A design method for resistance heating graphite electrode

Abstract

The present invention discloses a design method for a resistance-heating graphite electrode, establishes a one-dimensional heat conduction equation analysis method for the graphite electrode, and simultaneously considers the thermal conductivity influence of the graphite electrode caused by the internal heat source generated by the graphite electrode under the working current. Through deductive analysis, the length and inner and outer diameter structural optimization parameters that affect the heat loss of the graphite electrode are obtained, thereby optimizing the graphite electrode design, optimizing the thermal field design, and optimizing the energy loss of the equipment.

Description

Technical Field

[0001] The invention belongs to the technical field of single crystal furnaces, in particular to the field of structural design of resistance-heating graphite electrodes in single crystal furnaces. Background Art

[0002] In a high-temperature crystal growth furnace with resistance heating, graphite parts are used for heating to achieve the temperature distribution requirements of the thermal field. In the graphite heating system, the graphite electrode is the main heating and connecting component. A graphite heater is connected to the high-temperature end of the graphite electrode, and a copper electrode is connected to the other end of the graphite electrode. Cooling water is passed through the copper electrode, and the temperature is relatively low, forming the cold end of the graphite electrode. However, the internal heat source is generated by the working current inside the graphite electrode, and the heat from the high-temperature end is continuously conducted to the low-temperature end, causing heat loss in the entire thermal field, affecting the overall performance of the equipment. Therefore, the optimization of the graphite electrode structure design and the innovation of the method are crucial to the design of the entire thermal field and the energy loss of the equipment. However, the existing technology lacks an optimal structural optimization design scheme for the heat loss caused by the graphite electrode, and at the same time, the optimal heat loss of the graphite electrode heat conduction, and the corresponding optimal graphite electrode length and outer diameter structural parameters and design methods have not been established.

[0003] For example, a new technical solution is needed to solve the above technical problems. Summary of the Invention

[0004] Purpose of the invention: The present invention provides a method for designing a resistance heating graphite electrode, which is used to solve the technical problem of how to design the optimal values ​​of structural parameters such as the length and outer diameter of the graphite electrode when different structures such as the length and outer diameter of the graphite electrode will cause different degrees of heat loss.

[0005] Technical solution: To solve the above problems, the present invention can adopt the following technical solutions:

[0006] A method for designing a resistance heating graphite electrode comprises the following steps:

[0007] (1) Design the resistance heating graphite electrode into a cylinder;

[0008] (2) Establish the graphite electrode parameters: the outer diameter of the graphite electrode cross section is D2; the inner diameter of the graphite electrode cross section is D1; ​​the cross-sectional area of ​​the graphite electrode is s; the length of the graphite electrode is l; the working current of the graphite electrode is I; the temperature of the hot end of the graphite electrode is t2; the temperature of the cold end of the graphite electrode is t1; the thermal conductivity of the graphite material is λ; the resistivity of the graphite material is ρ; the uniform internal heat element is φ1; the heat conduction flow at the hot end is Q1; the heat conduction flow at the cold end is Q2; when the graphite electrode is provided with an inner channel running through the cylinder axially, the inner diameter of the graphite electrode cross section is D1>0, and when the graphite electrode is a solid structure, D1=0;

[0009] Among them, D1, D2, s, and l are parameters that need to be optimized; I, t2, t1, λ, ρ, and φ1 are known preset parameters; Q1 and Q2 are parameters that need to be analyzed to obtain results; the hot end and the cold end are the two ends of the resistance heating graphite electrode respectively;

[0010] (3) In actual graphite electrode operation, when the hot end position neither absorbs nor dissipates heat, that is, when Q1 = 0, the most ideal state of the graphite electrode is reached. In this state, the mathematical formula and Get the relationship between l, s, D2, and D1, and know that any one of them can be used to obtain the optimal solution of other parameters that need to be optimized through the m formula

[0011] (4) Based on the optimal structural parameters of the designed cylindrical graphite electrode, graphite electrodes with different cross-sectional shapes were obtained according to the principle of unchanged cross-sectional area and length. The resistance value and thermal conductivity of the graphite electrode after cross-sectional shape transformation were no different from those of the designed cylindrical graphite electrode.

[0012] Beneficial effects: Compared with the prior art, the present invention solves the problem of achieving the optimal heat loss result for a one-dimensional heat-conducting graphite electrode containing an internal heat source while meeting production requirements. The optimal values ​​of structural parameters such as the length and outer diameter of the graphite electrode are obtained. This avoids excessive waste of heat energy and makes the structural design of the graphite electrode more scientific, reasonable and well-founded. Compared with the prior art, the present invention obtains the optimal heat loss of the graphite electrode under the influence of the internal heat source of working current heat generation through analytical calculation, as well as the relationship between the optimal electrode length and inner and outer diameters under the corresponding optimal structure, which plays a key guiding role in the structural design of the thermal field. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a schematic diagram of the graphite electrode structure and heat conduction in the present invention. DETAILED DESCRIPTION

[0014] Please combine Figure 1 Figure 2 shows the structure of the designed resistive heating graphite electrode (or graphite heater). The resistive heating graphite electrode is designed as a cylinder. The graphite electrode parameters include: outer diameter of the graphite electrode cross section D2; inner diameter of the graphite electrode cross section D1; cross-sectional area s; length l; operating current I; hot-end temperature t2; cold-end temperature t1; thermal conductivity λ of the graphite material; resistivity ρ of the graphite material; uniform internal heat element φ1; hot-end heat flow Q1; cold-end heat flow Q2. When the graphite electrode has an inner channel running axially through the cylinder, the inner diameter of the graphite electrode cross section D1 is greater than 0. When the graphite electrode is solid, D1 is equal to 0.

[0015] Where D1, D2, s, and l are the parameters to be optimized; I, t2, t1, λ, ρ, and φ1 are known preset parameters; Q1 and Q2 are the parameters to be analyzed; the hot end and cold end are the two ends of the resistive heating graphite electrode. The boundary conditions for the cold and hot ends are x = 0, t = t1 for the cold end and x = l, t = t2 for the hot end; x is the x-axis with the cold end as the origin.

[0016] Because the graphite electrode has an axisymmetric structure and a uniform distribution of heat, a plane can be cut along the axial direction for analysis. A stable operating current flows through the heated graphite electrode, generating a uniform internal heat source. Heat is conducted from the high-temperature area on the right to the low-temperature area on the left, and the overall temperature distribution can be inferred through cross-sectional analysis.

[0017] From the one-dimensional steady-state heat conduction of a uniform internal heat source, the corresponding differential equation can be obtained:

[0018]

[0019] Integrating the above formula twice yields:

[0020]

[0021] Substituting the boundary conditions of the cold end and the hot end into x = 0, t = t1; x = l, t = t2, the temperature distribution formula of the graphite electrode can be obtained as follows:

[0022]

[0023] This formula is a quadratic equation about temperature with inherent heat source. At the same time, the temperature change rate formula can be obtained from the temperature distribution formula as follows:

[0024]

[0025] At the hot end of the graphite electrode at position x=l:

[0026] Substituting the boundary condition x=l of the hot end of the graphite electrode into the temperature change rate formula, the following formula can be obtained:

[0027]

[0028] By transforming the above formula, the heat flow Q1 at the hot end can be obtained as:

[0029]

[0030] After sorting, you can get

[0031]

[0032] because So the internal heat source can be obtained as:

[0033]

[0034] Substituting the internal heat source formula into Q1, we can get

[0035]

[0036] make So the above formula can be simplified to:

[0037]

[0038] In actual graphite electrode operation, when the hot end position neither absorbs nor dissipates heat, that is, when Q1 = 0, the most ideal state of the graphite electrode is reached. By solving the Q1 formula, we can get:

[0039]

[0040] The relationship between the length l and cross-sectional area s of the graphite electrode can be obtained through the m formula. Therefore, the relationship between the graphite electrode length l and the outer diameter D2 and inner diameter D1 of the graphite electrode can be obtained. It is known that any one of them can be solved by the m formula to obtain its optimal solution.

[0041] At the cold end of the graphite electrode at x=0:

[0042] Substituting the boundary condition x=0 at the hot end of the graphite electrode into the temperature change rate formula, we can obtain the following formula:

[0043]

[0044] By transforming the above formula, the heat flow Q2 at the cold end can be obtained as:

[0045]

[0046] So we can get

[0047]

[0048] because So the internal heat source can be obtained as:

[0049]

[0050] Substituting the internal heat source formula into Q2 yields

[0051]

[0052] make So the above formula can be simplified to:

[0053]

[0054] By comparing the hot end heat flow formula: and the cold end heat flow formula It is not difficult to find that Q1 and Q2 are the two solutions of a quadratic equation, and from the results we can see that is the heat flow value of one-dimensional heat conduction without heat source, and It is 1 / 2 times of the internal heat source. Therefore, from the structural form, it can be confirmed that this method can obtain the optimal graphite electrode structure and the optimal heat flow loss.

[0055] Therefore, this method can be used to obtain the optimal graphite electrode structure and heat loss. At the same time, the influencing results can be parameterized to produce the following table for later design use:

[0056] Electrode parameters

[0057]

[0058] The electrode heat dissipation model is calculated according to the one-dimensional steady-state heat conduction with internal heat source, and the optimal electrode area calculation method

[0059] Based on the optimal structural parameters of the designed cylindrical graphite electrode, graphite electrodes with different cross-sectional shapes were obtained according to the principle of unchanged cross-sectional area and length. The resistance value and thermal conductivity of the graphite electrode after cross-sectional shape transformation are no different from those of the designed cylindrical graphite electrode.

[0060] There are many methods and approaches to implement the technical solution of the present invention. The above is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications should also be considered within the scope of protection of the present invention. Any components not specified in this embodiment may be implemented using existing technologies.

Claims

1. A method for designing a resistance heating graphite electrode, characterized in that: The following steps are involved: (1) The resistance heating graphite electrode is designed as a cylinder. (2) Establish the graphite electrode parameters: the outer diameter of the graphite electrode cross section is D2; the inner diameter of the graphite electrode cross section is D1; ​​the cross-sectional area of ​​the graphite electrode is s; the length of the graphite electrode is l; the working current of the graphite electrode is I; the temperature of the hot end of the graphite electrode is t2; the temperature of the cold end of the graphite electrode is t1; the thermal conductivity of the graphite material is λ; the resistivity of the graphite material is ρ; the uniform internal heat element is φ1; the heat conduction flow at the hot end is Q1; the heat conduction flow at the cold end is Q2; when the graphite electrode is provided with an inner channel running through the cylinder axially, the inner diameter of the graphite electrode cross section is D1>0, and when the graphite electrode is a solid structure, D1=0; Among them, D1, D2, s, and l are parameters that need to be optimized; I, t2, t1, λ, ρ, and φ1 are known preset parameters; Q1 and Q2 are parameters that need to be analyzed to obtain results; the hot end and the cold end are the two ends of the resistance heating graphite electrode respectively; (3) In actual graphite electrode operation, when the hot end position neither absorbs nor dissipates heat, that is, when Q1 = 0, the most ideal state of the graphite electrode is reached. In this state, the mathematical formula and Get the relationship between l, s, D2, and D1, and know that any one of them can be used to obtain the optimal solution of other parameters that need to be optimized through the m formula; (4) Based on the optimal structural parameters of the designed cylindrical graphite electrode, graphite electrodes with different cross-sectional shapes were obtained according to the principle of unchanged cross-sectional area and length. The resistance value and thermal conductivity of the graphite electrode after cross-sectional shape transformation were no different from those of the designed cylindrical graphite electrode.

2. The method for designing a resistance heating graphite electrode according to claim 1, wherein: The verification step is also included: the cold end heat conduction flow Q2 is calculated by the formula make So the above formula is simplified to: By comparing the hot end heat flow formula: and the cold end heat flow formula It is not difficult to find that Q1 and Q2 are the two solutions of a quadratic equation, and from the results we can see that is the heat flow value of one-dimensional heat conduction without heat source, and It is 1 / 2 times of the internal heat source; therefore, from the structural form, it is confirmed that the optimal graphite electrode structure and the optimal heat flow loss can be obtained through step (3).

3. The method for designing a resistance heating graphite electrode according to claim 2, wherein: In step (3), the corresponding differential equation is obtained from the one-dimensional steady-state heat conduction of the uniform internal heat source: Integrating the above formula twice yields: Substitute the boundary conditions of the cold end and the hot end into x = 0, t = t1; x = l, t = t2; the temperature distribution formula of the graphite electrode is: At the same time, the temperature change rate formula is obtained through the temperature distribution formula as follows:

4. The method for designing a resistance heating graphite electrode according to claim 3, wherein: In step (3), The method to obtain is: At the hot end of the graphite electrode, position x = l Substituting the boundary condition x=l of the hot end of the graphite electrode into the temperature change rate formula, the following formula can be obtained: By transforming the above formula, the heat flow Q1 at the hot end can be obtained as: After sorting, you can get because So the internal heat source can be obtained as: Substituting the internal heat source formula into Q1, we can get make So the above formula can be simplified to: When Q1=0, the graphite electrode reaches the most ideal state. By solving the Q1 formula, we can get:

5. The method for designing a resistance heating graphite electrode according to claim 2, wherein: In the verification step, The method to obtain is: Substituting the boundary condition x=0 at the hot end of the graphite electrode into the temperature change rate formula, we can obtain the following formula: By transforming the above formula, the heat flow Q2 at the cold end can be obtained as: So we can get because So the internal heat source can be obtained as: Substituting the internal heat source formula into Q2 yields

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