperature gas heating, the performance of the electric heating element, as the core energy conversion and transfer component, directly determines the operational reliability, energy efficiency, and adaptability to extreme environments of the equipment. Electric heating elements generally adopt an integrated encapsulation structure of heating element-insulating thermally conductive filler-electric heating element sleeve. Among them, the insulating thermally conductive filler is the heat transfer bridge and the core of insulation protection. Its thermal conductivity directly affects the heat conversion efficiency, temperature field uniformity, and thermal response speed, and is also a key parameter to ensure structural stability under extreme working conditions.
[0003] Existing methods for calculating the thermal conductivity of insulating and thermally conductive fillers have several drawbacks: 1. Traditional destructive testing requires disassembling and slicing the heating element, resulting in the scrapping of expensive specimens and a lengthy testing cycle (several days to weeks), severely hindering equipment development and iteration; 2. High-precision testing equipment such as laser flare meters is expensive to purchase and maintain (several million yuan per unit), has extremely poor accessibility, and requires testing in an ideal laboratory environment, which is out of sync with the complex working conditions of heating elements, such as high temperature, vibration, and media corrosion. Furthermore, it has stringent requirements for sample morphology and dimensional accuracy, making it difficult to match the heterogeneous and irregular state of fillers in actual applications, thus limiting the reference value of test data. Therefore, we propose a method for calculating the thermal conductivity of insulating and thermally conductive fillers suitable for cylindrical heating elements. Summary of the Invention
[0004] The purpose of this invention is to provide a method for calculating the thermal conductivity of insulating thermally conductive filler adapted to cylindrical electric heating elements, so as to solve the problems mentioned in the background art.
[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for calculating the thermal conductivity of insulating thermally conductive filler adapted to cylindrical electric heating elements, comprising the following steps: S1, electric heating element structure construction: constructing a simplified heat conduction model that fits the actual configuration of the cylindrical electric heating element; S2, electric heating element parameter acquisition: acquiring relevant parameters required for calculation, including the structural parameters of the electric heating element, the operating parameters of the heating element, and the measured temperature parameters of the outer wall of the electric heating element sleeve, providing complete data input for subsequent calculations; S3, electric heating element sleeve inner wall temperature calculation: based on the steady-state heat conduction calculation formula of the cylindrical wall of the electric heating element, substituting the relevant parameters acquired in step S2, calculating the inner wall temperature of the electric heating element sleeve; S4, insulating thermally conductive filler thermal conductivity calculation: based on the steady-state heat conduction formula adapted to the insulating thermally conductive filler filling structure, combining the relevant parameters of the heating element acquired in step S2 and the inner wall temperature of the electric heating element sleeve calculated in step S3, calculating the thermal conductivity of the insulating thermally conductive filler.
[0006] Preferably, in step S1, the process of constructing the simplified heat conduction model is as follows: constructing the geometric boundaries and structural relationships of the heating element, the insulating thermally conductive filler layer, and the electric heating element sleeve; simplifying the heating element into a cylinder; simplifying the electric heating element sleeve into a cylindrical structure with an inner diameter, an outer diameter, and a total length; and the filling area between the heating element and the electric heating element sleeve is the insulating thermally conductive filler layer whose thermal conductivity is to be measured.
[0007] Preferably, in step S2, the structural parameters of the heating element include the thermal conductivity, inner diameter, outer diameter, total length, and equivalent radius of the heating element sleeve; the operating parameters of the heating element include the rated heating power and operating temperature of the heating element.
[0008] Preferably, in step S3, the steady-state heat conduction calculation formula of the cylindrical wall is a calculation formula based on the heat conduction of the metal sleeve, and the specific expression is shown in formula (1): (1);
[0009] Where T1 represents the inner wall temperature of the heating element sleeve; T2 represents the measured outer wall temperature of the heating element sleeve; W represents the rated heating power of the heating element; R1 represents the inner diameter of the heating element sleeve; R2 represents the outer diameter of the heating element sleeve; ln represents the natural logarithm function; H represents the total length of the heating element sleeve. This indicates the thermal conductivity of the heating element sheath.
[0010] Preferably, in step S4, the steady-state heat conduction formula of the adapted insulating and thermally conductive filler filling structure is specifically expressed as shown in formula (2): (2); in, Indicates the thermal conductivity of the insulating and thermally conductive filler; R0 represents the difference between the operating temperature of the heating element and the temperature of the inner wall of the heating element's sleeve; R0 represents the equivalent radius of the heating element.
[0011] Preferably, the formula for calculating the difference between the operating temperature of the heating element and the inner wall temperature of the heating element sleeve is as shown in formula (3): (3); Where T0 represents the operating temperature of the heating element.
[0012] Compared with existing technologies, the advantages of this invention are: 1. Convenient and efficient operation: It is compatible with various cylindrical heating elements, is not limited by the type of internal insulating and thermally conductive filler, and does not require disassembly or slicing of the heating element. Calculations can be completed simply through conventional parameter measurement and formula calculation. The process is simple and has a low operating threshold, perfectly matching the rapid design and parameter iteration pace of industrial R&D. 2. Economical and controllable cost: It eliminates the need to purchase high-precision testing equipment costing millions of yuan, such as laser flare meters, and also eliminates the need to build complex testing fixtures, saving the high costs of equipment purchase, maintenance, calibration, and sample pretreatment. At the same time, the calculation cycle is short, and it can be directly embedded into the conventional design chain of heating elements, significantly reducing the time and material costs of early-stage R&D and solution iteration. 3. Strong functional adaptability: It can quickly and accurately calculate the thermal conductivity of various insulating and thermally conductive fillers in different cylindrical electric heating elements, providing data support for thermal efficiency assessment; it can also use the calculation results to guide the design of parameters such as the equivalent radius and layout position of the core heating element, realizing the collaborative optimization of the entire process of electric heating element thermal design, and adapting to various industrial scenarios such as aerospace and ultra-high temperature gas heating; 4. Reliable calculation results: After simulation verification and actual application testing under multiple different working conditions, the absolute value of the error between the thermal conductivity of the insulating and thermally conductive filler calculated by this method and the professional simulation data and actual working condition data does not exceed 15%, which fully meets the engineering accuracy requirements of electric heating element thermal design in industrial scenarios and has extremely high industrial practical value. Attached Figure Description
[0013] Figure 1 This is a simplified heat conduction model diagram of the electrothermal element of the present invention; Figure 2 This is a schematic diagram of the steady-state heat conduction parameters of the cylindrical wall according to the present invention; Figure 3 This is a schematic diagram of the simulation model structure of the present invention; Figure 4 This is a schematic diagram of the temperature distribution of the resistance wire in the simulation model of this invention; Figure 5 This is a schematic diagram of the temperature distribution in the cross-section of the simulation model of the present invention; Figure 6 This is a schematic diagram of the temperature distribution structure of the simulated sleeve outer wall of the present invention.
[0014] In the diagram: 1. Heating element; 2. Insulating and thermally conductive filler layer; 3. Heating element sleeve. Detailed Implementation
[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0016] Please see Figures 1-6 The present invention provides a method for calculating the thermal conductivity of insulating thermally conductive filler for adaptable cylindrical electric heating elements, comprising the following steps: S1, Electric heating element structure construction: Constructing a simplified heat conduction model that fits the actual configuration of the cylindrical electric heating element. The process of constructing the simplified heat conduction model is as follows: Constructing the geometric boundaries and structural associations of the heating element 1, the insulating thermally conductive filler layer 2, and the electric heating element sleeve 3, simplifying the heating element as a cylinder, and simplifying the electric heating element sleeve as a cylindrical structure with an inner diameter, an outer diameter, and a total length. The filling area between the heating element and the electric heating element sleeve is the insulating thermally conductive filler layer for which the thermal conductivity is to be calculated; S2, Electric heating element parameter acquisition: Acquiring the relevant parameters required for the calculation, including The structural parameters of the heating element, the working parameters of the heating element, and the measured temperature parameters of the outer wall of the heating element sleeve provide complete data input for subsequent calculations; the structural parameters of the heating element include the thermal conductivity, inner diameter, outer diameter, total length, and equivalent radius of the heating element sleeve; the working parameters of the heating element include the rated heating power and working temperature of the heating element; S3, Calculation of the inner wall temperature of the heating element sleeve: Based on the steady-state heat conduction calculation formula of the cylindrical wall of the heating element, the relevant parameters collected in step S2 are substituted to calculate the inner wall temperature of the heating element sleeve; the steady-state heat conduction calculation formula of the cylindrical wall is the calculation formula based on the heat conduction of the metal sleeve, and the specific expression is shown in formula (1): (1); where T1 represents the inner wall temperature of the heating element sleeve; T2 represents the measured outer wall temperature of the heating element sleeve; W represents the rated heating power of the heating element; R1 represents the inner diameter of the heating element sleeve; R2 represents the outer diameter of the heating element sleeve; ln represents the natural logarithm function; H represents the total length of the heating element sleeve. S4. Calculation of thermal conductivity of insulating thermally conductive filler: Based on the steady-state heat conduction formula of the adapted insulating thermally conductive filler filling structure, combined with the relevant parameters of the heating element collected in step S2 and the inner wall temperature of the heating element sleeve obtained in step S3, the thermal conductivity of the insulating thermally conductive filler is calculated; The specific expression of the steady-state heat conduction formula of the adapted insulating thermally conductive filler filling structure is shown in formula (2): (2); where, Indicates the thermal conductivity of the insulating and thermally conductive filler; R0 represents the difference between the operating temperature of the heating element and the temperature of the inner wall of the heating element's sheath; R0 represents the equivalent radius of the heating element; the formula for calculating the difference between the operating temperature of the heating element and the temperature of the inner wall of the heating element's sheath is shown in formula (3): (3); where T0 represents the operating temperature of the heating element.
[0017] This embodiment provides a specific application: calculating the thermal conductivity of the insulating thermally conductive filler inside the sheath of an industrial electric heating element, providing a basis for evaluating the element's thermal efficiency.
[0018] 1. Obtain parameters
[0019] The total diameter (H) of the heating element is 1m, the inner radius (R1) is 0.029m, the outer radius (R2) is 0.032m, and the thermal conductivity of the stainless steel heating element is... =15W / (m・K), equivalent radius of resistance wire winding R0=0.0064m, heating power of resistance wire W=7000W, working temperature of resistance wire T0=1300℃, measured temperature of heating tube outer wall T2=500℃;
[0020] 2. Calculation of the inner wall temperature of the casing
[0021] Substituting the parameters into the formula for calculating the inner wall temperature of the casing derived from engineering practice in this invention, we obtain: ;
[0022] 3. Calculation of thermal conductivity of insulating and thermally conductive filler
[0023] Substituting the above data into the inverse relationship of the thermal conductivity of the insulating thermally conductive filler derived in this invention, the thermal conductivity of the insulating thermally conductive filler inside the heating element sleeve can be obtained: The thermal conductivity range is consistent with that of electrical-grade insulating thermally conductive fillers, verifying the effectiveness of the method of the present invention.
[0024] A comparison of the theoretical calculation and simulation results of the thermal conductivity of the insulating thermally conductive filler layer in the heating element sleeve according to the above embodiment: The purpose of this embodiment is to verify the engineering applicability of the theoretical calculation method for the thermal conductivity of the insulating thermally conductive filler layer in the heating element sleeve. By comparing the simulation data with the theoretical calculation results, the accuracy level of the theoretical model is clarified. Figure 3-6 First, a simplified model is set up, and the heating power of the heating element and the thermal conductivity of the insulating thermally conductive filler are given. The outer wall temperature of the heating element under corresponding operating conditions is obtained through calculation. By changing the radius of the heating element and the thermal conductivity of the thermally conductive filler, the outer wall temperature of the heating element under different operating conditions is obtained. Substituting parameters such as the outer wall temperature of the heating element, the heating power of the heating element, and the radius of the heating element into the calculation method, the theoretical calculated values of the insulating thermally conductive filler and the inner wall temperature of the heating element are obtained. The error is analyzed by comparing with the simulation. ; As can be seen from the comparison table, the calculation results of the method used in this invention under different working conditions have an error of about ±15% compared with the simulation set value, which has reference value for engineering applications.
[0025] This invention offers the following significant advantages: 1. Convenient and efficient operation: It is compatible with various cylindrical heating elements, is not limited by the type of internal insulating and thermally conductive filler, and requires no destructive processing such as disassembly or slicing of the heating element. Calculations can be completed simply through conventional parameter measurement and formula calculation. The process is simple, with a low operational threshold, perfectly matching the rapid design and parameter iteration pace of industrial R&D. 2. Economical and controllable cost: It eliminates the need to purchase high-precision testing equipment costing millions of yuan, such as laser flare meters, and avoids the need to build complex testing fixtures, saving the high costs of equipment procurement, maintenance, calibration, and sample pretreatment. Simultaneously, the calculation cycle is short, allowing direct integration into the conventional design process of heating elements, significantly reducing the time cost and material waste in early-stage R&D and solution iteration. 3. Strong functional adaptability: It can quickly and accurately calculate the thermal conductivity of various insulating and thermally conductive fillers in different cylindrical electric heating elements, providing data support for thermal efficiency assessment; it can also use the calculation results to guide the design of parameters such as the equivalent radius and layout position of the core heating element, realizing the collaborative optimization of the entire process of electric heating element thermal design, and adapting to various industrial scenarios such as aerospace and ultra-high temperature gas heating; 4. Reliable calculation results: After simulation verification and actual application testing under multiple different working conditions, the absolute value of the error between the thermal conductivity of the insulating and thermally conductive filler calculated by this method and the professional simulation data and actual working condition data does not exceed 15%, which fully meets the engineering accuracy requirements of electric heating element thermal design in industrial scenarios and has extremely high industrial practical value.
[0026] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A method for calculating the thermal conductivity of insulating and thermally conductive filler adapted to cylindrical electric heating elements, characterized in that, Includes the following steps: S1. Construction of heating element structure: Construct a simplified heat conduction model that fits the actual configuration of the cylindrical heating element; S2. Electric heating element parameter acquisition: Collect and obtain the relevant parameters required for the calculation, including the structural parameters of the electric heating element, the working parameters of the heating element, and the measured temperature parameters of the outer wall of the electric heating element sleeve, to provide complete data input for subsequent calculations; S3. Calculation of the inner wall temperature of the heating element sleeve: Based on the steady-state heat conduction calculation formula of the cylindrical wall of the heating element, the relevant parameters collected in step S2 are substituted to calculate the inner wall temperature of the heating element sleeve. S4. Calculation of thermal conductivity of insulating and thermally conductive filler: Based on the steady-state heat conduction formula of the filling structure of the insulating and thermally conductive filler, combined with the relevant parameters of the heating element collected in step S2 and the inner wall temperature of the heating element sleeve obtained in step S3, the thermal conductivity of the insulating and thermally conductive filler is calculated.
2. The method for calculating the thermal conductivity of the insulating thermally conductive filler adapted to a cylindrical electric heating element according to claim 1, characterized in that: In step S1, the process of constructing the simplified heat conduction model is as follows: The geometric boundaries and structural relationships of the heating element, the insulating thermally conductive filler layer, and the heating element sleeve are constructed. The heating element is simplified as a cylinder, and the heating element sleeve is simplified as a cylindrical structure with an inner diameter, an outer diameter, and a total length. The filling area between the heating element and the heating element sleeve is the insulating thermally conductive filler layer whose thermal conductivity is to be measured.
3. The method for calculating the thermal conductivity of the insulating thermally conductive filler for adapting cylindrical electric heating elements according to claim 2, characterized in that: In step S2, the structural parameters of the heating element include the thermal conductivity, inner diameter, outer diameter, total length, and equivalent radius of the heating element sleeve. The operating parameters of the heating element include its rated heating power and operating temperature.
4. The method for calculating the thermal conductivity of the insulating and thermally conductive filler for adapting cylindrical electric heating elements according to claim 3, characterized in that: In step S3, the steady-state heat conduction calculation formula of the cylindrical wall is a calculation formula based on the heat conduction of the metal sleeve, and the specific expression is shown in formula (1): （1）； Where T1 represents the temperature of the inner wall of the heating element sleeve; T2 represents the measured temperature of the outer wall of the heating element sleeve; W represents the rated heating power of the heating element; R1 represents the inner diameter of the heating element sleeve; R2 represents the outer diameter of the heating element sleeve; ln represents the natural logarithm function; H represents the total length of the heating element sleeve; This indicates the thermal conductivity of the heating element sheath.
5. The method for calculating the thermal conductivity of the insulating thermally conductive filler for adapting cylindrical electric heating elements according to claim 4, characterized in that: In step S4, the specific expression of the steady-state heat conduction formula of the adapted insulating and thermally conductive filler filling structure is shown in formula (2): （2）； in, Indicates the thermal conductivity of the insulating and thermally conductive filler; This indicates the difference between the operating temperature of the heating element and the temperature of the inner wall of the heating element's sheath. R0 represents the equivalent radius of the heating element.
6. The method for calculating the thermal conductivity of the insulating thermally conductive filler for adapting cylindrical electric heating elements according to claim 5, characterized in that: The formula for calculating the difference between the operating temperature of the heating element and the inner wall temperature of the heating element sleeve is shown in formula (3): （3）； Where T0 represents the operating temperature of the heating element.