CN112231860A - Optimization design method of rectangular cross-section-shaped microchannel heat sink based on genetic algorithm - Google Patents
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Abstract
The invention discloses an optimization design method of a microchannel heat sink with a rectangular cross section shape based on a genetic algorithm, which solves the problem that the operation is influenced by the sharp increase of heat productivity caused by the ultra-high speed operation of a microelectronic product, so that the product is limited to be updated; taking the total thermal resistance and the total pressure drop of the micro-channel as two optimization targets, and performing multi-target optimization design on the micro-channel size structure by using a genetic algorithm; performing simulation verification through comsol; the optimal size structure of the micro-channel heat and mass transfer performance of the micro-channel heat sink is obtained, the optimal design method of the micro-channel heat sink with the rectangular cross section shape based on the genetic algorithm can conveniently optimize the shape and size parameters of the heat dissipation coefficient of the micro-channel, and provide the optimal structure parameters of the heat and mass transfer performance.
Description
Technical Field
The invention relates to the field of microchannel transmission, in particular to an optimization design method of a microchannel heat sink with a rectangular cross section shape based on a genetic algorithm.
Background
With the rapid development of the present microelectronics and chip manufacturing technology, the microelectronics products gradually have the development trend of integration, miniaturization and high power, and the microchannel heat dissipation technology has the advantages of small volume, low thermal resistance, high heat dissipation efficiency, low flow and the like, so that the application of the microchannel heat dissipation technology in various fields is more and more extensive. Meanwhile, the operation mode tends to be ultrahigh in operation speed, so that the heat productivity of the microelectronic device is increased rapidly, the operation reliability and the service life of the microelectronic device are further reduced, the bottleneck of updating the microelectronic product is formed, and the design of a microchannel radiator with good heat transfer and mass transfer performance is urgent.
Disclosure of Invention
The invention aims to provide an optimal design method of a microchannel heat sink with a rectangular cross section shape based on a genetic algorithm, which can conveniently optimize the shape and size parameters of a radiating coefficient of a microchannel and provide optimal structural parameters of heat transfer and mass transfer performance.
The technical purpose of the invention is realized by the following technical scheme:
an optimal design method of a microchannel heat sink with a rectangular cross section shape based on a genetic algorithm comprises the following steps:
respectively establishing theoretical models of thermal resistance and pressure drop of the rectangular-section microchannel heat sink under the constraint of equal section area/equal section perimeter through a thermal resistance network model based on theoretical expressions of flow resistance and average convective heat transfer coefficient of the rectangular-section microchannel;
taking the total thermal resistance and the total pressure drop of the micro-channel as two optimization targets, and performing multi-target optimization design on the micro-channel size structure by using a genetic algorithm;
performing simulation verification through comsol;
and obtaining the structure with the optimal size of the micro-channel heat and mass transfer performance.
Preferably, the micro-channel dimension structure comprises the number N of micro-channel flow channels and the width W of the micro-channelcWidth W of micro-channel heat sink finbHeight H of microchannelc。
Preferably, the multi-objective optimization design of the micro-channel size structure by using a genetic algorithm specifically comprises the following steps:
according to two optimization targets of total thermal resistance of the microchannel heat sink and total pressure drop of the microchannel heat sink, the constraint condition under the equal cross-sectional area is
Taking the number N of micro-channel flow channels and the width W of the micro-channelcWidth W of microchannel heat sink finbHeight H of microchannelcAs design variables, respectively denoted as x1，x2，x3，x4Written in vector form X ═ X1，x2，x3，x4]；
Taking the total thermal resistance and total pressure drop of the microchannel heat sink as two objective functions of the optimization design, and respectively recording as f1(x) And f2(x)；
The constant cross-section area multi-objective optimization model is as follows:
respectively converting the two objective functions of the total heat sink and the total pressure drop into dimensionless intermediate objective functions by a weighting conversion method, and forming the two intermediate objective functions into a brand new objective function by a linear weighting method:
in the formula
Is the weight coefficient of the total thermal resistance of the micro-channel heat sink,
is the weight coefficient of the total pressure drop of the microchannel heat sink, and
f1max and f1min is the objective function f1Maximum and minimum values of f2max and f2min is the objective function f2Maximum and minimum values of;
and performing multi-objective optimization through a genetic algorithm selected by hybrid hybridization, and solving under the constraint condition of equal section area to obtain an optimal solution size structure.
Preferably, the theoretical model of the total pressure drop is specifically:
flow resistance R of rectangular cross-sectional shape microchannelHIs a theoretical formula of
The theoretical expression of the average convective heat transfer coefficient h is:
wherein HcIs a channel height, W, of a rectangular microchannelcIs the channel width of the microchannel with rectangular section, L is the channel length, mu is the viscosity coefficient of the working medium in the microchannel, kfIs the heat conductivity coefficient of the working medium of the microchannel;
obtaining the total pressure drop of the microchannel with the rectangular cross section:
where N is the total number of microchannel heat sink channels.
Preferably, the theoretical model of the thermal resistance is specifically:
the total thermal resistance of the micro-channel heat sink calculation unit is as follows:
Rtotal＝
Rbase+Rfluid+[RbaseconvΠ(Rwall+(RwallconvΠ(Rwall+Rbaseconv))
total thermal resistance R of microchanneltotalEach constituent R ofbase，Rfluid，Rbaseconv，Rwall，RwallconvThe calculation is as follows:
wherein k issIs the thermal conductivity of the aluminum material, (W/m.k);
is the microchannel mass flow rate, (kg/s); c. CρRepresents the specific heat capacity of water, (J/(kg. DEG C)); h is the convective heat transfer coefficient;
micro-channel heat sink total thermal resistance
Comprises the following steps:
in conclusion, the invention has the following beneficial effects:
through multi-objective optimization design of a theoretical model and a genetic algorithm, the optimal size and shape of mass transfer properties of the micro-channel heat sink sensing can be obtained, optimization of the shape and size parameters of a micro-channel heat dissipation system is achieved, and the performance stability and the service life of related devices are improved.
Drawings
FIG. 1 is a schematic block flow diagram of the process;
FIG. 2 is a schematic diagram of a rectangular microchannel heat sink structure;
FIG. 3 is a model of a thermal resistance network in a microchannel heat sink calculation region;
FIG. 4 is a schematic flow chart of a genetic algorithm;
FIG. 5 is a graph showing the influence of weighting coefficients on the size of a microchannel structure under the constraint of an equal cross-sectional area;
FIG. 6 is a graph of pressure drop and thermal resistance of a microchannel heat sink under equal cross-sectional area constraints under different weight combinations;
FIG. 7 is a comparison graph of thermal resistance theory and simulated values of thermal resistance under various sets of weight coefficient combinations;
FIG. 8 is a comparison graph of theoretical and simulated values of pressure drop for each set of weight coefficient combinations.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The microchannel heat dissipation technology has the advantages of small volume, low thermal resistance, high heat dissipation efficiency, low flow and the like, so that the application of the microchannel heat dissipation technology in various fields is more and more extensive. Because the size of the microchannel has a great influence on the heat transfer and mass transfer performance of the microchannel heat sink, in order to improve the heat transfer and mass transfer performance of the microchannel on the premise of not changing a radiator material and a microchannel cooling liquid working medium, the size structure of the microchannel, including the number N of the microchannel channels, the width Wc of the microchannel channels, the height Hc of the microchannel channels and the like, needs to be optimally designed. The current optimized design of microchannel heat sinks is rarely restricted to equal channel cross-sectional area and equal channel cross-sectional perimeter.
At present, the common optimization design method aiming at the microchannel heat sink comprises a genetic algorithm, a box algorithm, a simplified conjugate gradient algorithm, a direct search algorithm and the like, and compared with other algorithms, the genetic algorithm has the main advantages that: (1) the genetic algorithm has the characteristic of group search; (2) the genetic algorithm is based on probability rules, rather than deterministic rules, which makes the search more flexible; (3) the genetic algorithm directly uses the target function as search information without designing differentiation and derivation processes.
According to one or more embodiments, a method for optimally designing a microchannel heat sink with a rectangular cross-sectional shape based on a genetic algorithm is disclosed, as shown in fig. 1, and comprises the following steps:
respectively establishing theoretical models of thermal resistance and pressure drop of the rectangular-section microchannel heat sink under the constraint of equal section area/equal section perimeter through a thermal resistance network model based on theoretical expressions of flow resistance and average convective heat transfer coefficient of the rectangular-section microchannel;
taking the total thermal resistance and the total pressure drop of the micro-channel as two optimization targets, and performing multi-target optimization design on the micro-channel size structure by using a genetic algorithm;
performing simulation verification through comsol;
and obtaining the structure with the optimal size of the micro-channel heat and mass transfer performance.
The used genetic algorithm is processed by using a direct comparison method for constraint, and most of the constraint conditions obtained by the optimization problem are subjected to nonlinear equality constraint or nonlinear inequality constraint. This problem can be described by the following mathematical model:
wherein x is (x)1，x2，...，xn) Is an n-dimensional vector.
Defining a default function:
all equality constraints are processed by converting them into inequality constraints:
gI+j(x)＝ε-|hj(x)|＞＞0；j＝1，2，...J
in the formula: ε is the given positive fractional number. The extent of the default for each individual in each generation is measured by G (x).
The two individuals are compared according to the following criteria to judge the advantages and disadvantages of the individuals: respectively calculating default values of two individuals needing to be compared, if the default values are not equal, the individuals with gene advantages are the individuals with smaller default functions, and storing the genes of the individuals into the next generation; if the two default values are calculated to be exactly equal, the function values of the two individuals are calculated, and the individuals with gene dominance are the individuals with smaller functions.
The rectangular microchannel heat sink structure is shown in fig. 2, the number of channels of the microchannel heat sink is N, the total length of the microchannel heat sink is L ═ 6mm, and the thickness of the substrate is HbThe width was fixed at 0.1mm, and the total width was fixed at W of 6 mm. Symmetry exists between the microchannel heat sink channel structures, so the computing area takes half of the microgrooves and fins.
Flow resistance R based on existing rectangular cross-sectional shape microchannelsHAnd a theoretical expression of the average convective heat transfer coefficient h, and establishing the thermal resistance R of the rectangular-section microchannel heat sink under the equal section area through a thermal resistance network modeltotalAnd theory of pressure drop PAnd (4) modeling.
Flow resistance R of microchannel with rectangular cross section and rectangular cross sectionHThe theoretical formula of (c) is as follows:
the theoretical expression for the average convective heat transfer coefficient h is as follows:
in the formula, HcIs a channel height, W, of a rectangular microchannelcIs the channel width of the microchannel with rectangular section, L is the channel length, mu is the viscosity coefficient of the working medium in the microchannel, kfIs the heat conductivity coefficient of the working medium of the micro-channel.
Accordingly, the pressure drop of the rectangular-section microchannel with a rectangular cross section is as follows:
wherein N is the total number of the micro-channel heat sink channels.
Similarly, a micro-channel heat sink calculation area thermal resistance network model is shown in fig. 3, the total thermal resistance of the micro-channel total heat sink is solved by applying the thermal resistance network model, and the total thermal resistance of the micro-channel heat sink calculation unit is shown as follows:
Rtotal＝
Rbase+Rfluid+[RbaseconvΠ(Rwall+(RwallconvΠ(Rwall+Rbaseconv))
wherein the total thermal resistance R of the microchanneltotalEach constituent R ofbase，Rfluid，Rbaseconv，Rwall，RwallconvThe calculation formula is as follows:
wherein k issIs the thermal conductivity of the aluminum material, (W/m.k);
is the microchannel mass flow rate, (kg/s); c. CρRepresents the specific heat capacity of water, (J/(kg. DEG C)); h is the convective heat transfer coefficient.
Micro-channel heat sink total thermal resistance
The calculation is as follows:
according to the above, two optimization target theoretical formulas of the total thermal resistance of the microchannel heat sink and the total pressure drop of the microchannel heat sink are determined, and the constraint conditions under the equal cross-sectional area are as follows:
taking the number N of micro-channel flow channels, the micro-channelWidth WcWidth W of microchannel heat sink finbHeight H of microchannelcAs a design variable, is denoted by x1，x2，x3，x4Written in vector form X ═ X1，x2，x3，x4]. Taking the total thermal resistance and total pressure drop of the microchannel heat sink as two objective functions of an optimization algorithm, and recording as f1(x) And f2(x) In that respect The equal section area multi-objective optimization model is as follows:
the essence of the multi-objective optimization design is to coordinate a plurality of optimization objectives into one optimization objective, and when the optimization objectives are coordinated, a weighting conversion method is selected, namely, a single optimization objective is converted into a single dimensionless intermediate objective function, and then the two are combined into a brand new objective function by using a linear weighting method:
in the formula
Is the weight coefficient of the total thermal resistance of the micro-channel heat sink,
is the weight coefficient of the total pressure drop of the microchannel heat sink, and
f1max and f1min is the objective function f1Maximum and minimum values of f2max and f2min is the objective function f2Maximum and minimum values of. F under the constraint of constant cross-sectional area1max、f1min、f2max and f2min is shown in table 1:
TABLE 1 maximum and minimum values of thermal resistance and pressure drop under equal cross-sectional area constraints
Substituting the data in table 1 into a completely new objective function that can be used to optimize the problem under the constraint of equal cross-sectional area is:
the genetic algorithm flow is shown in fig. 4, and is described in detail as follows:
step 1: determining population size M, probability of variation pmThe parameters required for the algorithm are initialized.
Step 2: and calculating the objective function value and default function value of all individuals in the population.
And step 3: and judging whether the iteration number is larger than g or not, if so, turning to the step 8.
And 4, step 4: the hybrid selection algorithm of the previous section is performed.
And 5: the optimal individuals enter the next generation.
Step 6: according to probability pmAnd (5) carrying out mutation.
And 7: adding 1 to the iteration number, and turning to the step 3
And 8: the algorithm is terminated and the genetic algorithm is exited.
The hybrid hybridization selection algorithm is as follows:
randomly selecting two individuals p from parent individuals without duplication1And p2. Respectively carrying out integral arithmetic hybridization, linear hybridization, partial arithmetic hybridization, complementary arithmetic hybridization, linear partial hybridization, complementary linear partial arithmetic hybridization, uniform arithmetic hybridization and complementary uniform arithmetic hybridization 10 mixed hybridization operators, selecting an optimal group of filial generation seeds from the generated 20 groups of filial generation seeds for comparison with the parent generation, if the fitness function of the filial generation seeds is worse than that of the parent generation seeds, replacing the filial generation seeds, otherwise, carrying out no operation, and carrying out two individuals of the parent generationEntering the next round: the optimization algorithm is as follows:
random non-repeated selection of two parent individuals p from the current population1And p2。
Two parents are subjected to 10 selective cross operators to generate offspring s1，s2，…，s20。
Select s1，s2，…，s20Medium optimal solution sbest。
If sbestIs superior to p1And p2Any one of them, p is replaced by1And p2The worse of them.
The optimal solution under the constraint of the equal cross-sectional area is shown in table 2:
TABLE 2 optimal solution under equal cross-sectional area constraint
The genetic algorithm used by the invention focuses more on whether the individual is in accordance with the constraint or not, and is assisted by the objective function value. The method for optimally designing the micro-channel can be not only rectangular, but also applicable to common shapes such as round, triangle and the like.
FIG. 5 is a graph showing the effect of different combining weighting factors on the size of a microchannel structure. FIG. 6 shows the total pressure drop and the total thermal resistance of the microchannel heat sink under the constraint of equal cross-sectional area under different weight combinations.
In order to increase the reliability of the optimization, the microchannel heat sink under the condition of equal cross-sectional area constraint is subjected to numerical simulation and verification, and the results are shown in fig. 7 and 8.
The present embodiment is only for explaining the present invention, and it is not limited to the present invention, and those skilled in the art can make modifications of the present embodiment without inventive contribution as needed after reading the present specification, but all of them are protected by patent law within the scope of the claims of the present invention.
Claims (5)
1. An optimal design method of a microchannel heat sink with a rectangular cross section shape based on a genetic algorithm is characterized by comprising the following steps:
respectively establishing theoretical models of thermal resistance and pressure drop of the rectangular-section microchannel heat sink under the constraint of equal section area/equal section perimeter through a thermal resistance network model based on theoretical expressions of flow resistance and average convective heat transfer coefficient of the rectangular-section microchannel;
taking the total thermal resistance and the total pressure drop of the micro-channel as two optimization targets, and performing multi-target optimization design on the micro-channel size structure by using a genetic algorithm;
performing simulation verification through comsol;
and obtaining the structure with the optimal size of the micro-channel heat and mass transfer performance.
2. The genetic algorithm-based optimization design method for the microchannel heat sink with the rectangular cross section shape as claimed in claim …, wherein: the micro-channel dimension structure comprises the number N of micro-channel runners and the width W of a micro-channelcWidth W of micro-channel heat sink finbHeight H of microchannelc。
3. The optimal design method of the microchannel heat sink with the rectangular cross section shape based on the genetic algorithm as claimed in claim 1, wherein: the method for carrying out multi-objective optimization design on the micro-channel size structure by using the genetic algorithm specifically comprises the following steps:
according to two optimization targets of total thermal resistance of the microchannel heat sink and total pressure drop of the microchannel heat sink, the constraint condition under the equal cross-sectional area is
Taking the number N of micro-channel flow channels and the width W of the micro-channelcWidth W of microchannel heat sink finbHeight H of microchannelcAs design variables, respectively denoted as x1，x2，x3，x4Written in vector form X ═ X1，x2，x3，x4]；
Taking the total thermal resistance and total pressure drop of the microchannel heat sink as two objective functions of the optimization design, and respectively recording as f1(x) And f2(x)；
The constant cross-section area multi-objective optimization model is as follows:
respectively converting the two objective functions of the total heat sink and the total pressure drop into dimensionless intermediate objective functions by a weighting conversion method, and forming the two intermediate objective functions into a brand new objective function by a linear weighting method:
in the formula
Is the weight coefficient of the total thermal resistance of the micro-channel heat sink,
is the weight coefficient of the total pressure drop of the microchannel heat sink, and
f1max and f1min is the objective function f1Maximum and minimum values of f2max and f2min is the objective function f2Maximum and minimum values of;
and performing multi-objective optimization through a genetic algorithm selected by hybrid hybridization, and solving under the constraint condition of equal section area to obtain an optimal solution size structure.
4. The genetic algorithm-based optimization design method for the microchannel heat sink with the rectangular cross section shape according to claim …, wherein the theoretical model of the total pressure drop specifically comprises:
flow resistance R of rectangular cross-sectional shape microchannelHIs a theoretical formula of
The theoretical expression of the average convective heat transfer coefficient h is:
wherein HcIs a channel height, W, of a rectangular microchannelcIs the channel width of the microchannel with rectangular section, L is the channel length, mu is the viscosity coefficient of the working medium in the microchannel, kfIs the heat conductivity coefficient of the working medium of the microchannel;
obtaining the total pressure drop of the microchannel with the rectangular cross section:
where N is the total number of microchannel heat sink channels.
5. The genetic algorithm-based optimization design method for the microchannel heat sink with the rectangular cross section shape as claimed in claim …, wherein the theoretical model of the thermal resistance specifically comprises:
the total thermal resistance of the micro-channel heat sink calculation unit is as follows:
Rtotal＝
Rbase+Rfluid+[RbaseconvΠ(Rwall+(RwallconvΠ(Rwall+Rbaseconv))
total thermal resistance R of microchanneltotalEach constituent R ofbase，Rfluid，Rbaseconv，Rwall，RwallconvThe calculation is as follows:
wherein k issIs the thermal conductivity of the aluminum material, (W/m.k);
is the microchannel mass flow rate, (kg/s); c. CρRepresents the specific heat capacity of water, (J/(kg. DEG C)); h is the convective heat transfer coefficient;
micro-channel heat sink total thermal resistance
Comprises the following steps:
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| CN113591299B (en) * | 2021-07-28 | 2024-03-26 | 清华大学 | Method and system for judging comprehensive performance of different types of micro-channel radiators |
| WO2023029490A1 (en) * | 2021-09-02 | 2023-03-09 | 中兴通讯股份有限公司 | Parameter calculation method for two-phase cold plate |
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