Multi-orbit period space satellite thermal analysis and temperature prediction method and system

Abstract

The invention provides a thermal analysis and temperature prediction method and system for a multi-orbit cycle aerospace satellite, and the method comprises the steps: building a satellite three-dimensional physical model through finite element simulation software, setting the thermophysical parameters of all part materials, configuring a heat source and a contact thermal resistor in a solid heat transfer module, and carrying out the thermal analysis and temperature prediction. A space thermal environment and a satellite orbit attitude are defined in an orbit thermal load module, dynamic periodic control of heat source power is realized by utilizing an event module, and a step-by-step solving strategy is adopted: firstly, single-orbit periodic thermal load distribution is calculated, and then the single-orbit periodic thermal load distribution is periodically and repeatedly loaded in a plurality of orbit periods, so that the dynamic periodic thermal load control is realized. And finally, the temperature field change of the satellite in multi-orbit operation is obtained. The method effectively solves the problem that a traditional analysis method is difficult to give consideration to the multi-orbit periodic temperature accumulation effect and the dynamic thermal load change, significantly improves the prediction precision and calculation efficiency of the satellite thermal analysis, and provides a reliable basis for the thermal design of a spacecraft.

Description

Technical Field

[0001] This invention relates to the field of spacecraft thermal control technology, and in particular to a method and system for thermal analysis and temperature prediction of multi-orbit periodic space satellites. Background Technology

[0002] During their operation in orbit, space satellites are subjected to periodic external heat flows from direct sunlight, Earth's albedo, and infrared radiation, while changes in the power consumption of internal equipment create dynamic internal heat sources. Satellite temperature variations directly impact equipment performance and lifespan; therefore, accurate prediction of the temperature field across multiple orbital cycles is crucial.

[0003] Traditional thermal analysis methods often suffer from the following problems: they only consider the thermal load of a single orbit, neglecting the cumulative effect over multiple orbits; they do not fully account for the power step changes caused by equipment start-up and shutdown; and they are complex to model, computationally inefficient, and difficult to support engineering iterations. Therefore, a satellite temperature prediction method that balances accuracy and efficiency and is applicable to multi-orbit periods and dynamic thermal loads is needed. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for thermal analysis and temperature prediction of multi-orbit periodic aerospace satellites, aiming to solve the problems of insufficient consideration of periodic cumulative effects, difficulty in modeling dynamic heat sources, and low computational efficiency in the existing technology.

[0005] According to one objective of the present invention, the present invention provides a method for thermal analysis and temperature prediction of multi-orbit periodic space satellites, comprising the following steps: S1. Create a three-dimensional physical model of the aerospace satellite using finite element simulation software; S2. Set the material parameters for each component in the model; S3. Set the initial temperature, heat source parameters and contact thermal resistance in the solid heat transfer module; S4. Set the space thermal environment parameters and satellite orbit attitude in the orbit thermal load module; S5. Set the dynamic duty cycle of at least one heat source in the event module to simulate the periodic change of its power. S6. Mesh the model; S7. Set up the solver and perform step-by-step solution. First, calculate the thermal load distribution for a single orbital period. Then, periodically repeat the thermal load over multiple orbital periods to obtain the satellite temperature field under multiple orbital periods.

[0006] Furthermore, the three-dimensional physical model in step S1 includes the main frame of the space satellite, thruster, engine, solar panels, solar wing connector, sensors, observation antenna, circuit board, and payload instruments; wherein the sensors, observation antenna, and payload instruments are all connected to the circuit board.

[0007] Furthermore, in step S2, the material parameters set for different components include: The main frame is made of aluminum. The thruster, engine, sensors, observation antenna, and solar array connector are made of titanium alloy. The circuit board is made of FR4 material; The material of the load instrument is copper; The solar panel is made of silicon.

[0008] Furthermore, in step S3: The load instrument is configured as the first heat source; The thruster and engine are configured as a second heat source and a third heat source, and their dynamic heat dissipation rate is controlled by the event module. The contact surfaces of the sensors, observation antennas, payload instruments, and circuit boards, as well as the contact surfaces of the thrusters, engines, and main frame, are all designed for thermal contact and employ an equivalent thin thermal resistance layer model with a thermal resistance value of 0.01 K·m. 2 / W.

[0009] Furthermore, in step S4, a dual-band emissivity model is used to assign emissivity parameters to different surfaces of the satellite, wherein: The solar panel's outer surface has a solar emissivity of 0.99 and an ambient emissivity of 0.95. The remaining outer surface, excluding the solar panels, has a solar emissivity of 0.2 and an ambient emissivity of 0.85. The emissivity of the satellite's internal surface is set to 0.8.

[0010] Furthermore, in step S4, the orbital attributes are set as follows: circular orbit, altitude 400 km, inclination 50°, and local time of the ascending node is 15 h; the satellite attitude is set as: rotating around the +Z axis at an angular velocity of 720° / s.

[0011] Furthermore, the step-by-step solution in step S7 specifically includes: Step 1: Calculate the thermal load distribution of a single orbit, with an output time step of 0.02 orbital periods and a time range of 0 to 1 orbital period; Step 2: The single orbital thermal load obtained in Step 1 is periodically applied repeatedly over 4 orbital periods. The change in satellite temperature over time is calculated, and the output time step is 0.02 orbital periods, with a time range of 0 to 4 orbital periods.

[0012] Furthermore, the mesh division in step S6 uses coarser mesh cells to improve computational efficiency while ensuring computational accuracy.

[0013] A thermal analysis system for aerospace satellites includes a processor and a memory. The memory stores a computer program, which, when executed by the processor, implements the aforementioned method for thermal analysis and temperature prediction of multi-orbit periodic aerospace satellites.

[0014] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for thermal analysis and temperature prediction of multi-orbit periodic space satellites.

[0015] This invention integrates finite element simulation, multi-orbit cyclic load analysis, and dynamic heat source control to achieve efficient and accurate prediction of the temperature field of aerospace satellites. For the first time, it periodically extends the orbital thermal load in the time domain, effectively capturing the temperature accumulation effect under multi-orbit operation. It utilizes an event module to simulate instrument power-on and power-off behavior, realistically reflecting the impact of dynamic power consumption on temperature distribution. A dual-band emissivity model accurately characterizes the response characteristics of different surfaces to space radiation. Through a step-by-step solution strategy of single-orbit load calculation followed by multi-orbit cyclic loading, it significantly improves computational efficiency while maintaining accuracy. This method overcomes the limitations of traditional analysis, such as missing periodic effects, poor dynamic adaptability, and high computational resource consumption, providing a simulation tool for satellite thermal design that combines engineering practicality and reliability. Attached Figure Description

[0016] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0017] Figure 1 This is a process flow diagram of an embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of an embodiment of the present invention; Figure 3 This is a schematic diagram of the temperature field distribution from the simulation results of an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the orbital temperature visualization results from the simulation implemented in this invention. Figure 5 This is a schematic diagram of the temperature change curve over time based on the simulation results of this invention. Detailed Implementation

[0018] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. 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.

[0019] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention 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. Therefore, they should not be construed as limiting this invention.

[0020] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. Furthermore, the terms "installed," "connected," and "linked" should be interpreted broadly; for example, they may refer to a fixed connection, a detachable connection, or an integral connection; they may refer to a mechanical connection or an electrical connection; they may refer to a direct connection or an indirect connection through an intermediate medium; and they may refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0021] Example 1 like Figures 1-5 As shown, a method for thermal analysis and temperature prediction of multi-orbit periodic space satellites includes the following steps: S1. Create a three-dimensional physical model of the aerospace satellite using finite element simulation software; S2. Set the material parameters for each component in the model; S3. Set the initial temperature, heat source parameters and contact thermal resistance in the solid heat transfer module; S4. Set the space thermal environment parameters and satellite orbit attitude in the orbit thermal load module; S5. Set the dynamic duty cycle of the heat source power in the event module; S6. Mesh the model; S7. Set up the solver and solve step by step to obtain the multi-orbit periodic temperature field.

[0022] Specifically, in S1, the three-dimensional physical model includes: the main frame of the space satellite, thrusters, engines, solar panels, solar array connectors, sensors, observation antennas, and circuit boards or payload instruments. Sensors, observation antennas, and payload instruments are all connected to the circuit board; the payload instruments consist of three copper instrument bodies fixed to the circuit board, with different sizes corresponding to different heat dissipation rates.

[0023] In S2, the material parameters include: The main frame is made of aluminum. The thruster, engine, sensors, observation antenna, and solar array connector are made of titanium alloy; The circuit board is made of FR4 material; The load cell is made of copper. The solar panels are made of silicon.

[0024] In S3, the parameters set in the solid heat transfer module include: The initial temperature was 293.15 K; The load instruments are set as the first heat source, and the thruster and engine are set as the second and third heat sources, respectively. An equivalent thin thermal resistance layer with a thermal resistance value of 0.01 K·m is applied to the key contact surfaces. 2 / W; The solar panel is set as a generalized inward heat flux boundary.

[0025] The dynamic heat dissipation rates of the second and third heat sources are controlled by the event module, simulating power on / off behavior.

[0026] In S4, the space thermal environment parameters set in the orbital thermal load module include: Solar temperature 5780K, solar radiation flux 1414 W / m 2 ; Earth's albedo is 0.3, and Earth's infrared radiation flux is 225 W / m². 2 .

[0027] In S4, orbital properties include: The orbit is a circular orbit with an altitude of 400 km, an inclination of 50°, and a local time of 15 h at the ascending node.

[0028] In S4, the satellite attitude is set as follows: The primary axis is the +Z axis, and the secondary axis is the +X axis, rotating around the primary axis at 720° / s.

[0029] A dual-band emissivity model was used to set the solar and environmental emissivity for different surfaces.

[0030] The solar panel's outer surface has a solar emissivity of 0.99 and an ambient emissivity of 0.95. The remaining outer surface, excluding the solar panel, has a solar emissivity of 0.2 and an ambient emissivity of 0.85.

[0031] The emissivity of the satellite's internal surface is set to 0.8.

[0032] In S5, the event module is used to set the on and off time intervals of the thruster and engine to achieve periodic changes in heat rate.

[0033] In S6, coarser grid cells are used for mesh generation to improve computational efficiency.

[0034] In S7, the solver setup includes two steps: The first step is to calculate the thermal load distribution during a single orbital cycle; The second step involves repeatedly applying the thermal load over multiple orbital cycles and calculating the temperature response.

[0035] The time step of the first step is 0.02 orbital periods, and the output time range is 0 to 1 orbital period.

[0036] The second step has a time step of 0.02 orbital periods, and the output time range is 0 to 4 orbital periods.

[0037] A storage medium storing a computer program, which, when executed, implements the aforementioned method for thermal analysis and temperature prediction of multi-orbit periodic space satellites.

[0038] A thermal analysis system for aerospace satellites includes a processor and a memory. The memory stores a program, which, when executed by the processor, implements the aforementioned method for thermal analysis and temperature prediction of multi-orbit periodic aerospace satellites.

[0039] Example 2 like Figures 1-5 As shown in the figure, this embodiment of a method for thermal analysis and temperature prediction of multi-orbit periodic space satellites includes the following steps: Using COMSOL finite element simulation software and the model developer, a physical model of the aerospace satellite is created. The physical model of the aerospace satellite is a three-dimensional physical geometric model, including the main frame of the aerospace satellite, thrusters, engines, solar panels, solar wing connectors, sensors, observation antennas, circuit boards, and payload instruments. Set the material parameters of the space satellite physical model in the model developer; Set the internal heat transfer parameters of the space satellite in the solid heat transfer module of the model developer; Set the initial conditions, space radiation load, and internal heat dissipation parameters of the space satellite in the orbital thermal load module of the model developer; In the event module of the model developer, set the dynamic working cycle of the heat dissipation rate of the aerospace satellite heat source; Mesh the model in the model developer; Complete the solver settings in the model developer, perform the calculation, and obtain the simulation results of thermal analysis and temperature prediction for multi-orbit periodic aerospace satellites.

[0040] Specifically, in the physical model of the aerospace satellite, one end of the sensor, observation antenna, and payload instrument are all connected to the circuit board; the payload instrument includes three copper instrument bodies, which are fixed to the circuit board, and different sizes correspond to different heat dissipation rates.

[0041] The material parameters of the physical model of the space satellite are designed to ensure that the thermophysical properties are consistent with reality, including: In the materials library, aluminum is chosen as the material for the main frame of the aerospace satellite to ensure structural strength and thermal conductivity; titanium alloy is chosen as the material for the thruster, engine, sensors, observation antenna, and solar array connector to balance strength and temperature resistance; FR4 flame-retardant material is used for the circuit board to meet the characteristics of electronic component substrates; copper is used for the payload instruments to simulate high thermal conductivity heating components; and silicon is used for the solar panels to match photoelectric conversion characteristics.

[0042] Setting the internal heat transfer parameters of the space satellite in the solid heat transfer module of the model developer includes: The initial temperature was set to 293.15 K; The load instrument is set as the primary heat source, and the three copper instrument bodies are configured with different heat dissipation rates according to their different sizes. The thruster and engine are set as the second and third heat sources, respectively, and the base heat rate and dynamic heat rate are set. The dynamic heat rate shown is set by the heat rate working cycle of the heat source of the event module. The contact surfaces of sensors, observation antennas, payload instruments, and circuit boards, as well as the contact surfaces of thrusters, engines, and the main frame of the space satellite, are all designed as thermal contacts. The contact model is selected as an equivalent thin thermal resistance layer with a layer thermal resistance of 0.01 K*m. 2 / W; The solar panel is configured for heat flux, and its flux type is selected as generalized inward heat flux.

[0043] Setting initial conditions, space radiation loads, and internal heat dissipation parameters of the space satellite in the orbital thermal load module of the model developer includes: Initial conditions include solar properties, Earth properties, orbital properties, and the orientation of the spacecraft: In the solar properties, the solar temperature is set to 5780K and the solar radiation flux is set to 1414W / m². 2 ; In the Earth properties, select the longitude of the sub-spacecraft point from the list of planetary longitudes at the start time, set the albedo to 0.3, the solar planetary radiative flux to 0, and the environmental planetary radiative flux to 225 W / m². 2 .

[0044] In the orbital properties, the orbital type is a circular orbit, the altitude is 400 km, the inclination is 50°, and the local time of the ascending node is set to 15 h; In the direction of the space satellite, the main axis of the space satellite is in the +Z direction, the secondary axis is in the +X direction, and it rotates around the main axis with an angular velocity of 2*360.

[0045] To address the different characteristics of direct solar radiation (solar band), Earth's albedo and Earth's infrared radiation (environmental band), and the internal heat dissipation of space satellites, a dual-band model (solar band and environmental band) is adopted to adapt to the different characteristics of space radiation payloads (solar radiation and environmental radiation), and dual-band emissivity parameters are assigned to different surfaces of space satellites: Regarding the internal heat dissipation parameters of the space satellite, including the internal surface parameters, the surface emissivity of the internal surface parameters of the space satellite is 0.8; For space radiation loads, this includes the outer surface parameters of the solar panels and other outer surface parameters, among which: The emissivity of the outer surface parameters of the solar panel is 0.99 in the solar band and 0.95 in the ambient band.

[0046] The emissivity of the remaining external surface parameters is 0.2 in the solar band and 0.85 in space; The setting of the heat source's heat dissipation rate work cycle in the event module of the model developer includes: For the second and third heat sources, the instrument's opening and closing times are set to achieve dynamic changes in heat consumption rate and simulate working conditions under different operating conditions.

[0047] The grid division uses a coarser grid cell size to improve computational efficiency while ensuring computational accuracy.

[0048] The process of setting up the solver and performing the solution calculation in the model developer includes: In the model developer, under the Research 1 node, click "Step 1" and then "Step 2" in sequence. In the research settings, configure the time unit and output time step. In the research settings of "Step 1", the time unit is set to: s, the output time details are: orbital period, and the output time step is set to: range(0,0.02,1) to calculate the thermal load distribution of a single orbit. In the research settings of "Step 2", the time unit is set to s, the output time details are: orbital period, and the output time step is set to range(0,0.02,4). The thermal load of a single orbit is periodically repeated within 4 orbital periods to calculate the change of satellite temperature over time, covering the cumulative effect of multiple orbits.

[0049] Click "Calculate" in the research toolbar.

[0050] Example 3 like Figures 1-5 As shown in the figure, this embodiment presents a method for thermal analysis and temperature prediction of multi-orbit periodic space satellites. Taking a low-orbit remote sensing satellite as an example, COMSOL software is used for modeling and analysis. The specific steps are as follows: Constructing a three-dimensional geometric model of a satellite Create a 3D assembly in the COMSOL model developer that includes the main frame, thruster, engine, solar panels, connecting frame, sensors, antenna, circuit board and three copper payload instruments.

[0051] Set material parameters Main frame: Aluminum; Thrust, engine, sensors, antenna, and connecting frame: titanium alloy; Circuit board: FR4; Loading instrument: Copper; Solar panels: Silicon.

[0052] Solid heat transfer module settings Initial temperature: 293.15K; The load instrument is set as the first heat source, and the thruster and engine are set as the second and third heat sources, respectively. The heat dissipation rate of the latter two is controlled by the event module. A thermal resistance layer with a thermal resistance value of 0.01 K·m is applied to the critical contact surfaces. 2 / W; The solar panel is set as the generalized inward heat flux boundary.

[0053] Track thermal load module settings Solar radiation: 5780K, 1414 W / m 2 ; Earth's albedo: 0.3, Earth's infrared radiation: 225 W / m 2 ; Orbit parameters: circular orbit, altitude 400 km, inclination 50°, local time at the ascending node 15 h; Satellite attitude: Rotating around the +Z axis at 720° / s; The surface emissivity is modeled using a dual-band approach. Solar panels: solar wavelength 0.99, ambient wavelength 0.95; Other outer surfaces: solar band 0.2, environmental band 0.85; Internal surface emissivity: 0.8.

[0054] Event module settings The thruster and engine are set to turn on and off within a specified time interval to simulate the actual mission cycle.

[0055] Grid division A coarser grid is used to balance computational efficiency and temperature field capture capability.

[0056] Solver settings Step 1: Calculate the thermal load of a single orbit, with a time range of 0 to 1 orbital period and a step size of 0.02; Step 2: Repeat the thermal load over 4 orbital cycles and calculate the temperature response; Perform calculations and extract the temperature field and key point temperature history.

[0057] The above process can efficiently obtain the temperature distribution and variation trend of satellites under multiple orbital cycles, providing a reliable basis for thermal design.

[0058] This invention enables rapid simulation and temperature accumulation effect analysis of multi-track cyclic thermal loads; it combines an event interface to achieve dynamic power adjustment, which is closer to actual working conditions; and it balances computational efficiency and engineering accuracy through reasonable simplification and step-by-step solution.

[0059] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for thermal analysis and temperature prediction of multi-orbit periodic space satellites, characterized in that, Includes the following steps: S1. Create a three-dimensional physical model of the aerospace satellite using finite element simulation software; S2. Set the material parameters for each component in the model; S3. Set the initial temperature, heat source parameters and contact thermal resistance in the solid heat transfer module; S4. Set the space thermal environment parameters and satellite orbit attitude in the orbit thermal load module; S5. Set the dynamic duty cycle of at least one heat source in the event module to simulate the periodic change of its power. S6. Mesh the model; S7. Set up the solver and perform step-by-step solution. First, calculate the thermal load distribution for a single orbital period. Then, periodically repeat the thermal load over multiple orbital periods to obtain the satellite temperature field under multiple orbital periods.

2. The method for thermal analysis and temperature prediction of multi-orbit periodic space satellites according to claim 1, characterized in that, The three-dimensional physical model in step S1 includes the main frame of the space satellite, thruster, engine, solar panels, solar wing connector, sensors, observation antenna, circuit board, and payload instruments; wherein the sensors, observation antenna, and payload instruments are all connected to the circuit board.

3. The method for thermal analysis and temperature prediction of multi-orbit periodic space satellites according to claim 2, characterized in that, In step S2, the material parameters set for different components include: The main frame is made of aluminum. The thruster, engine, sensors, observation antenna, and solar array connector are made of titanium alloy. The circuit board is made of FR4 material; The material of the load instrument is copper; The solar panel is made of silicon.

4. The method for thermal analysis and temperature prediction of multi-orbit periodic space satellites according to claim 2, characterized in that, In step S3: The load instrument is configured as the first heat source; The thruster and engine are configured as a second heat source and a third heat source, and their dynamic heat dissipation rate is controlled by the event module. The contact surfaces of the sensors, observation antennas, payload instruments, and circuit boards, as well as the contact surfaces of the thrusters, engines, and main frame, are all designed for thermal contact and employ an equivalent thin thermal resistance layer model with a thermal resistance value of 0.01 K·m. 2 / W.

5. The method for thermal analysis and temperature prediction of multi-orbit periodic space satellites according to claim 1, characterized in that, In step S4, a dual-band emissivity model is used to assign emissivity parameters to different surfaces of the satellite, wherein: The solar panel's outer surface has a solar emissivity of 0.99 and an ambient emissivity of 0.

95. The remaining outer surface, excluding the solar panels, has a solar emissivity of 0.2 and an ambient emissivity of 0.

85. The emissivity of the satellite's internal surface is set to 0.

8.

6. The method for thermal analysis and temperature prediction of multi-orbit periodic space satellites according to claim 1, characterized in that, In step S4, the orbital properties are set as follows: circular orbit, altitude 400 km, inclination 50°, and local time of the ascending node is 15 h; the satellite attitude is set as: rotating around the +Z axis at an angular velocity of 720° / s.

7. The method for thermal analysis and temperature prediction of multi-orbit periodic space satellites according to claim 1, characterized in that, The step-by-step solution in step S7 specifically includes: Step 1: Calculate the thermal load distribution of a single orbit, with an output time step of 0.02 orbital periods and a time range of 0 to 1 orbital period; Step 2: The single orbital thermal load obtained in Step 1 is periodically applied repeatedly over 4 orbital periods. The change in satellite temperature over time is calculated, and the output time step is 0.02 orbital periods, with a time range of 0 to 4 orbital periods.

8. The method for thermal analysis and temperature prediction of multi-orbit periodic space satellites according to claim 1, characterized in that, The meshing in step S6 uses coarser mesh cells to improve computational efficiency while ensuring computational accuracy.

9. A thermal analysis system for aerospace satellites, characterized in that, It includes a processor and a memory, wherein the memory stores a computer program, and when the program is executed by the processor, it implements the multi-orbit periodic space satellite thermal analysis and temperature prediction method as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the multi-orbit periodic space satellite thermal analysis and temperature prediction method as described in any one of claims 1-8.

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