Heat calculation program and heat treatment apparatus

Abstract

To provide a thermal calculation program and a heat treatment apparatus capable of suppressing a decrease in calculation accuracy due to a temperature difference between both walls of an adiabatic wall when performing thermal calculation based on Fourier's law.SOLUTION: A computer executes: a correction step of correcting heat flux obtained according to Fourier's law for a thermal structure model describing a state of an insulated wall containing an insulating member, by multiplying or dividing a correction function whose argument is a ratio of specific heat at constant volume, which is the ratio of a specific heat at constant volume at any position in the thickness direction of the insulating member with respect to a specific heat at constant volume at a position on a surface of the insulating member; and a calculation step of obtaining a stationary solution of the thermal structure model using the corrected heat flux.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present invention relates to a heat calculation program and a heat treatment apparatus.

Background Art

[0002] Conventionally, a technique for performing heat calculation using computer simulation has been known. This technique can be applied to various structures including building materials (for example, see Patent Document 1) and heat insulation containers (for example, see Patent Document 2).

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0004] By the way, the above heat calculation can also be applied, for example, when estimating the temperature inside a heat treatment apparatus (that is, a vacuum carburizing furnace) for performing vacuum carburizing with a hydrocarbon-based gas under high temperature and reduced pressure. For example, it is assumed that a controller estimates the temperature inside the furnace and performs real-time temperature control inside the furnace using the obtained estimated value.

[0005] However, the methods disclosed in Patent Documents 1 and 2 are premised on solving the heat diffusion equation (or the heat conduction equation). Although the calculation accuracy of the heat calculation is high, the calculation time increases accordingly. As a result, there arises a problem that the real-time property of temperature control is impaired.

[0006] In addition, in order to ensure the real-time performance of temperature control, it is desirable to use a method that requires less computational effort to obtain a steady-state solution, for example, performing heat calculations using a differential equation according to Fourier's law. However, as the temperature difference between the temperature on one surface of the heat insulation wall and the temperature on the other surface opposite to the one surface (hereinafter, also referred to as "temperature difference between both wall surfaces") increases, another problem occurs in that "breakdown" of Fourier's law occurs and the calculation accuracy decreases. In particular, in a heat treatment apparatus such as a vacuum carburizing furnace, the temperature difference between both wall surfaces may reach approximately 1000 °C, and the above-described decrease in calculation accuracy becomes more prominent.

[0007] The present invention has been made in view of such problems, and an object thereof is to provide a heat calculation program and a heat treatment apparatus capable of suppressing a decrease in calculation accuracy caused by a temperature difference between both wall surfaces of a heat insulation wall when performing heat calculations based on Fourier's law.

Means for Solving the Problems

[0008] The heat calculation program according to the first aspect of the present invention multiplies or divides a heat flux obtained according to Fourier's law by a correction function having, as an argument, a specific heat ratio that is the ratio of the specific heat at constant volume in the thickness direction of the heat insulating material to the specific heat at constant volume at a position on the surface of the heat insulating material, with respect to a heat structure model describing the state of a heat insulation wall including a heat insulating material, thereby correcting the heat flux, and causes a computer to execute a calculation step of obtaining a steady-state solution of the heat structure model using the corrected heat flux.

[0009] In the heat calculation program according to the second aspect of the present invention, in the calculation step, constraint conditions of the heat structure model are given such that the temperature difference between the temperature on one surface of the heat insulation wall and the temperature on the other surface opposite to the one surface becomes 500 °C or more.

[0010] In the heat calculation program according to the third aspect of the present invention, constraint conditions of the heat structure model are given such that a heat transfer function having, as an argument, the temperature difference between the temperature on one surface of the heat insulation wall and the temperature of the outside air in contact with the one surface becomes an odd function.

[0011] In the heat calculation program according to the fourth aspect of the present invention, the correction function is an identity function of the constant specific heat ratio.

[0012] The heat treatment apparatus according to the fifth aspect of the present invention is an apparatus including an apparatus main body that treats the surface of an object to be treated and a controller that controls the apparatus main body. The apparatus main body includes a heat insulating material and includes a heat insulating wall provided so as to surround the object to be treated, and a heater that heats a heating chamber formed by the heat insulating wall. The controller multiplies or divides the heat flux obtained according to Fourier's law with respect to a heat structure model that describes the state of the heat insulating wall by a correction function having, as an argument, a constant specific heat ratio that is the ratio of the constant specific heat at an arbitrary position in the thickness direction of the heat insulating material to the constant specific heat at the position on the surface of the heat insulating material, thereby correcting the heat flux. The controller obtains a steady-state solution of the heat structure model using the corrected heat flux, calculates an estimated value of the temperature in the heating chamber from the steady-state solution, and performs heating control on the heater using the obtained estimated value.

Advantages of the Invention

[0013] According to the present invention, when performing heat calculation based on Fourier's law, it is possible to suppress a decrease in calculation accuracy caused by a temperature difference between both wall surfaces of the heat insulating wall.

Brief Description of the Drawings

[0014]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Embodiments for Carrying Out the Invention

[0015] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. For ease of understanding of the description, the same reference numerals are given to the same components in each drawing as much as possible, and duplicate descriptions are omitted.

[0016] [Overall Configuration of Heat Treatment Apparatus 10] FIG. 1 is a schematic cross-sectional view of a heat treatment apparatus 10 according to an embodiment of the present invention. This heat treatment apparatus 10 includes a vacuum carburizing furnace 12 (corresponding to the "apparatus main body"), a controller 14 (corresponding to the "computer"), a heating power source 16, and temperature sensors 18 and 20.

[0017] The vacuum carburizing furnace 12 is an apparatus for performing vacuum carburizing with a hydrocarbon-based gas under high temperature and reduced pressure. The vacuum carburizing furnace 12 includes a furnace body 22 that houses a workpiece W to be processed, and a frame body 24 attached inside the furnace body 22. Inside the frame body 24, a relatively large hollow rectangular parallelepiped-shaped heat insulating member 26, a relatively small hollow rectangular parallelepiped-shaped heat insulating member 28, and a plurality of heat insulating members 30 for connecting the heat insulating member 26 to the heat insulating member 28 are provided. The heat insulating members 26, 28, and 30 are made of a heat insulating material such as a ceramic fiber board, for example. By providing the two heat insulating members 26 and 28 spaced apart from each other, a space layer 32 that functions as a heat insulating layer is formed.

[0018] Inside the furnace body 22, a carburizing chamber 36 for performing vacuum carburizing is formed by being surrounded by the hollow heat insulating member 30. The furnace body 22 is provided with a furnace floor 38 that extends inward from the lower part of the furnace body 22 to the inside of the carburizing chamber 36. At the upper end of the furnace floor 38, the workpiece W is placed in a state of being accommodated in a tray or basket (not shown).

[0019] At the upper part of the furnace body 22, a plurality of heat dissipation tubes 40 (corresponding to a "heater") are attached so as to extend inwardly of the carburizing chamber 36. Each heat dissipation tube 40 is provided at a position widely covering the range from the upper end to the lower end of the carburizing chamber 36. Thereby, the space formed by the carburizing chamber 36 can be heated substantially evenly. The inside of the carburizing chamber 36 is set to a high temperature exceeding, for example, 900°C.

[0020] At the upper part and side part of the furnace body 22, a plurality of gas introduction nozzles 42 are provided so as to face the position of the workpiece W. By introducing hydrocarbon gas into the carburizing chamber 36 through the gas introduction nozzles 42 from a gas supply mechanism (not shown), a carburizing treatment can be performed on the surface of the workpiece W.

[0021] At the lower part of the furnace body 22, an exhaust pipe 44 that communicates the carburizing chamber 36 with the outside of the vacuum carburizing furnace 12 is provided. By operating a vacuum pump (not shown) to exhaust from the exhaust port 46, the pressure inside the carburizing chamber 36 can be adjusted.

[0022] The controller 14 has a processor 50 and a memory 52, and is a computer that operates and controls each part of the vacuum carburizing furnace 12. The controller 14 reads and executes the programs and data stored in the memory 52 to perform [1] supply control for supplying hydrocarbon gas into the carburizing chamber 36, [2] pressure control for adjusting the pressure inside the carburizing chamber 36, and [3] heating control for heating the inside of the carburizing chamber 36 synchronously or in parallel. For performing these operation controls, a flow rate sensor, a pressure sensor (both not shown), and temperature sensors 18 and 20 are connected to the controller 14.

[0023] The processor 50 acquires temperature signals from the temperature sensors 18 and 20, and calculates an estimated value of the temperature inside the carburizing chamber 36 (hereinafter also referred to as "furnace internal temperature") using the measured temperature. Then, the processor 50 performs heating control on each heat dissipation tube 40 by turning on and off the heating power supply 16 based on the estimated value calculated by itself. Here, the temperature sensor 18 is provided at a position in contact with the upper part of the furnace body 14, and the temperature sensor 20 is provided at a position around the vacuum carburizing furnace 12, respectively.

[0024] [Operation of Controller 14] [Overview of Temperature Control Operation] The heat treatment apparatus 10 in this embodiment is configured as described above. Subsequently, an example of the operation of the heat treatment apparatus 10, more specifically, the temperature control operation by the controller 14, will be described with reference to the flowchart of FIG. 2.

[0025] In step SP10 of FIG. 2, the controller 14 determines whether to continue the temperature control in the carburizing chamber 36. If the temperature control is to be continued (step SP10: YES), the process proceeds to the next step SP12.

[0026] In step SP12, the controller 14 determines whether the execution timing of the temperature control has arrived. If the execution timing has not yet arrived (step SP12: NO), the process returns to step SP10, and the controller 14 sequentially repeats steps SP10 and SP12 until the execution timing arrives. On the other hand, if the execution timing has arrived (step SP12: YES), the process proceeds to the next step SP14.

[0027] In step SP14, the controller 14 estimates the furnace temperature at the current time. This estimation method will be described in detail later with reference to FIGS. 3 to 6.

[0028] In step SP16, the controller 14 performs heating control for each heat dissipation pipe 40 by turning on or off the heating power supply 16 based on the estimated value of the furnace temperature calculated in step SP14. Specifically, the controller 14 performs temperature control so that the furnace temperature transitions according to a predetermined temperature sequence using a known method including so-called PID control.

[0029] After that, returning to step SP10, the controller 14 sequentially repeats the operations of steps SP10 to SP16. Then, when the controller 14 does not continue to control the temperature inside the carburizing chamber (step SP10: NO), it ends the operation of the flowchart shown in FIG. 2.

[0030] <Estimation of Furnace Temperature> Subsequently, the method for estimating the furnace temperature in step SP14 (FIG. 2) will be described in detail with reference to the flowchart of FIG. 3 and FIG. 4.

[0031] In step SP20 of FIG. 3, the controller 14 acquires temperature signals from the temperature sensors 18 and 20, and measures the outer wall temperature and the external temperature of the furnace body 22 respectively.

[0032] In step SP22, the controller 14 determines a combination of the thermal structure model and the solution method of the furnace body 14. This "thermal structure model" means a mathematical model that describes the state of the heat insulation wall including the heat insulation material. The "solution method" of the model includes the type of equation, constraint conditions, method of obtaining the solution, method of assigning the initial value, convergence conditions, etc.

[0033] FIG. 4 is a diagram schematically showing an example of a thermal structure model simulating the internal structure of the furnace body 22. More specifically, this figure shows a cross-section of a heat insulation wall formed by laminating three heat insulation materials. For example, a coordinate axis (X-axis) is defined in the direction from the inside to the outside of the furnace body 22. Regarding the position on the coordinate axis (unit: m), "inside the furnace" corresponds to the high-temperature side and "outside the furnace" corresponds to the low-temperature side respectively. As parameters necessary for specifying the heat transfer coefficients h1 and h2 (unit: W / m 2 ·K) and the temperature distribution T (unit: °C) in the steady state, [1] the thermal conductivities λ1 to λ3 (unit: W / m·K) of the heat insulation materials, [2] the thicknesses l1 to l3 (unit: m) of the heat insulation materials, [3] the surface area A (unit: m 2 ) of the heat insulation materials, [4] the fluid temperature Th (unit: °C) on the high-temperature side, [5] the fluid temperature Tc (unit: °C) on the low-temperature side, [6] the wall surface temperature Twh (unit: °C) on the high-temperature side, [7] the wall surface temperature Twc (unit: °C) on the low-temperature side, etc. are listed.

[0034] In step SP24 of FIG. 3, the controller 14 gives an initial value of the temperature distribution to be calculated. For example, when solving a non-linear differential equation using the Newton-Raphson method (hereinafter, also simply referred to as the "Newton method"), it is desirable to give a value closer to the steady state solution as the initial value so as not to be trapped in a so-called local solution.

[0035] In step SP26, the controller 14 updates the temperature distribution given in step S24 using an iterative approximation method including the Newton method. The controller 14 may sequentially update the temperature at each position by the "forward difference method" from the high temperature side to the low temperature side, or may sequentially update the temperature at each position by the "backward difference method" from the low temperature side to the high temperature side. The interval between positions (ΔX) can be set to various values, for example, 1 mm interval, 5 mm interval, etc. As will be described later, the corrected heat flux is used for updating the temperature distribution.

[0036] In step SP28, the controller 14 determines whether or not a predetermined convergence condition is satisfied after the update in step SP26. An example of the convergence condition is that the difference in the heat flux entering and leaving the adiabatic wall becomes a minute value. If it is determined that the convergence condition is not yet satisfied (step SP28: NO), the controller 14 returns to step SP26 and sequentially repeats steps SP26 and SP28 until the convergence condition is satisfied. On the other hand, if it is determined that the convergence condition is satisfied (step SP28: YES), the process proceeds to the next step SP30.

[0037] In step SP30, the controller 14 determines the temperature distribution and heat transfer coefficient finally obtained in step SP26 as the steady state solution, and estimates the furnace temperature using the obtained temperature distribution. In this way, the controller 14 ends the flowchart of FIG. 3 (step SP16 of FIG. 2).

[0038] <Features of the heat calculation method> Subsequently, the features of the heat calculation method in this embodiment will be described with reference to FIGS. 5 and 6.

[0039] (1. Improvement of Fourier's Law) As an example of an equation used in heat calculation, a heat diffusion equation can be cited. However, while using the heat diffusion equation increases the calculation accuracy of heat calculation, it also takes more calculation time accordingly. That is, since it is difficult to ensure real-time performance, it is not suitable for online temperature control.

[0040] Therefore, in order to reduce the amount of calculation for obtaining a steady-state solution, it is conceivable to perform heat calculation using a differential equation according to "Fourier's Law". Specifically, this Fourier's Law is given by the following equation (1). Here, Q is the heat flux (unit: W / m 2 ), A is the surface area of the heat-insulating wall (unit: m 2 ), λ is the thermal conductivity (unit: W / m·K), and T is the temperature (unit: K), respectively.

[0041] [Number]

[0042] However, as the temperature difference between the two wall surfaces of the heat-insulating wall increases, "breakdown" of Fourier's Law occurs, and another problem occurs in that the calculation accuracy of heat calculation decreases when the temperature difference generally exceeds 500°C. In particular, in a heat treatment apparatus 10 such as a vacuum carburizing furnace 12, the temperature difference between the two wall surfaces often exceeds 800°C, and the above-described decrease in calculation accuracy becomes more prominent.

[0043] Therefore, by improving Fourier's Law shown in equation (1), calculation accuracy almost equivalent to that in the case of the heat diffusion equation can be obtained. The heat flux Q is obtained according to the following equation (2).

[0044] [Number]

[0045] As understood from Formula (1) and Formula (2), the corrected heat flux Q is obtained by multiplying the heat flux Q calculated according to Fourier's law by a correction function f(·). This correction function is a continuous function that satisfies f(1)=1 and has various function shapes such as polynomial functions and exponential functions. From the perspective of achieving both improved calculation accuracy and reduced calculation amount, it is more preferable that the correction function is an identity function (y = x).

[0046] In addition, rCv, which is the argument of the correction function, is the ratio of the specific heat at constant volume (hereinafter referred to as the "specific heat ratio at constant volume") and is a dimensionless physical quantity. Specifically, rCv is obtained according to the following Formula (3).

[0047]

Equation

[0048] Here, Cp(·) is the specific heat at constant pressure, and ρ(·) is the density. Also, Tb is the surface temperature of the heat insulation material, and T corresponds to the temperature at an arbitrary position in the thickness direction of the heat insulation material. That is, the "specific heat ratio at constant volume" is the ratio of the specific heat at constant volume at an arbitrary position in the thickness direction of the heat insulation material to the specific heat at constant volume at a position on the surface of the heat insulation material.

[0049] Figure 5 is a diagram showing an example of the correction function. The horizontal axis of the graph indicates the position in the thickness direction (unit: mm), and the vertical axis of the graph indicates the value of the correction function (unit: dimensionless). Here, the position of the surface on the high-temperature side is set as X = 0, and the position of the surface on the low-temperature side is set as X = D. As understood from the graph of this figure, in the case of forward difference, the specific heat at constant volume at an arbitrary position is normalized by the specific heat at constant volume at X = 0. That is, the correction function has the property that its value is 1 at X = 0 and gradually increases as X increases. On the other hand, in the case of backward difference, the specific heat at constant volume at an arbitrary position is normalized by the specific heat at constant volume at X = D. That is, the correction function has the property that its value is 1 at X = D and gradually decreases as X decreases.

[0050] In this way, by correcting the heat flux using a correction function with the constant specific heat ratio as an argument, the difference in "specific heat" can be reflected in Fourier's law. As a result, the decrease in calculation accuracy due to the temperature difference between the two wall surfaces of the adiabatic wall is suppressed.

[0051] (2. Shape of the heat transfer function) Figure 6 is a diagram showing an example of the shape of the heat transfer function. The horizontal axis of the graph indicates the temperature difference (unit: °C), and the vertical axis of the graph indicates the heat flux (unit: unit; W / m 2 ). This "temperature difference" means the value obtained by subtracting the surface temperature (Twc) from the external temperature (Tc). The overall heat transfer function Qout is represented, for example, as the sum of a first function indicating "radiative heat transfer" and a second function indicating "convective heat transfer".

[0052] Here, assuming that the heat flux Qin on the input side is constant, the case where the heat flux Qout on the output side is balanced becomes the steady-state solution of the temperature distribution. Therefore, when obtaining the steady-state solution using Newton's method, as shown in Figure 6, it is desirable that the heat transfer function of the heat flux Qout is a monotonically increasing function. For this reason, constraint conditions may be imposed so that the heat transfer function becomes an odd function, or constraint conditions may be imposed so that it becomes a composite function connecting a plurality of even functions divided into the positive or negative sides.

[0053] <Effect by correction of heat flux> Figure 7 is a diagram showing an example of the effect of improving the calculation accuracy by correcting the heat flux. This graph shows the temperature distribution obtained by heat calculation. That is, the horizontal axis of the graph indicates the position in the thickness direction (unit: mm), and the vertical axis of the graph indicates the temperature (unit: °C). "Comparative example (without correction)" corresponds to the steady-state solution of the temperature distribution obtained using Equation (1). On the other hand, "Example (with correction)" corresponds to the steady-state solution of the temperature distribution obtained using Equation (2).

[0054] As can be understood from this figure, a divergence occurs in the graphs of both around the part where the temperature gradient changes rapidly (X = 80 to 100 mm). On the other hand, the steady-state solution of the temperature distribution obtained using the heat diffusion equation generally agrees with the graph of the "Example". In other words, even when performing heat calculations using Fourier's law with the correction of the heat flux, a decrease in the calculation accuracy is suppressed.

[0055] As described above, in the heat calculation program and method according to this embodiment, one or more computers (here, the controller 14) multiply or divide the heat flux obtained according to Fourier's law by a correction function having as an argument the ratio of the specific heat at constant volume at an arbitrary position in the thickness direction of the heat insulating material to the specific heat at constant volume at the position on the surface of the heat insulating material with respect to the heat flux regarding the heat structure model describing the state of the heat insulating wall including the heat insulating material, thereby performing a correction step (SP26 in FIG. 3) of correcting the heat flux, and an arithmetic step (SP28) of obtaining a steady-state solution of the heat structure model using the corrected heat flux.

[0056] In this way, by correcting the heat flux using a correction function having as an argument the ratio of the specific heat at constant volume, the difference in "specific heat" can be reflected with respect to Fourier's law. As a result, a decrease in the calculation accuracy due to the temperature difference between both wall surfaces of the heat insulating wall is suppressed.

[0057] Further, in the arithmetic step, constraint conditions of the heat structure model may be given such that the temperature difference between the temperature on one surface of the heat insulating wall and the temperature on the other surface opposite to the one surface becomes 500 °C or more. As this temperature difference increases, the degree of violation of Fourier's law tends to increase, and accordingly, the effect of maintaining the calculation accuracy by the correction using the correction function appears more prominently.

[0058] Further, constraint conditions of the heat structure model may be given such that a heat transfer function having as an argument the temperature difference between the temperature on one surface of the heat insulating wall and the temperature of the outside air in contact with the one surface becomes an odd function. The convergence of the steady-state solution is enhanced by the heat transfer function being symmetric about the origin.

[0059] Further, the correction function may be an identity function of the specific heat ratio at constant volume. This makes it easier to achieve both an improvement in calculation accuracy and a reduction in the amount of calculation.

[0060] Further, the heat treatment apparatus 10 in this embodiment includes an apparatus main body (here, a vacuum carburizing furnace 12) that processes the surface of a workpiece (here, a work W), and a controller 14 that controls the vacuum carburizing furnace 12. The vacuum carburizing furnace 12 includes heat insulating walls (here, heat insulating members 26, 28, 30) that contain a heat insulating material and are provided so as to surround the work W, and a heater (here, a heat radiation tube 40) that heats the inside of a heating chamber (here, a carburizing chamber 36) formed by the heat insulating walls.

[0061] Then, the controller 14 corrects the heat flux by multiplying or dividing a correction function having the specific heat ratio at constant volume as an argument, obtains a steady-state solution of the thermal structure model using the corrected heat flux, calculates an estimated value of the temperature in the carburizing chamber 36 from the steady-state solution, and performs heating control on the heat radiation tube 40 using the obtained estimated value. As a result, compared with the case of estimating the temperature in the carburizing chamber 36 using the heat diffusion equation, the amount of calculation for obtaining the steady-state solution is reduced, so it becomes easier to ensure the real-time performance of the temperature control accordingly.

[0062] [Modification Example] Note that the present invention is not limited to the above-described embodiment, and it goes without saying that it can be freely changed without departing from the gist of the present invention. Alternatively, each configuration may be arbitrarily combined as long as there is no technical contradiction.

[0063] In the above-described embodiment, the case where the outer wall temperature and the external temperature are measured using the temperature sensors 18 and 20 to estimate the temperature in the carburizing chamber 36 has been described, but the arrangement of the temperature sensors is not limited to this form. For example, a heat-resistant temperature sensor may be provided in the carburizing chamber 36 to estimate the temperature of the work W. Further, if the external temperature of the vacuum carburizing furnace 12 is maintained within a known management range, the configuration of the temperature sensor 20 may be omitted.

[0064] In the above-described embodiment, the case where the controller 14 that forms part of the heat treatment apparatus 10 executes the heat calculation program has been described. However, the configuration of the apparatus is not limited to this. For example, a general-purpose computer independent of the vacuum carburizing furnace 12 may execute the heat calculation program for the purpose of computer simulation.

Explanation of Signs

[0065] 10… Heat treatment apparatus, 12… Vacuum carburizing furnace (apparatus main body), 14… Controller (computer), 26, 28, 30… Heat insulating members, 36… Carburizing chamber (heating chamber), 50… Processor, 52… Memory, W… Workpiece (object to be processed)

Claims

1. Regarding a thermal structure model that describes the state of a heat insulation wall including a heat insulating material, a correction step of correcting the heat flux obtained according to Fourier's law by multiplying or dividing the heat flux by a correction function having as an argument a specific heat ratio that is the ratio of the specific heat at a given volume at an arbitrary position in the thickness direction of the heat insulating material to the specific heat at a given volume at a position on the surface of the heat insulating material; An arithmetic step of obtaining a steady-state solution of the thermal structure model using the corrected heat flux; A heat calculation program characterized by causing a computer to execute the above.

2. In the arithmetic step, the constraint conditions of the thermal structure model are applied such that the temperature difference between the temperature on one surface of the heat insulation wall and the temperature on the other surface opposite to the one surface is 500 °C or more. The heat calculation program according to Claim 1.

3. The constraint conditions of the thermal structure model are applied such that a heat transfer function having as an argument the temperature difference between the temperature on one surface of the heat insulation wall and the temperature of the outside air in contact with the one surface becomes an odd function. The heat calculation program according to Claim 1 or 2.

4. The correction function is an identity function of the specific heat ratio. The heat calculation program according to any one of Claims 1 to 3.

5. A heat treatment apparatus including an apparatus main body that processes the surface of an object to be processed and a controller that controls the apparatus main body, wherein the apparatus main body includes a heat insulation wall that includes a heat insulating material and is provided so as to surround the object to be processed; a heater that heats the heating chamber formed by the heat insulation wall; and the controller corrects the heat flux obtained according to Fourier's law regarding a thermal structure model that describes the state of the heat insulation wall by multiplying or dividing the heat flux by a correction function having as an argument a specific heat ratio that is the ratio of the specific heat at a given volume at an arbitrary position in the thickness direction of the heat insulating material to the specific heat at a given volume at a position on the surface of the heat insulating material, obtains a steady-state solution of the thermal structure model using the corrected heat flux, calculates an estimated value of the temperature in the heating chamber from the steady-state solution, and performs heating control on the heater using the obtained estimated value. A heat treatment apparatus.

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