JP2003223470A - Heat sink thermal analyzer, heat sink thermal analysis method and program allowing computer to execute method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a heat sink thermal analyzer performing a heat analysis of a heat sink at high speed in a simple operation. <P>SOLUTION: A heat transfer coefficient calculation part 12 calculates the heat transfer coefficient of a fin part of the sink part by calculating only a base part of the heat sink modeled by including the heat transfer coefficient of the base part of the heat sink. An area conversion part 13 deduces a first circular shape having the same area as the area of a main surface of the base part of the heat sink and a second circular shape having the same area as the contact area of a heating body to be fitted to the heat sink, and models the heat sink into a shape with the first circular shape and the second circular shape disposed as a concentric circle. A temperature arithmetic part 14 operates a temperature distribution using a heat transmission equation to be applied to the modeling. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a heat sink thermal analysis apparatus for calculating effective temperature parameters and the like during thermal design of a heat sink, a heat sink thermal analysis method and a program for causing a computer to execute the method, and a particularly simple temperature derivation formula. TECHNICAL FIELD The present invention relates to a heat sink thermal analysis apparatus that can perform thermal analysis in a short time using a computer, a heat sink thermal analysis method, and a program that causes a computer to execute the method.

[0002]

2. Description of the Related Art The technological progress of microprocessors used in personal computers has been remarkable, and they are becoming more highly integrated, faster, and more sophisticated. On the other hand, the heat generation density of microprocessors continues to increase,
It is essential to use heat sinks, heat pipes, and highly efficient cooling devices that combine fans with them.

In the business of heat sinks and heat pipes, it is considered that not only the quality and price of the products themselves, but also the ability of thermal design play an important role in receiving orders. That is, when designing a heat sink or the like, it is necessary to determine the material, shape, and size, and to make a trial calculation of its heat dissipation capability. The heat dissipation capability of a heat sink is usually known by performing a thermal analysis simulation on a computer. Also for the user side, regarding the heat sink of the desired shape and size,
It is desirable to be able to immediately check the specifications such as heat dissipation characteristics and compare the performance.

The thermal analysis simulation is realized by applying an analysis method such as the difference method or the finite element method to the heat conduction problem. For example, in the example in which the finite element method is applied, the analysis object is a plurality of triangular elements. The temperature is divided so that the heat conduction equation is best satisfied within each element. Therefore, software that realizes a thermal analysis simulation is required to simultaneously solve a huge number of heat conduction equations (differential equations) related to accuracy to obtain the solution.

Most of thermal analysis simulation software used in the past is composed of three programs called a preprocessor, a solver, and a postprocessor. A preprocessor is a program that models the heat sink that is the target of thermal analysis.Data in a format that can be input to the solver according to the input of information about the size and material of the heat sink, information about the heating element, conditions for heat removal, etc. Output the set.

The solver is a program for reading a data set output from the preprocessor and calculating simultaneous solutions of the above-mentioned many heat conduction equations. The post processor is a program that visually displays the calculation result of the solver, which is merely a list of numerical values, in a temperature table, a temperature distribution chart, or the like.

Since such thermal analysis simulation software is not only large in execution program size but also required to find the solution of several thousand simultaneous differential equations, it is usually equipped with a high-speed processor. It runs on a relatively expensive computer.

[0008]

However, the above-mentioned conventional thermal analysis simulation software requires 1) familiarity with operation. 2) The operation is complicated. 3) Calculation takes time. 4) Due to the equipment and calculation time, it is difficult to handle at the meeting. There was such a problem.

Due to the above problems, the following problems have occurred in the business of developing and selling heat sinks. 1) When a sales representative receives a request from a customer to change the specifications of a heat sink, in order to present the cooling effect after the specification change, perform thermal analysis again using the above-mentioned thermal analysis simulation software. It had to be, and an earlier response was expected. 2) The thermal analysis simulation took too long, and the design required a great deal of time.

The present invention has been made in view of the above, and reduces the amount of calculation by modeling heat transfer in a solid and solving it mathematically to speed up the calculation, and further to input parameters necessary for the calculation. An object of the present invention is to provide a heat sink thermal analysis device, a heat sink thermal analysis method, and a program for causing a computer to execute the method, in which the operability is improved by simultaneously displaying the calculation results in a table format.

[0011]

In order to achieve the above object, the heat sink thermal analysis apparatus according to claim 1 includes the heat transfer coefficient of the fin portion of the heat sink in the heat transfer coefficient of the base portion of the heat sink. The heat transfer coefficient calculating means for calculating the heat transfer coefficient of the heat sink of only the base portion to be modeled, the first circular shape having the same area as the area of the main surface of the base portion of the heat sink, and the heat sink are attached to the heat sink. A second circular shape having the same area as the contact area of the heating element, and modeling the heat sink into a shape in which the first circular shape and the second circular shape are arranged as concentric circles. And a temperature calculation means for calculating the temperature distribution of the heat sink modeled by the modeling means.

According to a second aspect of the heat sink thermal analysis apparatus, the heat transfer coefficient of the heat sink of only the base portion is modeled by including the heat transfer coefficient of the fin portion of the heat sink in the heat transfer coefficient of the base portion of the heat sink. A heat transfer coefficient calculating means for calculating a coefficient, and the base portion is divided into a plurality of areas around a heat generating element attached to the heat sink, and the area has the same area as the area of the base portion in each of the divided areas. 1 fan shape and a second fan shape having the same area as the area of the heating element portion in each divided region are derived, and the first fan shape is obtained in each divided region.
The fan shape and the second fan shape are overlapped with each other with the central angles thereof coincided with each other to form a third fan shape, and the heat sink is
Modeling means for modeling each third fan shape in a concentric shape so that the apex angles coincide with each other, and temperature calculating means for calculating the temperature distribution of the heat sink modeled by the modeling means. It is characterized by having.

According to a third aspect of the heat sink thermal analysis apparatus of the present invention, the modeling means is
The base portion is divided into a plurality of regions based on the position information of the heating element with respect to the base portion.

According to a fourth aspect of the heat sink thermal analysis apparatus of the present invention, the modeling means is
Each of the plurality of heating elements arranged on the base portion is modeled, and the temperature calculation means calculates the temperature distribution for each of the plurality of models by the modeling means, and calculates the plurality of calculated temperature distributions. The feature is that the temperature distribution of the entire heat sink is calculated by overlapping.

According to a fifth aspect of the heat sink thermal analysis apparatus, a heat conduction equation of the heat sink including a fin portion is modeled into a columnar shape or a fan column shape (column having a fan shape in cross section). It is characterized in that it comprises arithmetic expression storage means for storing and temperature operation means for calculating the temperature distribution of the heat sink using the heat conduction equation.

According to a sixth aspect of the heat sink thermal analysis device, at least information regarding the shape of the heat sink, information regarding the physical properties of the heat sink, information regarding the shape of the heating element to which the heat sink is attached, and the physical properties of the heating element. Input means for inputting information as input information, temperature calculating means for calculating the temperature distribution of the heat sink using five or less heat conduction equations derived in advance for each heating element and the input information, and the temperature calculation Display means for displaying the calculation result of the means together with the input information.

According to a seventh aspect of the present invention, in the heat sink thermal analysis device according to the above invention, a storage means for storing the calculation result by the temperature calculation means for each calculation condition, and a desired calculation result stored in the storage means. And display means for displaying.

According to the eighth aspect of the present invention, in the heat sink thermal analysis device according to the above invention, the predetermined condition of the heat sink that is one of the calculation conditions is determined by using the calculation condition and the calculation result necessary for the calculation by the temperature calculation means. It is characterized in that an optimum parameter calculating means for calculating the optimum value of the parameter is provided.

According to a ninth aspect of the heat sink thermal analysis method, the heat transfer of the heat sink having only the base portion is modeled by including the heat transfer coefficient of the fin portion of the heat sink in the heat transfer coefficient of the base portion of the heat sink. A heat transfer coefficient calculating step for calculating a coefficient; a first circular shape having the same area as the area of the main surface of the base portion of the heat sink; and a second circular area having the same contact area of the heating element attached to the heat sink. And derive the circular shape of
A modeling step for modeling the heat sink into a shape in which the first circular shape and the second circular shape are arranged as concentric circles, and a temperature for calculating a temperature distribution of the heat sink modeled by the modeling step. It is characterized by including a calculation step.

According to a tenth aspect of the heat sink thermal analysis method of the present invention, the heat transfer coefficient of the heat sink of only the base portion is modeled by including the heat transfer coefficient of the fin portion of the heat sink in the heat transfer coefficient of the base portion of the heat sink. A heat transfer coefficient calculating step of calculating a coefficient, and dividing the base portion into a plurality of regions centering on a heating element attached to the heat sink, and having the same area as the area of the base portion in each of the divided regions. 1 fan shape and the second area having the same area as the area of the heating element portion in each divided area
And the fan shape of the first fan shape and the second fan shape in the respective divided regions are overlapped with each other so that the center angles of the first fan shape and the second fan shape are coincident with each other. A modeling step of modeling each third fan shape into a shape in which the third fan shapes are concentrically arranged so that the apex angles match,
A temperature calculation step of calculating a temperature distribution of the heat sink modeled by the modeling step.

According to the eleventh aspect of the heat sink thermal analysis method, at least information regarding the shape of the heat sink, information regarding the physical properties of the heat sink, information regarding the shape of the heating element to which the heat sink is attached, and the physical properties of the heating element are provided. An input step of inputting information as input information, a temperature calculation step of calculating a temperature distribution of the heat sink using less than three heat conduction equations derived in advance and the input information, and a calculation result of the temperature calculation means. Is displayed together with the input information.

According to a twelfth aspect of the present invention, in the heat sink thermal analysis method according to the above invention, the calculation result storage step of storing the calculation result of the temperature calculation step for each calculation condition and the calculation result storage step are stored. A history display step for displaying a desired calculation result,
It is characterized by including.

According to a thirteenth aspect of the present invention, in the heat sink thermal analysis method according to the above-mentioned invention, the predetermined condition of the heat sink which is one of the calculation conditions is determined by using the calculation condition and the calculation result necessary for the calculation in the temperature calculation step. It is characterized by including an optimum value calculation step for calculating the optimum value of the parameter.

The program according to the invention of claim 14 enables a computer to execute the heat sink thermal analysis method described in claims 9 to 13.

[0025]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of a heat sink thermal analysis apparatus, a heat sink thermal analysis method, and a program for causing a computer to execute the method according to the present invention will be described in detail below with reference to the drawings. The present invention is not limited to this embodiment.

(First Embodiment) First, a heat sink thermal analysis apparatus according to the first embodiment will be described. The heat sink thermal analysis apparatus according to the first embodiment can calculate the temperature distribution of the heat sink when the heating element is arranged on the center of the base surface of the heat sink without performing complicated calculation.
The feature is that it can be derived accurately.

FIG. 1 is a block diagram showing a schematic configuration of a heat sink thermal analysis apparatus according to the first embodiment. Figure 1
The heat sink thermal analysis device shown in FIG. 1 includes an input unit 11, a heat transfer coefficient calculation unit 12, an area conversion unit 13, a temperature calculation unit 14, a fin information processing unit 15, a fan information processing unit 16, and a display unit 17.
And an arithmetic expression storage unit 25.

The input section 11 is a means for inputting various input parameters necessary for thermal analysis, execution instructions, etc., and is a keyboard or other pointing device. In particular, here, by the input unit 11, the heating element data 21 regarding the heating element to be cooled by the heat sink,
Base data about heat sink base plate 2
2 and the fin data 23 regarding the fin of the heat sink
Then, environmental data 24 regarding a fan or the like attached to the heat sink is input.

The heat transfer coefficient calculation unit 12 uses at least the heat generating element data 21, the base data 22 and the fin data 23 described above and a predetermined heat transfer coefficient deriving formula to calculate the heat transfer coefficient of the fin surface and modeling described later. It is a means for calculating the converted heat transfer coefficient. The area conversion unit 13 is means for deriving a cylinder in a state in which the areas of the main surface of the base (the surface in contact with the heating element) and the side surfaces and the area of the main surface of the heating element (the surface in contact with the base) are held. is there. In other words,
It is a means for replacing the base with a cylinder having the same surface area.

The temperature calculation unit 14 calculates the heat transfer coefficient calculated by the heat transfer coefficient calculation unit 12 for the cylindrical heat sink modeled by the area conversion unit 13, the above-mentioned heating element data 21, and the base data. 22 and fin data 23
And a calculation formula stored in advance in the calculation formula storage unit 25 to calculate the temperature distribution of the heat sink. The calculation formula storage unit 25 stores, as a calculation formula, the final form of the heat conduction equation that is established inside and outside the portion corresponding to the modeled cylindrical heating element, and the energy based on the heat energy conservation law. The balance equation and the heat conduction equation established in the thickness direction of the columnar shape are stored. In particular, the number of these arithmetic expressions (specifically three) is
It is extremely small compared to the thousands of thermal conduction differential equations required in conventional thermal analysis simulation software. This is one of the features of the present invention, which realizes high-speed thermal analysis. The details of the above arithmetic expression will be described later.

The fin information processing unit 15 uses the fin data 2
3 is a means for processing information derived for the fin portion such as fin pitch, fin spacing, fin efficiency, etc. Further, the fan information processing unit 16 is based on the environmental data 24 such as the front wind speed of the fan attached to the heat sink and the fin information calculated by the fin information processing unit 15, and the inter-fin wind speed, the air volume and the pressure loss (pressure loss). Is a means for processing information regarding the operation of the fan.

The display unit 17 is a means for displaying the data calculated by the temperature calculation unit 14, the fin information processing unit 15, and the fan information processing unit 16 in a tabular form, and is a CRT.
Examples include displays and LCDs.

The heat sink thermal analysis device shown in FIG. 1 can be replaced by a general-purpose computer system. In that case, each operation of the heat transfer coefficient calculation unit 12, the area conversion unit 13, the temperature calculation unit 14, the fin information processing unit 15, and the fan information processing unit 16 described above is realized by a computer program executed on the CPU of the computer. To be done. Further, the arithmetic expression stored in the arithmetic expression storage unit 25, the heating element data 21, the base data 22, the fin data 23, and the environment data 24 are stored in a storage device mounted on the computer.

The operation of the heat sink thermal analysis apparatus, that is, the heat sink thermal analysis method will be described below. FIG. 2 is a diagram showing a display example of data input / output in the heat sink thermal analysis device.

First, the operator operates the screen 10 shown in FIG.
In the input item table 102 above 0, data about the base of the heat sink to be analyzed is input. Specifically, as shown in the figure, the base width, the base length, the base thickness, the thermal conductivity of the base, the specific gravity of the base, and the like. The data regarding these bases are the above-mentioned base data 2
Stored as 2.

Further, in the same input item table 102, data about the fin of the heat sink to be analyzed is input. Specifically, as illustrated, the fin height, fin thickness, number of fins, fin thermal conductivity, fin specific gravity, and the like. Data about these fins is stored as the fin data 23 described above.

Further, in the input item table 102, data on the heating element to which the heat sink is attached is input. Specifically, as illustrated, the width of the heating element, the length of the heating element, the amount of heat generation, and the like. The data relating to these heating elements is stored as the heating element data 21 described above.

Furthermore, the operator is required to enter the same input item table 10
In 2, the data such as the front wind velocity brought by the fan attached to the heat sink and the environmental temperature serving as the temperature reference are input as the environmental data 24. The front wind speed indicates the wind speed flowing between the fins.

Further, on the screen 100 shown in FIG. 2, the correspondence between the shape of the heat sink to be analyzed and the input item is displayed in the heat sink display frame 101. In FIG. 2, as an example, a heat sink with comb fins is shown. In the figure, reference numeral 104 indicates a heating element. In this way, by displaying the shape of the heat sink to be analyzed, the definition of the input items becomes clear, input errors can be prevented, and the shape image of the heat sink currently being analyzed can be confirmed. be able to.

When the data input to the input items shown above is completed, the thermal analysis process is automatically started.

FIG. 3 is a flowchart showing a thermal analysis process by the heat sink thermal analysis apparatus according to the first embodiment. In the heat sink thermal analysis device, the heat transfer coefficient calculation unit 12 first calculates the surface area of the fin using the fin data 23 described above (step S10).
1) Calculate the heat transfer coefficient on the fin surface (step S1)
02). The surface area S _fin of the _fin is calculated using the fin height, fin length (same as the base length), fin thickness, and the number of fins among the input items shown in FIG.

Further, the heat transfer coefficient calculating unit 12 uses the above-mentioned base data 22 and the heat transfer coefficient α _fin of the fin surface calculated in step S102 to determine a heat sink composed of a base portion and a fin portion. The heat transfer coefficient α'converted to the base surface is calculated so that it can be handled as one base (step S103). Heat transfer coefficient α '
Is calculated by multiplying the heat transfer coefficient α _fin of the fin by the area ratio of the fin.

FIG. 4 is an explanatory view for explaining the conversion of the heat transfer coefficient and the conversion of the area described later. In FIG. 4A, a heat sink in which the base and the fins are integrated is shown. However, in the heat sink thermal analysis device according to the present invention, as described above, the heat transfer coefficient of the fin portion is changed to the heat transfer coefficient of the base portion. Converted to, only the base is subjected to thermal analysis. Therefore, at this stage, the shape of the thermal analysis target is
It can be handled as a single plate as shown in FIG. 4 (b), which realizes reduction and simplification of the number of heat conduction equations required for thermal analysis.

Next, the heat sink thermal analysis device uses the above-mentioned heating element data 21 and base data 22 for one base modeled as shown in FIG. The area of the base surface (main surface) and the area of the contact portion of the heating element with the base surface are calculated (step S104). Specifically, the area of the base surface (main surface) is calculated using the base width and base length of the input items, and the area of the contact portion of the heating element is the width of the heating element and the length of the heating element. Is calculated.

Then, the area conversion unit 13 performs step S1.
Two circles in which the area of the base and the area of the heating element calculated in 04 are held are derived, and the radius of each circle is calculated (step S105). In particular, this replacement of the base with a circle realizes modeling in which the circle corresponding to the heating element is arranged in the center of the circle corresponding to the base, as shown in FIG. 4C. Yes (step S105). Specifically, in the cylindrical shape shown in FIG. 4C, if the radius of the inner circle is R ₁ and the radius of the outer circle is R ₂ , then

[Equation 1] Expressed as

Subsequently, the heat sink thermal analysis device starts thermal analysis, that is, derivation of the temperature distribution, by the temperature calculation unit 14 with respect to the heat sink modeled in step S105. Derivation of the temperature distribution by the temperature calculation unit 14 is performed by calculating the heat transfer coefficient α ′ calculated by the heat transfer coefficient calculation unit 12, the heating element data 21 and the base data 22 described above.
Using the fin data 23 and the arithmetic expression stored in the arithmetic expression storage unit 25, a step S106 for establishing an equation outside the heating element, a step S107 for establishing an equation inside the heating element, and an inside of the heating element. Step S108 of setting boundary conditions between the inside and outside of the heating element, Step S109 of solving simultaneous equations inside and outside the heating element, and Step S11 of establishing an equation in the thickness direction of the modeled heat sink.
0, and step S1 of setting the boundary conditions in the thickness direction according to the process of deriving the simultaneous equations of step S109.
11 and step S112 of solving the equation in the thickness direction,
Is realized by

The steps S106 to S1 described above will be described below.
The process 12 will be specifically described. In this temperature calculation, paying attention to the fact that “heat spreads concentrically”,
After the heat conduction equation for the cylindrical shape shown in (c) is established to calculate the temperature distribution, the thermal resistance in the thickness direction is adjusted as a correction value. The cylindrical temperature distribution can be represented by an analytical connection of heat conduction equations that are established outside and inside the region where the heating element is located.

First, the equation outside the heating element (R ₁ ≤r ≤R ₂ ), that is, the equation used in the above step S106 will be described. FIG. 5 is an explanatory diagram for explaining the equations of the outer side and the inner side of the heating element. In the equation outside the heating element, as shown in FIG. 5A, the center of the heating element region 40 is r = 0, and r = R ₁ corresponding to the radius of the heating element region 40 corresponds to the radius of the base. Ring areas with widths up to r = R ₂ are of interest.

In FIG. 5A, paying attention to the concentric minute portions 41 of the ring region, if the heat quantity calculated from the change in inclination is set equal to the heat quantity taken away, a differential equation is set up.

[Equation 2] Becomes Here, θ indicates the temperature, λ indicates the thermal conductivity of the base, L indicates the thickness, α ′ indicates the reduced heat transfer coefficient calculated in step S103, and r indicates the minute portion 41. Indicates the inner diameter of.

To summarize this,

[Equation 3] Becomes

Where

[Equation 4] Put,

[Equation 5] We will find the solution by the series solution method.

I) As the step of obtaining the first solution, first, the above equation (3) is applied.

[Equation 6] And then substituting this equation (4) into equation (1) above,

[Equation 7] Is obtained.

In order for this expression (5) to always hold, it is necessary that all the coefficients of the same degree be equal. When n is changed, A _n = 0 when n is an odd number and n ² when n is an even number
A _n = 4A _n-2 . from now on,

[Equation 8] Is asked.

Therefore, this equation (6) is converted into the above equation (3).
By substituting into

[Equation 9] Is obtained. Here, when A ₀ = 1 is set, it matches the modified Bessel function of the first kind BesselI (r). Let this solution be J.

Ii) Next, as a step for obtaining the second solution,

[Equation 10] And put. Similar to i), this equation (8)

[Equation 11] Write down.

Then, this equation (9) is converted into the above equation (1).
, The logarithmic term disappears because J is the solution of equation (1). After that, substituting J'and rearranging,

[Equation 12] Is obtained.

In this equation (10), when k and n are changed, B _n = 0 when n is an odd number as in i).
When n is an even number, k = s, n = 2s, n is added to each term.
= 2s-2 is substituted and arranged,

[Equation 13] Is obtained. When this equation (11) is transformed, after all,

[Equation 14] Is obtained.

Further, in this equation (12), s is 1
When changing from s to s and adding each,

[Equation 15] Next to

[Equation 16] Is obtained.

After all,

[Equation 17] Is required.

Here, if α '=-1 and B ₀ = -γ,
It matches the modified Bessel function of the second kind BeselK (r).

Finally, the above equations (7) and (1)
3) and the temperature θ outside the heating element (R ₁ ≦ r ≦ R ₂ ) is

[Equation 18] Can be expressed as This formula (14) is the step S1.
06 is an equation used in the arithmetic expression storage unit 2
5 is stored in advance. As a specific process of step S106, after the formula (14) stored in the arithmetic formula storage unit 25 is taken out, the converted heat transfer coefficient α ′ calculated in step S103 and the heat conductivity obtained from the base data 22 are obtained. By using λ and the like, m represented by the above equation (2) is calculated and the equation (14) is specified. The method of obtaining C and D will be described in the following description. Also, in the following equation, BeselI (x) is abbreviated as I (x), and Be
sselK (x) is abbreviated as K (x).

Next, the equation inside the heating element (0 ≦ r ≦ R ₁ ), that is, the equation used in the above step S107 will be described. The equation inside the heating element is for the heating element region 40, as shown in FIG. Here, in FIG. 5B, the heating element region 40
Attention is paid to the concentric minute portions 42 of.

When the calorific value per unit volume is q ₀ ,

[Formula 19] Is obtained. In this equation (15), the first term (heat transfer term) on the right side is significantly smaller than the second term (heat generation term), so if omitted,

[Equation 20] Is obtained.

Here, if q ₀ / λ = 4k _con , then equation (16) becomes

[Equation 21] However, when r = 0, the temperature gradient becomes 0, so
c = 0.

After all, the temperature θ inside the heating element (0 ≦ r ≦ R ₁ ) is calculated from the equation (17) as follows:

[Equation 22] Can be expressed as This formula (18) is step S1.
Is the equation used in the calculation formula storage unit 2
5 is stored in advance. Note that a = -k.

Modeled heat sink temperature θ
_a is obtained by the analytic connection of the above equations (14) and (18),

[Equation 23] It is represented by. Since a, b, C, and D in this equation are unknowns, if these values are determined, the target temperature θ _a of the heat sink can be obtained.

Therefore, the above equations (14) and (18)
By defining the boundary condition in (step S1
08)), a, b, C, D are obtained (corresponding to step S109). First, as an adiabatic condition at the end, at r = R ₂ ,

[Equation 24] Holds.

That is,

[Equation 25] And C can be represented by D. Where k =
K is a _{'(mR 2) / I'} (mR 2). In addition, K '(mR
₂ ) and I ′ (mR ₂ ) can be derived as known values using a commonly known modified Bessel function calculation method (Allen's approximation formula), but the description thereof is omitted here.

In order to analytically connect the above equations (14) and (18) in order to express the outside temperature and the inside temperature of the heating element by one equation, the boundary condition is smoothed at r = R ₁ . It is necessary to connect, that is, θ in both equations must be the same (conservation law of heat quantity). That is,

[Equation 26] Holds.

Here, I (mR ₁ ), K (mR ₁ ), I ′
(MR ₁ ) and K ′ (mR ₁ ) can be derived as known values using a commonly known modified Bessel function calculation method. That is, according to the equations (23) and (21), a is

[Equation 27] Is represented by D.

Further, according to the equation (24), the equation (22) and the equation (21), b is also

[Equation 28] Is represented by D. After all, the above-mentioned coefficients C, a,
Any of b can be expressed as a function of D, and if the unknown D is determined, the temperature θ _a can be obtained.

Therefore, as a further condition, the heat radiation amount of the heat sink needs to match the heat generation amount of the heating element.

[Equation 29] That energy balance is established. This formula (26)
Substituting the above equation (19) into

[Equation 30] Is obtained.

Q is known as the input item shown in FIG. 2, and α'is determined in step S103,
Further, a, b, and C are equations (21), (24), and (2
Since it is represented by D as shown in 5), the unknown value D is finally determined by the equation (27), and the heat sink temperature θ _a is obtained. The integral calculation of Expression (27) can be obtained by using a Simpson's expression.

Next, an equation in the thickness direction of the modeled heat sink is established (corresponding to step S110).
Will be described. FIG. 6 is an explanatory diagram for explaining the equation in the thickness direction. As for the equation in the thickness direction, as shown in FIG. 6, in the heat sink modeled in the shape of a cylinder, the heat quantity Q _i corresponding to the heat quantity of the heating element enters from the top, but the heat quantity Q _t that goes out is as described above. Formula (20), Formula (2
2), which is obtained using the condition of equation (23).

Heat is taken from the lateral direction, but using a virtual heat transfer coefficient α ″,

[Equation 31] If (provided that the outer circumference is u and the cross-sectional area is S), the solution is

[Equation 32] Can be written. Here, it is assumed that m ′ has a constant value regardless of the location.

The boundary condition is

[Expression 33]

[Equation 34]

[Equation 35] Since there are 3 variables, it can be solved in principle.

In the above equation (31), β = 1 / [S · (-
λ) · m '], e₂= E₁-ΒQ _iCan be written. Yo
From the above equation (32),

[Equation 36] Becomes

Substituting this equation into the above equation (33),

[Equation 37] Is obtained.

When m't is large on the left side, β, that is, 1 /
Since it exhibits the behavior of m ′ (in short, it becomes a graph of the form y = 1 / x), it can be said that it is a “function of a good property” for the Newton method.

When the solution is obtained by Newton's method from the point where m'is sufficiently small, it converges in about 5 times, but in the actual calculation, it is preferable to program 10 or more times as a precaution.

The temperature of the heat sink thus calculated is obtained as the temperature rise value from the ambient temperature in the first embodiment (step S113). Specifically, this temperature rise value is output as the temperature of the heat sink at the portion in contact with the heating element, as in the temperature item displayed in the output item table 103 shown in FIG. In addition, in FIG. 2, the temperature rise value of the heat sink for each of the case where there is no heat pipe (HP), the case where the medium quality HP is used, the case where the high quality HP is used, and the case where the special quality HP is used are shown. it's shown. Thus, by pre-storing several types of HP information whose cooling effect is known, the performance of the heat sink when HP is added can be presented.

The output item table 103 shown in FIG.
As the information provided from the fin information processing unit 15 described above, the fin pitch, the fin interval, and the fin efficiency are displayed. In particular, the information about the fin information is useful as an index indicating the difficulty in actually manufacturing the heat sink.

Further, in the output item table 103 shown in FIG.
Spread efficiency is also displayed as information about the base. Here, the spread efficiency is a dimensionless number indicating how much heat is spread in the base, which is a concept similar to the fin efficiency, and is data that can be calculated by a predetermined arithmetic expression based on the base data 22. .

Further, in the output item table 103 shown in FIG. 2, as the information provided from the fan information processing section 16, the wind speed (front surface), the wind speed (between fins), the temperature rise value of the air, the air volume and the pressure loss. Is displayed. In particular, this fan information and the above-mentioned information about the heat pipe are not indicators of the direct performance of the heat sink, but since there is a high possibility that the fan and the heat pipe will be used together when using the heat sink, the information will not be presented. , It will be useful for the side that uses the heat sink.

In addition to the items shown in the output item table 103 of FIG. 2, information on a heat conductive cushioning member (silicone grease, silicone rubber, etc.) to be interposed between the heating element and the heat sink, and mounting of the heat sink. Information about the electric heating element (Peltier module or the like) may be presented.

FIG. 7 is an explanatory diagram for explaining a comparison between the thermal analysis result by the conventional simulation software and the thermal analysis result by the present invention. In the table shown in FIG. 7A, the size of the copper heat sink = 88 [mm] × 64 [m
m], fin height = 40 [mm], fin thickness =
0.5 [mm], number of fins = 32, fin pitch =
2.0 [mm], heating value of heating element = 79 [W], front wind speed = 3.71 [m / s], environmental temperature = 0 ° C.,
Furthermore, regarding the ratio of the temperature rise value when the thickness of the heat sink and the size of the part where the heating element contacts the heat sink (heat source size) are the conditions shown in the same table, the ratio of the temperature rise value when analyzed by other software simulation It shows a case of analysis by the heat sink thermal analysis device according to the invention.

Further, regarding the temperature rise value analyzed by the heat sink thermal analysis apparatus according to the present invention, the error is also shown at the same time. Here, the error is calculated by 100 × (difference in temperature rise value) / (reference temperature rise value). Figure 7
7B is a diagram in which the errors shown in the table of FIG. 7A are graphed.

As shown in FIG. 7, the difference between the analysis result by the other software simulation and the analysis result by the heat sink thermal analysis device according to the present invention and the error with respect to the reference temperature rise value are both 3% or less. Considering the effect that the present invention realizes high-speed thermal analysis and simple operation, the decrease in analysis accuracy lost at the cost is negligibly small.

As described above, according to the heat sink thermal analysis apparatus and the heat sink thermal analysis method of the first embodiment, the heat sink is modeled into a cylindrical shape that is mathematically easy to handle, and is applicable to the modeling. By preliminarily storing several heat conduction equations, the temperature distribution of the heat sink can be calculated in a short time.

In particular, the conventional thermal analysis simulation is
Although a few minutes to several tens of minutes of analysis time was required for even a slight change in specifications, the heat sink thermal analysis apparatus according to the present invention simplifies the heat conduction equation and thus completes the analysis in a few seconds. be able to. This means that when the heat sink thermal analysis device according to the present invention is realized by a portable computer such as a notebook computer, the customer can immediately show the performance of the heat sink with respect to the specification change. . On the contrary, the customer side (user side) can immediately check the heat radiation characteristics and the like of the heat sinks of various shapes and sizes, and thus can select the heat sink having the optimum specifications desired by the customer side.

Furthermore, since the input / output display shown in FIG. 2 and the operations performed by the various processing units shown in FIG. 1 are processes that can be realized on so-called office applications such as word processors and spreadsheet software, sales A user such as a person in charge can use a user interface with an application that he or she is familiar with, and the problems such as the necessity of operation proficiency and complexity in the conventional thermal analysis simulation software can be solved.

(Second Embodiment) Next, a heat sink thermal analysis device according to a second embodiment will be described. The heat sink thermal analysis apparatus according to the second embodiment uses the same thermal analysis process as in the first embodiment even when the heating element is arranged at an arbitrary position on the base surface. The feature is that the distribution can be derived.

Since the schematic structure of the heat sink thermal analysis apparatus according to the second embodiment is the same as that of FIG. 1, its explanation is omitted here. The difference between the second embodiment and the first embodiment is the internal processing of the area conversion unit 13 and the temperature calculation unit 14. Embodiment 2 will be described below focusing on this difference.
The operation of the heat sink thermal analysis device according to the above will be described.

FIG. 8 is a diagram showing an input item table in a display example of data input / output in the heat sink thermal analysis device. Since the heat sink thermal analysis apparatus according to the second embodiment is characterized by deriving the temperature distribution when the heating element is arranged at an arbitrary position on the base surface, as shown in FIG. Input items for the position (x) of the heating element and the position (y) of the heating element are added. Note that other displays such as the output item table are common to those in FIG. Therefore, when the data input to the input items shown in FIG. 8 is completed, the thermal analysis process is automatically started.

FIG. 9 is a flowchart showing the thermal analysis processing by the heat sink thermal analysis apparatus according to the second embodiment. Note that in FIG. 9, steps S201 to S20
3, S211 to S214 are steps S1 shown in FIG.
Since it is the same as 01 to S103 and S110 to S113, their description is omitted here. Therefore, the description will be sequentially given from step S204 in FIG.

The heat sink thermal analysis device includes an area conversion unit 1
3 for one base modeled as shown in FIG. 4B, using the above-mentioned information about the position of the heating element, the base including the area where the heating element is arranged is divided into a predetermined number of divisions. Split with. FIG. 10 is an explanatory diagram for explaining division of the base and the heating element. Here, as shown in FIG. 10A, an example is shown in which the lower left apex of the base surface 210 is the origin and the heating element 211 is arranged so that its center is located at the coordinates (x ₀ , y ₀ ). To list. Further, in order to simplify the explanation, the above-mentioned predetermined number of divisions is set to 4.

In the coordinate space on the base surface shown in FIG. 10A, the base surface 210 and the heating element 211 have x = x _0.
And y = y _0, the line is divided into four. That is, as shown in FIG. 4B, the four divisions result in a first division region including the base region F ₁ and the heating element region H _1, and a second division region including the base region F ₂ and the heating element region H _2. A region, a third divided region including the base region F ₃ and the heating element region H _3, and a fourth divided region including the base region F ₄ and the heating element region H ₄ are generated.

Then, the area conversion section 13 calculates the area of each base region and each heating element region by using the heating element data 21 including the position information and the base data 22 (step S204). Specifically, the areas of the base regions F _{1 to} F ₄ are calculated using the base width, the base length, and the position information (x, y) of the heating element among the input items, and the heating elements H _{1 to} H ₄ are calculated.
The area of is calculated using a value obtained by dividing the width of the heating element and the length of the heating element into two equal parts.

Next, the area conversion unit 13 is shown in FIG.
As shown in, the fan shape having the same area as the area of each base region calculated in step S104 and the fan shape having the same area as the area of each heating element region are derived, and the radius of each fan shape is calculated (step S205). To replace the base region with a sector, first, as described in the first embodiment, the area obtained by multiplying the area of the base region by 2π / (central angle which is a condition for division) is used. It is realized by calculating circles having the same area. The same applies to the replacement of the heating element region with a fan shape. For example, in the first divided area, the radius R ₁ (1) of the fan shape H ₁ ′ that replaces the heating element area H ₁
And the radius R ₂ (1) of the sector F ₁ 'replaced with the base region F ₁
Is

[Equation 38] Expressed as

Similarly, the radii R ₁ (2) to R ₁ (4) of the sectors H ₂ 'to H ₄ ' replaced with the heating element regions H _{2 to} H ₄ and the base regions F _{2 to} F ₄ are defined. Radius R _{2 of the} replaced fan shape F ₂ 'to F ₄ '
(2) to R ₂ (4) are also determined.

Then, the heat sink thermal analysis device starts thermal analysis, that is, derivation of the temperature distribution, by the temperature calculation unit 14 with respect to the heat sink modeled in step S205. Derivation of the temperature distribution by the temperature calculation unit 14 is performed by calculating the heat transfer coefficient α ′ calculated by the heat transfer coefficient calculation unit 12, the heating element data 21 and the base data 22 described above.
Using the fin data 23 and the arithmetic expression stored in the arithmetic expression storage unit 25, a step S206 of establishing an equation outside the heating element for each division unit and an equation inside the heating element for each division unit are established. Step S207, step S208 for setting boundary conditions inside and outside the heating element for each division unit, step S209 for simultaneously solving equations inside and outside the heating element for each division unit, and calculation for each division unit. S210 for synthesizing different temperatures, step S211 for establishing an equation in the thickness direction of the modeled heat sink, and step S212 for setting boundary conditions in the thickness direction in accordance with the process of deriving simultaneous equations in step S209, And step S213 of solving the equation in the thickness direction.

Here, in the thermal analysis in the second embodiment, it is necessary to establish the equations inside and outside the heating element for each division unit (first to fourth division areas) as described above to obtain a solution. However, since the base region and the heating element region in each division unit are fan-shaped as described above, the thermal analysis is performed in steps S206 to S209 for the circle having the same radius as that fan-shaped in the first embodiment. Step S10
This can be realized by applying the calculations of 6 to S109 and multiplying the left side of the energy balance expression represented by Expression (27) by the central angle / 2π. However, as a new condition, it is necessary that the temperature of the position corresponding to the center of the heating element be the same in all the divided areas.

Specifically, taking the temperature θ ₁ of the first divided region as an example, at a ₁ , b ₁ , C ₁ , D ₁ corresponding to the coefficients a, b, C, D of the equation (27), , A ₁ , b ₁ , and C ₁ can be represented by D ₁ by the same procedure as in the first embodiment.
Further, the temperatures θ _{2 to} θ ₄ in the _{second to} fourth divided regions can be similarly expressed by D _{2 to} D ₄ .

Here, if the temperatures at the centers of the heating elements match.
Condition (θ₁= Θ₂), Θ ₁= Θ₂Is b₁= B₂
Can be expressed as b₁And b₂Is equation (25)
Each,

[Formula 39] So, in the end,

[Formula 40] Becomes Where l ₂ is

[Formula 41] Is.

Expression (41) holds in other divided areas, and is expressed as a general expression.

[Equation 42] Is obtained.

As described above, the energy balance equation of each divided area is the central angle / 2π on the left side of equation (27).
Since it is obtained by multiplying by
_{When 1} is determined, D ₂ , D ₃ , and D ₄ are determined, and a _i , b _i ,
C _i (i = 1 to 3) is also determined. In this way, the temperatures θ _{1 to} θ ₄ of each divided area are obtained (step S210).

As described above, according to the heat sink thermal analysis device and the heat sink thermal analysis method according to the second embodiment, the base surface is divided into a plurality of regions with the position of the heating element as the center, and each division is performed. Since the thermal analysis process similar to that of the first embodiment is used for the region, even when the heating element is arranged at an arbitrary position on the base surface,
The effects of the first embodiment can be enjoyed.

In the second embodiment described above, the case where the number of divisions is set to 4 has been described as an example, but the same can be applied to other numbers of divisions. For example,
16 division, 64 division, 256 division, etc. can be adopted. Also, the thermal analysis result can be illustrated by a method using a weighted average.

(Third Embodiment) A heat sink thermal analysis apparatus according to the third embodiment will be described. Embodiment 3
As described in the second embodiment, the heat sink thermal analysis device according to the second embodiment uses the same thermal analysis process as in the second embodiment when there are a plurality of heating elements arranged at arbitrary positions on the base surface. The temperature distribution of the heat sink can be derived by superimposing the obtained temperatures.

FIG. 11 is an explanatory diagram for explaining superposition of temperature distributions in the heat sink thermal analysis device according to the third embodiment. As shown in FIG. 11, for example, a heating element 231 and a heating element 232 are formed on the base surface 210.
Considering a state in which the heat generating elements are arranged at arbitrary positions, first, the temperature distribution Th ₁ is obtained for the heat generating element 231 by the procedure described in the second embodiment, and similarly, the heat generating element 23 is obtained.
For 2, the temperature distribution Th ₂ is obtained by the procedure described in the second embodiment. Then, these temperature distributions Th ₁ and Th
Simply stack the _two . From this, the temperature distribution Th _{3 of the} entire heat sink can be known.

As described above, according to the heat sink thermal analysis device and the heat sink thermal analysis method of the third embodiment, even when a plurality of heating elements are arranged at arbitrary positions on the base surface. Since the temperature distribution of the entire heat sink can be known by superposing the thermal analysis results according to the second embodiment, the effects of the first embodiment can be enjoyed even in this case.

Since the calculation is fast, for example, other input items and temperatures are designated, and predetermined input items are automatically changed to 1) match the PG diagram, and 2) optimize the base thickness. 3) It is possible to automatically perform optimization such as optimization of the number of fins (for example, a back-calculation method by providing an optimum parameter calculation means), and it is also possible to display them on the screen. Furthermore, the past thermal analysis results when the value of the input item is changed can be held as a database and displayed as a calculation history or reference data.

In the first to third embodiments described above, the comb-shaped heat sink is taken as an example in the example shown in FIG. 2, but other types of heat sinks such as a pin fin type and a lattice type may be used. The present invention can be similarly applied.

In the temperature calculation explained above,
The modified Bessel function was shown as the final simplified equation form, but it was replaced with a quadratic function or a linear function,
Further simplification can be achieved.

In the first to third embodiments described above, the heat transfer coefficient calculating unit 12 and the area converting unit 1 described above are used.
When each operation of 3, the temperature calculation unit 14, the fin information processing unit 15, and the fan information processing unit 16 is realized by a computer program, the computer program can be executed in various forms described below.

First, a CD on which the program is recorded
-A recording medium such as a ROM or a memory card is read by a computer system serving as a heat sink thermal analysis device, and the program is executed directly or after installation.

Secondly, a computer system which is a heat sink thermal analysis device uses a WWW (World Wide Web) server or FTP (FiFi) via a communication line such as the Internet.
le Transfer Protocol) Download the program from another device such as a server, then install and execute it.

Thirdly, by using a terminal device such as a personal computer, ASP (Application Service Provide)
r) Access the server and execute the program on the ASP server to receive the same service as the heat sink thermal analysis method.

[0119]

As described above, according to the heat sink thermal analysis device and the heat sink thermal analysis method of the present invention, the heat sink can be modeled into a cylindrical shape that is mathematically easy to handle, and can be applied to the modeling. By storing several different heat conduction equations in advance, the conventional thermal analysis simulation required several minutes to several tens of minutes for even a slight change in specifications, while the heat sink temperature This has the effect that the analysis can be completed in a few seconds.

Further, according to the heat sink thermal analysis apparatus and the heat sink thermal analysis method of the present invention, a plurality of heat sinks each having one or more heating elements arranged at arbitrary positions are arranged around each heating element. By modeling the fan-column shape in a concentric arrangement and storing several heat conduction equations applicable to the modeling in advance, multiple heating elements can be arranged at arbitrary positions. Even with the heat sink in the open state, the temperature analysis of the entire heat sink can be completed in a few seconds.

Further, according to the heat sink thermal analysis apparatus and the heat sink thermal analysis method of the present invention, since it is possible to perform thermal analysis by several simplified heat conduction equations, existing applications such as office applications can be used. Therefore, there is an effect that problems such as necessity of operation proficiency level and complexity, which have occurred in conventional thermal analysis simulation software, are solved.

According to the program of the present invention, it is possible to cause the computer to execute the heat sink thermal analysis method described above. Therefore, by downloading the program through a recording medium recording the program or a communication line, The heat sink thermal analysis method can be executed.

[Brief description of drawings]

FIG. 1 is a block diagram showing a schematic configuration of a heat sink thermal analysis device according to a first embodiment.

FIG. 2 is a diagram showing a display example of data input / output in the heat sink thermal analysis apparatus according to the first embodiment.

FIG. 3 is a flowchart showing a thermal analysis process by the heat sink thermal analysis apparatus according to the first embodiment.

FIG. 4 is an explanatory diagram for explaining conversion of a heat transfer coefficient and conversion of an area described later in the first embodiment.

FIG. 5 is an explanatory diagram for explaining the equations of the outer side and the inner side of the heating element in the first embodiment.

FIG. 6 is an explanatory diagram for explaining an equation in a thickness direction in the first embodiment.

FIG. 7 is an explanatory diagram for explaining a comparison between a thermal analysis result by conventional simulation software and a thermal analysis result by the present invention in the first embodiment.

FIG. 8 is a diagram showing an input item table in a display example of input / output data in the heat sink thermal analysis device according to the second embodiment.

FIG. 9 is a flowchart showing a thermal analysis process by the heat sink thermal analysis device according to the second embodiment.

FIG. 10 is an explanatory diagram for explaining division of a base and a heating element in the second embodiment.

FIG. 11 is an explanatory diagram for explaining superposition of temperature distributions in the heat sink thermal analysis device according to the third embodiment.

[Explanation of symbols]

11 Input section 12 Heat transfer coefficient calculator 13 Area conversion unit 14 Temperature calculator 15 Fin information processing unit 16 Fan information processing unit 17 Display 21 Heating element data 22 Base data 23 Fin data 24 Environmental data 25 Calculation formula storage 100 screens 101 heat sink display frame 102,202 Input item table 103 Output item table 210 Base surface 211, 231, 232 heating element

Claims (14)

[Claims] 1. A heat transfer coefficient calculating means for calculating the heat transfer coefficient of a heat sink having only a base portion modeled by including the heat transfer coefficient of a fin portion of the heat sink in the heat transfer coefficient of the base portion of the heat sink, A first circular shape having the same area as the area of the main surface of the base portion of the heat sink and a second circular shape having the same area as the contact area of the heating element attached to the heat sink are derived, and the heat sink is obtained. And modeling means for modeling the first circular shape and the second circular shape as concentric circles, and temperature calculating means for calculating the temperature distribution of the heat sink modeled by the modeling means. And a heat sink thermal analysis device comprising: 2. A heat transfer coefficient calculating means for calculating the heat transfer coefficient of the heat sink of only the base portion modeled by including the heat transfer coefficient of the fin portion of the heat sink in the heat transfer coefficient of the base portion of the heat sink, A first fan shape having the same area as the area of the base portion in each of the divided areas, and the divided areas, with the base portion divided into a plurality of areas around the heating element attached to the heat sink. And a second fan shape having the same area as the area of the heating element part in the first fan shape and the second fan shape having the same central angle in each of the divided regions. And the overlapping state is the third fan shape,
Modeling means for modeling the heat sink into a shape in which each third fan shape is concentrically arranged so that the apex angles thereof coincide with each other, and a temperature distribution of the heat sink modeled by the modeling means is calculated. A heat sink thermal analysis device comprising: a temperature calculation means. 3. The heat sink thermal analysis apparatus according to claim 2, wherein the modeling unit divides the base portion into a plurality of regions based on position information of the heating element with respect to the base portion. . 4. The modeling means models each of the plurality of heating elements arranged on the base portion, and the temperature computing means calculates a temperature distribution for each of the plurality of models by the modeling means. The temperature distribution of the entire heat sink is calculated by superposing a plurality of calculated temperature distributions together with the calculation.
Alternatively, the heat sink thermal analysis device according to item 3. 5. An arithmetic expression storage unit for storing a heat conduction equation of the heat sink when a heat sink including a fin portion is modeled in a cylindrical shape or a fan shape, and a temperature of the heat sink using the heat conduction equation. A heat sink thermal analysis device comprising: a temperature calculation means for calculating distribution. 6. An input means for inputting at least information regarding the shape of a heat sink, information regarding physical properties of the heat sink, information regarding the shape of a heating element to which the heat sink is attached, and information regarding physical properties of the heating element as input information. Temperature calculation means for calculating the temperature distribution of the heat sink using five or less heat conduction equations derived in advance for each heating element and the input information, and the calculation result of the temperature calculation means is displayed together with the input information. A heat sink thermal analysis device comprising: a display means. 7. A storage means for storing a calculation result by the temperature calculation means for each calculation condition, and a display means for displaying a desired calculation result stored in the storage means. Item 7. The heat sink thermal analysis device according to any one of items 1 to 6. 8. An optimum parameter calculating means for calculating an optimum value of a predetermined parameter of a heat sink, which is one of the calculation conditions, by using a calculation condition and a calculation result necessary for the calculation by the temperature calculating means. The heat sink thermal analysis device according to claim 1, wherein the heat sink thermal analysis device is a heat sink thermal analysis device. 9. A heat transfer coefficient calculation step for calculating a heat transfer coefficient of a heat sink having only a base portion modeled by including a heat transfer coefficient of a fin portion of the heat sink in a heat transfer coefficient of the base portion of the heat sink, A first circular shape having the same area as the area of the main surface of the base portion of the heat sink and a second circular shape having the same area as the contact area of the heating element attached to the heat sink are derived, and the heat sink is obtained. A modeling step for modeling the first circular shape and the second circular shape as concentric circles, and a temperature calculation step for calculating the temperature distribution of the heat sink modeled by the modeling step. And a heat sink thermal analysis method including: 10. A heat transfer coefficient calculating step of calculating a heat transfer coefficient of a heat sink having only a base portion modeled by including a heat transfer coefficient of a fin portion of the heat sink in a heat transfer coefficient of the base portion of the heat sink, A first fan shape having the same area as the area of the base portion in each of the divided areas, and the divided areas, with the base portion divided into a plurality of areas around the heating element attached to the heat sink. And a second fan shape having the same area as the area of the heating element part in the first fan shape and the second fan shape having the same central angle in each of the divided regions. And the overlapping state is the third fan shape,
A modeling step of modeling the heat sink into a shape in which the respective third fan shapes are concentrically arranged so that the apex angles match, and a temperature distribution of the heat sink modeled by the modeling step is calculated. A heat sink thermal analysis method, comprising: a temperature calculation step. 11. At least information regarding the shape of the heat sink, information regarding the material properties of the heat sink,
The input step of inputting information about the shape of the heating element to which the heat sink is attached and information about the physical properties of the heating element as input information, and the heat sink using less than three heat conduction equations derived in advance and the input information. And a display step of displaying a calculation result of the temperature calculation means together with the input information, the heat sink thermal analysis method. 12. A calculation result storage step of storing a calculation result of the temperature calculation step for each calculation condition, and a history display step of displaying a desired calculation result stored in the calculation result storage step. The heat sink thermal analysis method according to any one of claims 9 to 11. 13. An optimum value calculation step for calculating an optimum value of a predetermined parameter of a heat sink, which is one of the calculation conditions, using a calculation condition and a calculation result necessary for the calculation in the temperature calculation step. The heat sink thermal analysis method according to claim 9, wherein the heat sink thermal analysis method is a heat sink thermal analysis method. 14. A program for causing a computer to execute the method according to any one of claims 9 to 13.