Heat sink design method and heat sink design program

Abstract

To provide a heat sink design method and a heat sink design program, which enable an increase in the amount of heat dissipation while reducing the volume of a space in which a heat dissipation element is arranged.SOLUTION: A heat dissipation element is composed of a three-dimensional structure with a set of edges connecting a set of nodes arranged three-dimensionally, the nodes connected by the edges are selected on the basis of graph theory, and a population search based optimization algorithm and a response surface methodology are used together to adjust the topology of the three-dimensional structure.SELECTED DRAWING: Figure 6

Description

[Technical field]

[0001] The present invention relates to a heat sink used for dissipating heat from electronic devices such as computers, and to a design method and design program for the heat sink. [Background technology]

[0002] Conventional heat sinks have a structure in which multiple plate-like fins are provided parallel to one another on one surface of a base material, and are formed by casting, extrusion molding, machining, or other methods using materials with high thermal conductivity, such as aluminum (see, for example, Patent Documents 1 and 2). In these heat sinks, many fins of the same shape are arranged at regular intervals, which creates an air flow along the fins, contributing to improved heat dissipation efficiency. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 57-193049 [Patent Document 2] Japanese Patent Application Publication No. 63-235031 Summary of the Invention [Problem to be solved by the invention]

[0004] However, in conventional heat sinks, in order to achieve a specified heat dissipation efficiency, a large number of fins are arranged across one entire surface of the base material, and although there is space between adjacent fins, the heat sink essentially occupies a volume equivalent to that of a solid body with the fins at both ends as side walls and the base material as the bottom wall.

[0005] Therefore, the present invention has an object to provide a heat sink that can increase the amount of heat dissipation while reducing the volume of the space in which the heat dissipation element is placed, as well as a design method and design program for the heat sink. Another object of the present invention is to provide a design method and design program for a heat sink that can provide stable heat dissipation performance regardless of the installation position. [Means for solving the problem]

[0006] In order to solve the above problems, the heat sink design method of the present invention is a method for designing a heat sink equipped with a heat dissipation element, in which the heat dissipation element is composed of a three-dimensional structure having a set of edges (lines connecting points) connecting a set of nodes (points) arranged in a three-dimensional manner, the nodes connected by the edges are selected based on graph theory, and the topology of the three-dimensional structure is adjusted by combining a population search-based optimization algorithm and response surface methodology.

[0007] The heat sink design program of the present invention is a design program for a heat sink having a heat dissipation element constituted by a three-dimensional structure having a set of edges connecting a set of nodes arranged in three dimensions, and is characterized by comprising a step of selecting, by an arithmetic circuit, nodes to be connected by edges based on graph theory, and a step of adjusting, by an adjustment circuit, the topology of the three-dimensional structure by using a combination of a population search-based optimization algorithm and response surface methodology. Effect of the Invention

[0008] According to the present invention, it is possible to realize a heat sink that can increase the amount of heat dissipation while reducing the volume of the space in which the heat dissipation elements are arranged. In addition, by using a population search-based optimization algorithm in combination with response surface methodology, it is possible to efficiently realize optimization calculations of a three-dimensional structure expressed by graph theory, and it is possible to find a design method that can simultaneously improve the heat dissipation performance and reduce material costs compared to heat sinks of conventional configurations. In addition, according to this design method and design program, it is possible to realize a heat sink that can increase the amount of heat dissipation while reducing the volume of the space in which the heat dissipation elements are arranged, and that exhibits stable heat dissipation performance regardless of the installation position. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 is a block diagram showing an example of the configuration of a computing device that can be used for a heat sink design program according to an embodiment of the present invention. [Diagram 2] FIG. 13 is a diagram showing an example of a groove pattern engraved in a flow channel expressed by graph theory. [Diagram 3] FIG. 2 is a diagram showing an example of a three-dimensional lattice structure in an embodiment of the present invention. [Figure 4] 1 is a flowchart showing a procedure of optimization calculation in an embodiment of the present invention. [Diagram 5] FIG. 2 is a diagram showing a model of a target region and boundary conditions of a thermal fluid analysis according to an embodiment of the present invention. [Figure 6] 1 is a graph in which a scatter diagram of sample data searched by an optimization calculation in an embodiment of the present invention is plotted in an objective function space. [Figure 7] This is a visualization of the structure of a ready-made heat sink and the generated flow field. [Figure 8] FIG. 1 is a visualization of the structure and generated flow field of sample 09-001, one of the heat sinks relating to a two-objective optimum solution with a three-dimensional lattice structure in an embodiment of the present invention. [Figure 9]FIG. 1 is a visualization of the structure and generated flow field of sample 08-001, one of the heat sinks relating to a two-objective optimum solution with a three-dimensional lattice structure in an embodiment of the present invention. [Figure 10] FIG. 1 is a visualization of the structure and generated flow field of sample 10-002, among the heat sinks relating to a two-objective optimum solution with a three-dimensional lattice structure in an embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a heat sink design method and a design program according to an embodiment of the present invention will be described in detail with reference to the drawings.

[0011] The heat sink in this embodiment includes a heat dissipation element, and the heat dissipation element includes a three-dimensional structure including a set of edges that connect a set of nodes arranged three-dimensionally. The nodes are nodes or vertices that constitute the start and end points of each heat dissipation element. The edges are branch-like, edge-like, linear, or columnar elements that connect two nodes that constitute one heat dissipation element. The thickness of the edge and the cross-sectional shape perpendicular to the direction in which the edge extends can be set according to the specifications of the heat sink, the tolerance in the manufacturing process, and the like. The set of nodes connected by the set of edges is selected based on the graph theory described below, and the topology of the three-dimensional structure is adjusted by using a population search-based optimization algorithm and response surface methodology in combination.

[0012] Any algorithm can be used as the population search-based optimization algorithm. For example, in addition to the genetic algorithm described below, a memetic algorithm, a path recombination method, an ant colony method, a particle swarm optimization method, and a differential evolution method can be used.

[0013] The set of nodes may be a set of nodes distributed in a three-dimensional space, or may be a set of nodes arranged at any position on the substrate. The shape of the substrate is not particularly limited, but may be, for example, a plate with a flat surface, a curved surface, a sphere, a hemisphere, etc. In addition, arranging the nodes on the substrate may include arranging the nodes on the surface of the substrate, as well as on the back surface, side surface, or inner surface opposite the surface.

[0014] When some of the nodes are arranged on the substrate, the remaining nodes are arranged in a three-dimensional space away from the substrate. The edge is set to extend in any out-of-plane direction with respect to the surface of the substrate. Here, the out-of-plane direction of the surface of the substrate is the direction away from the surface, and more specifically, for a node arranged on the surface of the substrate, it is the direction away from the surface at the arrangement position. In addition, the out-of-plane direction can be the same for all of the nodes arranged on the surface of the substrate, but it may be different from each other for some or all of the nodes arranged on the surface.

[0015] In the above-mentioned configuration in which some of the nodes are arranged on the substrate, the remaining nodes can be arranged so that multiple layers are stacked in the out-of-plane direction of the substrate surface, forming a three-dimensional lattice structure as a whole. The number of layers can be set arbitrarily.

[0016] In addition, the shape in plan view from the normal direction of the surface of the base material can be any shape as long as the topology of the three-dimensional structure is adjusted. Examples of such plan view shapes include a square, a triangle, other regular polygons, and a circle.

[0017] Furthermore, in a configuration in which some of the nodes are arranged on the substrate, the set of edges is composed of a first edge that starts from a node arranged on the surface of the substrate, and a second edge that is connected to the first edge directly or via another edge. In a three-dimensional lattice configuration in which the set of nodes is arranged so as to stack multiple layers in the out-of-plane direction of the surface of the substrate, the first edge and the second edge are each set to extend at an angle of less than a predetermined angle, for example, less than 45 degrees, with respect to the stacking direction.

[0018] The topology is adjusted to maximize or minimize based on an objective function related to the heat sink. The number of objective functions can be set arbitrarily according to the specifications of the heat sink. Examples of the objective functions include an index representing the heat dissipation efficiency of the heat sink, an index representing the material cost of the heat sink, and an index representing the thermal fluid performance related to the heat sink. These indexes can be used alone as the objective function, or two or more of them can be used in combination. When an index representing the heat dissipation efficiency of the heat sink is used, the topology is adjusted to maximize this index, and when an index representing the material cost of the heat sink is used, the topology is adjusted to minimize this index. The index representing the thermal fluid performance is adjusted to maximize, for example, the flow rate per unit time.

[0019] Examples of the index representing the heat dissipation efficiency of a heat sink and the thermal fluid performance of the fluid related to the heat sink include the total heat transfer amount Q of the heat sink, the temperature gradient, and the shape ratio (intake / exhaust ratio) of the vent at the bottom of the heat sink to the vent at the top of the heat sink, while examples of the index representing the material cost of the heat sink include the volume V of the material constituting the heat sink and the unit price of the material. The respective indexes are not limited to the above examples, and for example, the volume V of the material may be used as an index representing the heat dissipation efficiency of the heat sink. Also, each index may be combined in any ratio. The total heat transfer amount Q is evaluated, for example, with the base material as the heat source and the working fluid as air.

[0020] Here, when considering the manufacture of the heat sink, the topology adjustment preferably includes the identification of the manufacturing limit for the design value of the set of nodes and the set of edges. When the heat sink is manufactured by a 3D printer or other additive manufacturing, the identification of the manufacturing limit in the additive manufacturing is included, and for example, feedback based on the experimental results of the heat transfer performance and inherent distortion of the heat sink manufactured by additive manufacturing is included.

[0021] As the response surface methodology used for adjusting the topology, for example, the Kriging model can be used.

[0022] The design of a heat sink is carried out by executing a design program on a device with a computing function, such as a computer or a smartphone, which is equipped with a computing circuit, an adjustment circuit, a memory circuit, etc. An example of such a computing device is a computer whose schematic configuration is shown in Figure 1.

[0023] The computer shown in FIG. 1 includes a control circuit 11, and an arithmetic circuit 12, an adjustment circuit 13, a memory unit 14, an input unit 15, and a display unit 16, which are connected to the control circuit 11. The control circuit 11, the arithmetic circuit 12, and the adjustment circuit 13 are configured as arithmetic devices included in the computer. The memory unit 14 is a storage device in which information necessary for design is stored in advance. The input unit 15 is a keyboard, a touchpad, or other input device, and is capable of inputting information necessary for design. The display unit 16 is a display or other display device, and is capable of displaying information input from the input unit 15, information stored in the memory unit 14, the results of calculation by the arithmetic circuit 12, the results of adjustment by the adjustment circuit 13, and design information by a design program.

[0024] The above design program includes at least a step of selecting nodes to be connected by edges based on graph theory using a calculation circuit 12, and a step of adjusting the topology of the three-dimensional structure using a combination of a population search-based optimization algorithm and response surface methodology using an adjustment circuit 13.

[0025] This embodiment will be described in more detail below. In this embodiment, a heat sink used to remove heat from electronic devices such as computers is designed by topology optimization. Although many previous studies have focused on improving the performance of heat sinks, here we also focus on material costs and tackle multi-objective optimization. In the past, the inventors have considered the two-dimensional extrusion structure of heat sink fins as a structure similar to natural objects (such as tree branches, plant veins, and bronchi), and expressed this using a recursive data format grammar called Lindenmayer Systems (L-systems). By using multi-objective optimization, they created a new heat sink that has equivalent performance to existing designs but can significantly reduce material costs.

[0026] In contrast to this, in this embodiment, the three-dimensional lattice structure of the heat sink is newly targeted and expressed by graph theory, thereby achieving multi-objective optimization of a more complex and fine heat sink.

[0027] <Graph Theory> Graph theory is a theory that abstracts how nodes are connected by a set of nodes (vertices) and a set of edges (branches) that connect them. For example, when looking at a route map for a train or bus, the issue is how stations (nodes) are connected by routes (edges), but the specific curves of the tracks are often not an essential issue. In other words, the main important information is how stations are connected, and this is the role of graph theory.

[0028] Here, an example of the pattern of grooves (micromixers) carved into a flow channel expressed by graph theory is shown in Figures 2(a) and (b). If the groove pattern shown in Figure 2(b) is expressed as edges connecting 3 x 3 = 9 nodes as shown in Figure 2(a), the total number of edges when all the nodes are connected is 9 C 2 = 36. This graph is represented using the following 9 × 9 adjacency matrix A:

[0029]

number

[0030] In the adjacency matrix A, A ij = 1 means that there is an edge connecting nodes i and j, and A ij =0 means there is no edge. Also, A ij The diagonal terms denoted by =· are meaningless. In this example, the edges that do not affect the mixing efficiency, specifically, the grooves parallel to the flow direction, are ij As the 9 edges indicated by =* can be excluded, 27 edges are ultimately left. In other words, the groove pattern can be expressed by 27 parameters (design variables).

[0031] <Definition of the optimization problem> In this embodiment, the three-dimensional lattice structure of the heat sink is expressed as edges connecting 7×7×3=147 nodes (node ​​spacing=8.3 mm) as shown in FIG. 3(a). In other words, the nodes arranged in 7×7 are laminated in three layers in the lamination direction Ds along the normal direction Dn of the surface 21 of the substrate 20. Considering the symmetry of the flow occurring in the flat-laid heat sink, the design area can be reduced to 1 / 8 (10 nodes, represented by light gray areas) in each layer (7×7=49 nodes) as shown in FIG. 3(b). Furthermore, the first and second layers (10×2=20 nodes, represented by large circles P1) and the second and third layers (10×2=20 nodes, represented by small circles P2) are designed independently.

[0032] As shown in Figure 3(c), each layer is connected. 20 C 2 Of the 190 edges, only 34 edges are selected that can be printed, i.e., the angle between the stacking direction Ds is 45 degrees or less, as shown in Fig. 3(d). As a result, 34 × 2 = 68 edges remain. Therefore, a 3D lattice structure can be expressed using 68 design variables.

[0033] The design variables are given as real numbers between 0 and 1, with a value between 0 and 0.2 indicating that there is no edge, and a value between 0.2 and 1 indicating that there is an edge. Each edge is replaced with a solid cylinder with a diameter of 2.6 mm. By cutting out the portion that protrudes from the design domain (50 mm x 50 mm x 15 mm) and attaching a base part 30 (50 mm x 50 mm x 6 mm) to the bottom, solid data such as that shown in Figure 3(e) can be obtained.

[0034] The objective function includes an index representing the heat dissipation efficiency as the performance of the heat sink and an index representing the material cost. In this embodiment, the topology is maximized based on the total heat transfer amount Q, and is minimized based on the lattice volume V (the volume of the three-dimensional lattice structure). The total heat transfer amount Q is evaluated by thermal fluid analysis, and the lattice volume V is replaced with the total edge length and analytically evaluated by a self-made code. In addition, a constraint is considered that all edges are connected to the base portion 30 so that all edges contribute to heat transfer.

[0035] In this embodiment, a genetic algorithm (hereinafter referred to as "GA"), which is a population search-based optimization algorithm that simulates the evolution of living organisms, is used as a calculation method for optimization. GA can be applied to various optimization problems regardless of the nature of the objective function (differentiability, nonlinearity, multimodality, etc.), and is expected to discover a global optimum solution without falling into a local optimum solution. GA is a powerful solution method for thermo-fluid dynamics problems described by nonlinear governing equations and optimization problems in which performance changes sensitively (i.e., multimodally) due to changes in the topology of the structure, which are the targets of this embodiment. A wide variety of GAs have been proposed so far, but here we use Non-Dominated Sorting Genetic Algorithm II (hereinafter referred to as "NSGA-II"), which is the most famous in the world and has many performance verifications and applications.

[0036] On the other hand, GA requires the evaluation of the objective function for a large number of solutions that make up the population, so the total cost required for optimization calculations becomes enormous. In particular, when evaluating the objective function through large-scale numerical calculations such as thermal fluid analysis, it is not realistic to use GA alone in terms of calculation costs. Therefore, in order to reduce calculation costs, a response surface (also known as a surrogate model) is used in combination (response surface methodology). A response surface is an approximation of the response of f(x), which is a black box, as the algebraic formula B shown below, by learning sample data of the output (objective function) f(x) relative to the input (design variable) x.

[0037]

number

[0038] The output value for any input value can be instantly estimated through algebraic formula B, which significantly reduces the calculation time required for objective function evaluation and the entire optimization. However, since the response surface is only an approximation of the objective function, and any errors that occur there affect the quality of the optimal solution that is ultimately obtained, it is necessary to handle the approximation errors carefully in the solution search process.

[0039] In this embodiment, the Kriging response surface is used as the response surface. While other response surfaces model only the algebraic expression B, which is an approximation value of the objective function f(x), Kriging can model both the approximation value (algebraic expression B) and its uncertainty, i.e., the approximation error (shown in the following equation).

[0040]

number

[0041] By referring to this uncertainty C, we can probabilistically identify the location on the response surface where the global optimum is expected to exist. Here, for the objective function f(x) to be maximized, the optimal value f max The expected improvement from the actual value, EI[f(x)] (Expected Improvement), is calculated using the following formula:

[0042]

number

[0043] Here, F is a probability distribution that follows a normal distribution with mean B and variance C, and PDF(F) is the probability density distribution of F. Instead of maximizing the original objective function f(x), a solution x* that maximizes the expected value EI[f(x)] on the Kriging response surface is searched for through optimization calculations. The objective function f(x*) evaluated at this x* is added as new sample data, and the Kriging response surface is then updated. By repeatedly adding sample data in this manner, it is possible to simultaneously search for a global optimum solution and improve the accuracy of the response surface.

[0044] The procedure of optimization calculation in this embodiment is shown in Fig. 4. The first objective function, the total heat transfer amount Q, is evaluated by thermal fluid analysis under conditions where sample data is given, and is approximately evaluated using a Kriging response surface under other conditions. The second objective function, the lattice volume V, is replaced with the total edge length and analytically evaluated using a self-made code.

[0045] In the procedure shown in Fig. 4, first, initial sample data (total of 98 points) is created uniformly in the 68 design variable space by Latin Hypercube Sampling (LHS) (step S1). Then, structural data of the heat sink corresponding to each point is created, and Q is evaluated by thermal fluid analysis. Then, a Kriging response surface that approximates Q is constructed (step S2).

[0046] Next, a Pareto optimal solution where EI[Q] estimated on the Kriging response surface is maximized and volume V (analysis value of the total edge length) is minimized is searched for using NSGA-II (population size 200, number of generations 200, mutation rate approximately 1.5%) (step S3). Here, a Pareto optimal solution means a solution that is not inferior to any other solution for all objective functions. From the innumerable Pareto optimal solution sets obtained in the two-objective function space, two limit solutions, the maximum solution of expected value EI[Q] and the minimum solution of volume V, and the remaining solution set is divided into three by the K-means method, and the three solutions closest to each center of gravity are subjected to thermal fluid analysis. These results (maximum of five points in total) are added to the sample data, and the Kriging response surface is updated (step S4). By repeating the above update process, a Pareto optimal solution is efficiently searched for with the minimum number of thermal fluid analyses (i.e., the number of sample points).

[0047] Next, a convergence check is performed (step S5). For example, the convergence check is performed by checking whether EI[Q] has converged to be less than a predetermined threshold or whether the topology of the shape of the edge heat dissipation element has not been updated.

[0048] In the convergence check, if it is determined that convergence has not occurred (No in step S5), a sample is added to the current sample point to update the Kriging model (step S1).

[0049] On the other hand, if it is determined that the solution has converged (Yes in step S5), the optimization process ends. By the above procedure, the Pareto solution can be efficiently searched for with the minimum number of iterations.

[0050] <Thermofluid analysis> The thermal fluid analysis is performed in the region A1 and boundary conditions shown in a cube in FIG. 5. The working fluid is air. The bottom surface of the heat sink (bottom surface Ab of region A1) is used as the heat source, and a constant temperature of 323.15 K is given as the first boundary condition. Around region A1, a third boundary condition (293.15 K) is set so that heat is sufficiently dissipated. Here, the Boussinesq approximation is used to model natural convection. The total heat transfer amount Q of the heat sink is evaluated using the pressure-based solver of the commercially available fluid analysis software "ANSYS Fluent 2019 R1.2". The governing equations are the continuity equation, the steady incompressible Navier-Stokes equation, and the steady energy equation. In addition, the pseudo-unsteady algorithm of the pressure-based coupled solver is enabled using the pseudo-transient method. As a result, an unsteady term is efficiently added to the governing equation, improving stability and convergence. Table 1 shows the calculation scheme used in this embodiment.

[0051] [Table 1]

[0052] The computational grid for thermal fluid analysis is generated by the cut cell method (minimum element size 0.2 mm). Compared to general object-fitting grid methods, the cut cell method can automatically generate grids even for complex structures explored in the topology optimization process. In addition, unlike the Cartesian grid method, which expresses the object surface with simple stepped cells, the cut cell method cuts cells that intersect with the object surface to extract a grid that follows the object, and has the characteristic that the conservation law is satisfied because the inspection volume is defined even next to walls.

[0053] <Results and Discussion> The scatter plot of the initial sample data (point P11) and the additional sample data searched by the optimization calculation is shown in the objective function space (horizontal axis: total heat transfer amount Q (unit: W), vertical axis: volume V (unit: m 3)) is shown in Figure 6. The additional sample data are (a) the result (point P12) of two-objective optimization of maximizing the total heat transfer amount Q and minimizing the volume V (the response surface was updated 10 times), and (b) the result (point P13) of single-objective optimization of only maximizing the total heat transfer amount Q (the response surface was updated 18 times). In the two-objective optimization in (a) above, the response surface was updated 10 times, and in the single-objective optimization in (b) above, the response surface was updated 18 times.

[0054] Among these sample data, the heat sink of the embodiment that is the Pareto optimal solution is indicated by a small circle point P14. In addition, as a comparative example, a ready-made heat sink (21F50) having comb-tooth-shaped heat dissipation elements and a two-dimensional fin structure formed by extrusion molding, as shown in FIG. 7, is indicated by point P15. The heat sink indicated by point P15 has the same size as the heat sink of the embodiment that is the Pareto optimal solution, as shown by point P14, with a fin part of 50 mm x 50 mm x 15 mm and a base part of 50 mm x 50 mm x 6 mm. Furthermore, data for a structure in which lattices are arranged on all edges (full lattice structure) as shown in FIG. 3(e) is also plotted as point P16.

[0055] As shown in Figure 6, the two-objective optimal solution (point P14) has improved both the total heat transfer amount Q and the volume V compared to the initial sample data (P11). For example, the two-objective Pareto optimal solution with the largest Q (09-001, the first additional sample data obtained in the ninth update) has improved (increased) the total heat transfer amount Q by 22% and reduced (decreased) the volume V by 53% compared to the existing product (P15). In addition, the distribution of the additional sample data (point P14) by two-objective optimization shows that there is a trade-off relationship between maximizing the total heat transfer amount Q and minimizing the volume V. Next, when we focus on the point (14-001) with the largest total heat transfer amount Q among the one-objective optimal solutions (point P13), it is located near the sample of the two-objective optimal solution (09-001) (the sample shown in Figure 8). From this, we can say that the two-objective optimal solution (09-001) has almost reached the design limit for maximizing the total heat transfer amount Q, in other words, it is impossible to maximize the total heat transfer amount Q any further.

[0056] Next, a representative optimum solution and a ready-made product will be described. The structure of the heat sink and visualization of the flow field generated in the heat sink are shown in Figs. 7 to 10. Fig. 7 shows a ready-made product (shown as sample name "21F50" in Fig. 6) in which a plurality of plate-like fins F are provided in parallel to each other, and Figs. 8 to 10 show a two-objective optimum solution with a three-dimensional lattice structure. The sample shown in Figs. 8 to 10 has a three-dimensional lattice structure in which a heat dissipation element having a set of edges E is laminated in the normal direction Dn of the surface 21 of the substrate 20 in three layers L1, L2, and L3 from the substrate 20 side in the normal direction Dn of the surface 21 of the substrate 20. Furthermore, when this sample is viewed along the normal direction Dn of the surface 21 of the substrate 20, it has a quadrilaterally symmetrical shape that is symmetrical to each other in four directions D1, D2, D3, and D4 corresponding to the four sides of the square substrate 20.

[0057] Figure 8 shows the first additional sample data obtained in the ninth update (shown as "sample name 09-001" in Figure 6), Figure 9 shows the first additional sample data obtained in the eighth update (shown as "08-001" in Figure 6), and Figure 10 shows the second additional sample data obtained in the tenth update (shown as "10-002" in Figure 6).

[0058] 7 to 10, (a) is a perspective view showing the overall shape of the sample, and (b) to (d) show the heat distribution in the range described below. The higher the density of the black, the higher the temperature.

[0059] In FIG. 7, (b) shows the heat distribution in a height range close to the substrate 120 in the normal direction Dn of the substrate 120, (c) shows the heat distribution in an intermediate height range between the range shown in (b) and the range shown in (d), and (d) shows the heat distribution in the highest range.

[0060] In each of Figures 8 to 10, (b) shows the heat distribution in the lower layer of the lattice structure, i.e., the first layer L1 and second layer L2 on the substrate 20 side, (c) shows the heat distribution in the upper layer of the lattice structure, i.e., the second layer L2 and third layer L3, and (d) shows the heat distribution in the third layer L3 (the farthest layer).

[0061] In the ready-made product (sample name: 21F50) shown in Fig. 7, the surrounding cold air enters the heat sink along the gaps between adjacent fins F, i.e., from only two directions Da and Db along the direction in which the fins F extend, and as can be seen from (b), (c), and (d), the air that is heated by receiving heat from the heat sink rises away from the base material 120. In the ready-made product shown in Fig. 7, air is taken in only from the directions Da and Db corresponding to the two sides of the square-shaped base material 120 in a plan view seen along the normal direction Dn of the base material 120, so the heat absorption and dissipation performance is easily affected by the posture and direction in which the heat sink is attached.

[0062] On the other hand, in the dual-objective optimization solution shown in Figures 8 to 10, the heat sink structure is symmetrical in all four directions, D1, D2, D3, and D4, which correspond to the four sides of the base material 20. As shown in (b) and (c) of each figure, the air taken in is heated in the center and released from the third layer L3 as shown in (d). From this, it can be seen that the mounting direction has a smaller effect on the performance of the optimized heat sink shown in Figures 8 to 10 compared to the ready-made product shown in Figure 7, and it can be said that a robust design has been achieved.

[0063] Furthermore, the dual-objective optimal solutions in Figs. 8 to 10 are compared. A common configuration of these lattice structures is that there are gaps Gb (intakes, vents) on the sides of the first layer L1 to the second layer L2, which are the lower layers of the lattice structure, and the lattice is dense in the center of the second layer L2 to the third layer L3, which are the upper layers of the lattice structure. The arrangement density of the edges E is higher in the center than in the outer parts of the surface direction of the surface 21 of the substrate 20 in the layers farther from the substrate 20, that is, from the first layer L1 to the third layer L3. In addition, the third layer L3 has gaps Gt (vents) that open upward in the normal direction Dn of the substrate 20.

[0064] The above-mentioned intakes make it possible to take in cold air from the surroundings from all four sides of the heat sink (four directions D1 to D4), which is believed to ensure that air can reach the center of the heat sink sufficiently. In contrast, in the ready-made product shown in Fig. 7, the intakes are only at positions corresponding to two sides of the base material 120 that is rectangular in plan view, and depending on the surrounding air flow, it is expected that air will only flow in from one of the intakes, so it is not easy for the air taken in from the surroundings to reach the center of the heat sink.

[0065] In the heat sink of the dual-objective optimum solution shown in Figures 8 to 10, dense lattices are concentrated in the center where most of the air passes so that the air taken in can sufficiently remove heat from the heat sink, which prevents the air that has entered from escaping through the gap Gb (intake) and makes it easier to form a flow toward the third layer L3, making it easier for the air that has removed heat within the heat sink and warmed up to be discharged from the third layer L3, which is thought to be a significant effect in improving heat dissipation performance. Furthermore, in the heat sink of the dual-objective optimum solution shown in Figures 8 to 10, the layer below the lattice structure has a gap Gb (vent) as an intake, and while satisfying the configuration of densely arranged lattices in the center of the third layer L3, the lattices can be appropriately thinned out to adjust the balance between performance (Q) and material cost (V).

[0066] In contrast, with the existing product shown in Figure 7, as described above, the air that flows in does not easily reach the center, and it does not have a structure to suppress the air flow in the center and make it easier for the air to escape upwards. Therefore, near the intake, the air that flows in from the periphery and the air that has been warmed inside the heat sink mix, causing the air flow to stagnate, making it difficult to achieve sufficient heat dissipation performance.

[0067] As described above, in this embodiment, multi-objective optimization was performed on the three-dimensional lattice structure of the heat sink, aiming at improving performance and reducing material costs. As a result, the optimization calculation could be efficiently realized by optimizing the lattice structure expressed by graph theory using GA and Kriging response surface in combination. Then, a three-dimensional lattice structure that can realize performance improvement and material cost reduction compared to existing products (two-dimensional extrusion fin structure) was found. This three-dimensional lattice structure is novel, achieving both heat dissipation performance and low material cost, which is not seen in conventional heat sinks. Furthermore, the characteristics of the lattice structure for performance improvement and the thermal fluid phenomenon that supports it were identified. [Explanation of symbols]

[0068] 11 Control circuit 12 Arithmetic circuit 13 Adjustment circuit 14 Storage section 15 Input section 16 Display 20, 120 base material 21 Surface 30 Base A1 area Ab bottom D1, D2, D3, D4, Da, Db direction Dn Normal direction Ds Stacking direction E-edge F Fin Gb Air gap (vent) Gt Vent (vent) L1, L2, L3 3D lattice structure layers

Claims

1. A method for designing a heat sink with a heat dissipation element, comprising the steps of: The heat dissipation element is configured by a three-dimensional structure having a set of edges connecting a set of three-dimensionally arranged nodes; the nodes connected by the edges are selected based on graph theory; adjusting the topology of the three-dimensional structure by using a population search-based optimization algorithm in combination with response surface methodology; A method for designing a heat sink, comprising the steps of: (a) providing a response surface based on a Kriging response surface;

2. A design program for a heat sink having a heat dissipation element constituted by a three-dimensional structure having a set of edges connecting a set of three-dimensionally arranged nodes, selecting, by a calculation circuit, the nodes connected by the edges based on graph theory; adjusting the topology of the three-dimensional structure by a tuning circuit using a population search based optimization algorithm in combination with response surface methodology; Equipped with A heat sink design program, characterized in that a Kriging response surface is used as the response surface in the response surface methodology.

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