Two-dimensional thermal diffusivity algorithm and measurement method for heat dissipation modules

Abstract

This invention relates to a two-dimensional thermal diffusivity algorithm and measurement method for a heat dissipation module. One-dimensional algorithms are only applicable to heat pipes; this invention specifically develops a two-dimensional thermal diffusivity algorithm and measurement method for products such as vapor chambers and 3DVCs. On the bottom surface of a vapor chamber of a heat dissipation module, two measurement points are selected from the edge of the heat source to the outer side of the vapor chamber. The temperature of these two measurement points is then measured, and the thermal diffusivity, or λ value, of the vapor chamber can be obtained through equation (1), where equation (1) is the analytical solution obtained after solving the two-dimensional energy equation. Using this algorithm, testing instruments can measure two-dimensional products with area diffusion physical phenomena, such as vapor chambers, 3DVCs, and water-cooled plates.

Description

[Technical Field]

[0001] This invention provides a two-dimensional thermal diffusivity algorithm and measurement method for a heat dissipation module, which is related to the measurement technology of thermal diffusivity performance, and in particular, refers to an energy measurement method for the thermal diffusivity of a heat dissipation module that diffuses in the XY direction by area. [Previous Technology]

[0002] A heat dissipation module is a device widely used in heat-generating chip modules (such as CPU / GPU) in computers. Most known heat dissipation modules consist of a metal base plate (aluminum or copper) or a vapor chamber with multiple heat dissipation fins mounted on it. The base plate is then attached to a heat source, thereby conducting the heat energy of the heat source from the center outwards and upwards through the multiple heat dissipation fins to achieve the effect of heat dissipation.

[0003] The aforementioned technology, which uses a vapor chamber or VC base plate as a heat dissipation module to connect with the heat source, does not require this thermal expansion rate measurement method on older generation chips when overclocking is not needed. However, in new generation chips and AI chips that require high computing performance, overclocking is the most effective way to improve computing performance. Therefore, how to define and measure vapor chambers or two-phase flow devices such as 3DVC has become an important issue in the computer cooling industry; since the base plate of a water cooling system is also a two-dimensional temperature diffusion product, this measurement method can also be applied.

[0004] Traditional methods for measuring thermal resistance value are based on the value obtained when thermal equilibrium is reached, which is not related to time. However, the thermal diffusivity of a heat dissipation module is defined as the speed of energy transfer. It is a specific measurement technique with data support. Only after obtaining the correct thermal diffusivity coefficient with instruments can system engineers optimize the overclocking performance of the computer. [Summary of the Invention]

[0005] The main objective of this invention is to propose a method for measuring the transient thermal diffusivity of a two-dimensional heat dissipation module, which is a specific measurement technique with data support.

[0006] Another objective of this invention is to provide a method for measuring the transient thermal dissipation performance of a heat dissipation module, which can provide users with specific measurement results, allowing system engineers to optimize the overclocking performance of computers and maximize the heat dissipation performance of the heat dissipation module.

[0007] In order to achieve the above objective, the present invention proposes a method for measuring the transient thermal diffusivity of a two-dimensional VC or heat dissipation module. In order to simplify the two-dimensional mathematical equation, the single variable R (radius) of the cylindrical coordinate is first used to replace the two variables X and Y of the rectangular coordinate. The conversion relationship between the two coordinates is R = (X2 + Y2)1 / 2. After the equation of the cylindrical coordinate is solved, R = (X2 + Y2)1 / 2 is used to replace the rectangular coordinate equation back. The measurement method follows steps A) to D): A) Determine a first measurement point (edge ​​of the heat source) and a second measurement point (outermost side of the base plate): Define the surface of the heat dissipation module used to attach to a heat source as a heat-conducting surface, define the center point of the area of ​​the heat-conducting surface that is attached to the heat source as a heat center point, and define a circle or rectangle on the heat-conducting surface with the heat center point as the center; B) Measure the temperature: Attach the heat dissipation module to the heat source, and under the condition that the heat source is heating steadily, measure the temperature change of the first measurement point and the second measurement point over time, and the heat dissipation state of the heat dissipation module no longer changes, that is, it enters a steady state; C) Substitute into the calculation formula: Substitute the temperature and distance of the first measurement point and the second measurement point into the following formulas (2) and (3) to calculate, and the M value can be obtained. For the relevant positions such as R1 / R2, please refer to Figure 1.

[0008]

[0009]

[0010] Where, , , ;Where, I0 / I1 / K0 / K1 is the Bessel function in mathematics, M is the ratio of heat conduction to heat convection intensity, h is the convective heat transfer coefficient, K is the heat conduction coefficient, ra is the characteristic radius (distance from the center of the base plate to R2), T is the temperature, t is the time, R is the position variable, R1 is the distance between the first measurement point and the center of the heating point, and R2 is the distance between the second measurement point and the center of the heating point.

[0011] M can be obtained from the above equations (2) and (3); D) Result: Substitute the distance R1 between M and the first measurement point obtained in step C) and the temperature T1 at a certain moment t1 in the transient state into equation (1) to obtain the value of the thermal diffusivity α. The value of the thermal diffusivity α is used to represent the transient thermal diffusivity of the heat dissipation module.

[0012]

[0013] The above equation (1) can be replaced by R=(X2+Y2)1 / 2 (base plate part) and a=(X12+Y12)1 / 2 to return to the rectangular coordinate equation as shown in equation (6):

[0014]

[0015] Where X / Y is the position of the base plate, and X1 / Y1 is the position of the heat source.

[0016] Accordingly, the present invention provides a specific and well-founded algorithm and measurement technique that can be used in the industry. Furthermore, the present invention can provide users with specific measurement results to determine whether the transient overclocking performance of the measured heat dissipation module can meet the customer's required specifications.

Implementation Method

[0017] To illustrate the technical features of the present invention in detail, the following preferred embodiments are described in conjunction with the accompanying drawings, wherein:

[0018] As shown in Figure 1, a method for measuring the transient thermal diffusivity of a heat dissipation module according to a preferred embodiment of the present invention mainly involves the following steps:

[0019] A) Determine the positions of a first measurement point R1 (A1) and a second measurement point R2 (A2): Since the physical phenomenon of heat diffusion is that thermal energy is transferred from the heat source located in the center of the base plate (such as the CPU or GPU of a computer) to the outside of the vapor chamber in a ring-shaped radial isotherm and diffuses outward to the heat dissipation fins at the top, it is reasonable to use cylindrical coordinates to obtain the mathematical analytical solution of the energy equation. However, since both the chip heat source and the contact base plate are rectangular, for the sake of calculation accuracy, the first measurement point R1 is attached to the side of the heat source, and the position of the second measurement point R2 must be located at one of the four positions at the same radius distance of 0° / 90° / 180° / 270° on the outside of the vapor chamber. Figure 1 shows the position point at 0°.

[0020] B) Temperature measurement: The heat dissipation module is attached to the heat source, and under the condition that the heat source is heating stably, the temperature changes of the first measurement point R1 (B1) and the second measurement point R2 (B2) over time are measured respectively, and the temperature rise curve of the heat dissipation module no longer changes over time, that is, it enters the steady state range.

[0021] C) Substitute into the calculation formula: Substitute the temperature and distance of the first measurement point R1 and the second measurement point R2 into the following formulas (2) and (3) to calculate the M value (ratio of thermal convection coefficient to conductivity) of the VC heat dissipation module:

[0022]

[0023]

[0024] After obtaining the value of M, substitute it into the main equation (1) of this algorithm to obtain the temperature distribution equation at a certain time point t:

[0025]

[0026] (5)

[0027] Among them, , , , .

[0028] Where I0 / I1 / K0 / K1 is the Bessel function in mathematics, M is the ratio of heat conduction to heat convection intensity, h is the convective heat transfer coefficient, K is the heat conduction coefficient, q is the input heat, ra is the characteristic radius, is the unitless temperature, T is the temperature (°C), is the unitless time, t is the time (seconds), R is the unitless relative position (r / ra), λn is the Eigen eigenvalue, is the ratio of the heat source radius to the base plate radius, and is the final thermal diffusivity to be obtained.

[0029] The value of M is the data of the ratio of heat conduction to heat convection intensity measured on the instrument. After substituting it into the above equation (1) for calculation, the correct temperature rise equation can be obtained.

[0030] D) Result: By substituting the temperature T1 of the first measurement point R1 at a certain moment t1 in the transient state into the correct temperature rise equation obtained in step C), the value of the thermal diffusivity α of this heat spreader can be obtained.

[0031] The above describes the various steps of the measurement method of the present invention.

[0032] The key technical point of this case lies in the two-dimensional transient heating energy equation, which can usually only be calculated by simulation analysis. It is difficult to obtain a correct analytical solution of parameters using mathematical methods to serve as the algorithm for the thermal diffusivity. If the thermal diffusivity is to be measured on a testing instrument, a correct analytical solution of parameters is necessary as the core program of the algorithm for the thermal diffusivity. Therefore, how to calculate the analytical solution of the two-dimensional transient heating energy equation is the biggest challenge of this invention. As shown in Figure 2, the right side is a combination diagram of a commonly used heat spreader + fin module, and the right side is a front view of the base plate. By observing the physical phenomena of heat transfer, the energy of the CPU chip diffuses from the center to the outside in a ring-shaped isotherm. Therefore, the two variables X and Y in the rectangular coordinate energy equation can be converted to cylindrical coordinates through R=(X2+Y2)1 / 2, reducing the two variables to one variable. The final analytical solution will be presented as a combination of the Bessel function and the Fourier infinite series. According to calculations, the accuracy can reach 99.9% as long as the fiveth term of the Fourier series is reached. That is, the accuracy of this solution can represent the correct analytical solution. Each term of the Fourier series must have a corresponding eigenvalue λn and eigenterm An. λn can be solved recursively using equation (4), and An is shown in equation (5).

[0033]

[0034] (5)

[0035] As shown on the left side of Figure 3, the ratio of the radius of the wafer to the radius of the base plate is a=0.1. At the position of R1=0.1 and at the position of R2=1, the time versus temperature rise curve plotted by equation (1) is shown on the right side of Figure 3. At first, the temperature rise changes greatly. As time increases, it gradually saturates and finally the temperature no longer changes, entering the stable heat transfer range.

[0036] As shown in Figure 4, by converting R=(X2+Y2)1 / 2 to rectangular coordinates, Figure 4A is the temperature distribution diagram of =1, with the highest temperature reaching 0.226; Figure 4B is the temperature distribution diagram of =2, with the highest temperature reaching 0.275; Figure 4C is the temperature distribution diagram of =3, with the highest temperature reaching 0.3; Figure 4D is the temperature distribution diagram of =4, with the highest temperature reaching 0.325. At first, the temperature rise changes greatly, and as time goes on, it gradually saturates, and finally the temperature no longer changes and enters the stable heat transfer range.

[0037] The above equation (1) can be replaced by R=(X2+Y2)1 / 2 to return to the rectangular coordinate equation as shown in equation (6).

[0038]

[0039] Accordingly, the present invention provides a specific and well-founded algorithm and measurement technique that can be used in the industry. Furthermore, the present invention can provide users with specific measurement results to determine whether the transient overclocking performance of the measured heat dissipation module can meet the customer's required specifications.

[0040] As can be seen from the above, the present invention is a specific and well-founded measurement technique that can provide users with specific measurement results, namely the thermal diffusivity α, so that users can judge the quality of the heat dissipation effect of the measured heat dissipation module. [Simplified Explanation of the Diagram]

[0041] [Figure 1] is a flowchart (right side) showing the relevant positions of the dimension markings in an embodiment of the present invention (left side). [Figure 2] is a schematic diagram of the combination of the vapor chamber and the heat dissipation module in an embodiment of the present invention. [Figure 3] is a planar curve of the vapor chamber temperature rise curve T vs. time plotted by the algorithm of the present invention. [Figure 4] is a three-dimensional view of the temperature distribution of the vapor chamber at time τ = 1 / 2 / 3 / 4 plotted by the algorithm of the present invention.

Claims

1. A method for measuring the transient thermal diffusivity of a heat dissipation module, using equation (1) as the core calculation program of the measuring instrument, and equations (2) and (3) as the methods for obtaining the value of M in the stable region; comprising: (5) where, , , where, M is the ratio of thermal conductivity to thermal convection intensity, h is the convective heat transfer coefficient, K is the thermal conductivity coefficient, q is the input heat, ra is the characteristic radius, h is the unitless temperature, T is the temperature (0°C), h is the unitless time, t is the time (seconds), R is the unitless relative position (r / ra), λn is the Eigen characteristic value, h is the ratio of the heat source radius to the base plate radius (rb / ra), and λn is the final thermal diffusion value to be obtained. Substituting the temperature and distance between the first measurement point R1 and the second measurement point R2 into the following formulas (2) and (3) will yield the M value (ratio of thermal convection coefficient to thermal conductivity) of the VC heat dissipation module: Substituting the temperature T1 of R1 at a certain moment t1 in the transient state into formula (1) will yield the value of the thermal diffusion coefficient α, which represents the transient thermal diffusion performance of the heat dissipation module.

2. The transient thermal diffusivity measurement method of the heat dissipation module as described in claim 1, wherein the permeability R=(X2+Y2)1 / 2, equation (1) can be transformed into the core calculation program of rectangular coordinates, which can draw a three-dimensional temperature distribution diagram of rectangular coordinates; as in equation (6): where M is the ratio of thermal conduction to thermal convection intensity, h is the convective heat transfer coefficient, K is the thermal conductivity coefficient, q is the input heat, X / Y is the position of the base plate, X1 / Y1 is the position of the heat source, is the unitless temperature, T is the temperature (0°C), is the unitless time, t is the time (seconds), λn is the Eigen characteristic value, and is the thermal diffusivity to be obtained.

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