仿生正形尾鳍结构微通道流动与传热特性数值研究及结构优化

doi:10.11949/0438-1157.20231069

摘要/Abstract

摘要：

基于鱼类尾鳍在流动过程中的重要作用，仿生设计并建立了正形尾鳍结构微通道物理模型，研究了仿生尾鳍肋间距对微通道综合传热性能的影响，提取了尾鳍结构凹陷长轴相对长度 $D t / W c h$ 、决定尾鳍结构最大宽度的 $b t / W c h$ 以及决定尾鳍结构最大高度的张角 $α t$ 三个结构参数，数值分析了结构参数对仿生微通道平均摩擦因数、平均Nusselt数、综合性能因子以及热阻和泵功的影响规律；并通过均匀试验分析回归拟合和遗传算法多目标优化得到了正形尾鳍结构参数的最优解。结果表明，综合性能因子随着仿生肋间距的增大而减小，当间距为4 mm时，正形尾鳍结构微通道的综合性能因子变化范围为1.74~1.89，综合传热性能明显优于矩形光滑通道；随着 $D t / W c h$ 的增加、 $b t / W c h$ 的减小或 $α t$ 的增加，尾鳍结构微通道的综合传热性能提升，其中凹陷长轴相对长度 $D t / W c h$ 和高度张角 $α t$ 影响较大。结构参数为 $D t / W c h$ =0.476、 $b t / W c h$ =0.135、 $α t$ =146.96°时，微通道性能有较大提升。

关键词: 微通道, 尾鳍, 仿生, 数值模拟, 传热

Abstract:

Motivated by the vital role of fish tail fins in fluid flow, microchannel with homocercal fin is designed. Three key structural parameters are identified: the relative length of the tail fin depression along its major axis $D t / W c h$ , the relative width of the tail fin $b t / W c h$ and the angle determining the maximum height of the fin $α t$ . The effects of structural parameters on average friction coefficient, average Nusselt number, overall performance factor, thermal resistance, and pump power of the bionic microchannel are analyzed numerically. The optimal solution to the structural parameters of the conformal caudal fin was obtained through uniform test analysis, regression fitting and genetic algorithm multi-objective optimization. The results show that the overall performance factor of the bionic homocercal fin microchannel ranges from 1.74 to 1.89, indicating significantly better comprehensive heat transfer performance compared to the rectangular smooth channel. Increasing the relative length $D t / W c h$ and angle $α t$ and decreasing width $b t / W c h$ improves the microchannel’s heat transfer performance, with the relative length $D t / W c h$ and the angle $α t$ having the greatest influence. Optimal microchannel performance is achieved when the structural parameters are $D t / W c h$ =0.476, $b t / W c h$ =0.135, and $α t$ =146.96°.

Key words: microchannel, tail fin, bionic, numerical simulation, heat transfer

中图分类号:

TK 124

李娟, 曹耀文, 朱章钰, 石雷, 李佳. 仿生正形尾鳍结构微通道流动与传热特性数值研究及结构优化[J]. 化工学报, 2024, 75(5): 1802-1815.

Juan LI, Yaowen CAO, Zhangyu ZHU, Lei SHI, Jia LI. Numerical study and structural optimization of microchannel flow and heat transfer characteristics of bionic homocercal fin microchannels[J]. CIESC Journal, 2024, 75(5): 1802-1815.

图/表 35

图1 微通道3D示意图

Fig.1 3D structure of microchannel and parameters

表1 仿生结构几何尺寸

Table 1 Geometric dimensions of the biomimetic structure

几何参数	尺寸
尾鳍结构圆直径(D_t)	1.2 mm
尾鳍结构凹陷长半轴长(a_t)	0.6 mm
尾鳍结构凹陷短半轴长(b_t)	0.24 mm
尾鳍结构高度张角(α_t)	180°

表2 固液相物性参数

Table 2 Physical properties of solid and liquid

材料	密度/(kg/m³)	比热容/(J/(kg·K))	热导率/(W/(m·K))
去离子水	998.2	4183	—
6063铝合金	2690	900	218

表3 实验工况

Table 3 Experimental conditions

工况	进口Reynolds数	进口流速/(m/s)	体积流量/(ml/min)
1	400	0.5034	90.60
2	550	0.6922	124.59
3	700	0.8809	158.58
4	850	1.0697	192.54
5	1000	1.2585	226.53
6	1150	1.4472	260.49
7	1300	1.6360	294.48

图2 尾鳍结构微通道(MC-T)局部网格划分示意图

Fig.2 Grid division of microchannel with shark-tail structure (MC-T)

表4 网格独立性验证

Table 4 Validation of grid independence

序号	网格数量/个	平均摩擦因数(f_ave,sim)	摩擦因数误差	平均Nusselt数(Nu_ave,sim)	Nusselt数误差
1	118万	0.1875	2.01%	7.09	6.27%
2	170万	0.1860	1.29%	6.86	3.12%
3	200万	0.1849	0.62%	6.76	1.76%
4	252万	0.1841	0.10%	6.70	0.55%
5	314万	0.1840	—	6.68	—

表5 热入口段Nusselt数

Table 5 Thermal entry region Nusselt number

x^*	Nu_x_,4	x^*	Nu_x_,4	x^*	Nu_x_,4
0.0001	26.7	0.00714	7.63	0.025	5.87
0.0025	10.4	0.00833	7.32	0.033	5.77
0.005	8.44	0.01	7	0.05	5.62
0.00556	8.18	0.0125	6.63	0.1	5.45
0.00625	7.92	0.0167	6.26	1	5.35

图3 数值模拟有效性验证

Fig.3 Validation of numerical simulation

图4 平均Nusselt数随Reynolds数的变化

Fig.4 Variation of average Nusselt number with Reynolds number

图5 总热阻随Reynolds数的变化

Fig.5 Variation of total thermal resistance with Reynolds number

图6 综合性能因子随Reynolds数的变化

Fig.6 Variation of comprehensive performance factor with Reynolds number

表6 不同间距微通道参数

Table 6 Different interval parameter of MC-T

参数	a型	b型	c型	d型	e型
尾鳍结构数量	19	17	15	14	13
间距/mm	4	4.5	5	5.5	6

图7 尾鳍微通道结构示意图

Fig.7 Schematic diagram of MC-T structure

图8 尾鳍间距对微通道平均摩擦因数的影响

Fig.8 Variation of average friction coefficient with interval

图9 尾鳍间距对微通道平均Nusselt数的影响

Fig.9 Variation of average Nusselt number with interval

图10 尾鳍间距对综合性能因子的影响

Fig.10 Variation of comprehensive performance factor with interval

图11 Dt/Wch对微通道平均摩擦因数的影响

Fig.11 Effect of Dt/Wch on average friction coefficient

图12 Dt/Wch对微通道平均Nusselt数的影响

Fig.12 Effect of Dt/Wch on average Nusselt number

图13 Dt/Wch对微通道综合性能因子的影响

Fig.13 Effect of Dt/Wch on comprehensive performance factor

图14 Dt/Wch对总热阻和泵功的影响

Fig.14 Effect of Dt/Wch on total thermal resistance and pumping power

图15 bt/Wch对微通道平均摩擦因数的影响

Fig.15 Effect of bt/Wch on average friction coefficient

图16 bt/Wch对微通道平均Nusselt数的影响

Fig.16 Effect of bt/Wch on average Nusselt number

图17 bt/Wch对微通道综合性能因子的影响

Fig.17 Effect of bt/Wch on comprehensive performance factor

图18 bt/Wch对总热阻和泵功的影响

Fig.18 Effect of bt/Wch on total thermal resistance and pumping power

图19 αt对微通道平均摩擦因数的影响

Fig.19 Effect of αt on average friction coefficient

图20 αt对微通道平均Nusselt数的影响

Fig.20 Effect of αt on average Nusselt number

图21 αt对微通道综合性能因子的影响

Fig.21 Effect of αt on comprehensive performance factor

图22 αt对总热阻和泵功的影响

Fig.22 Effect of αt on total thermal resistance and pumping power

表7 U11（113）均匀设计

Table 7 U11（113） uniform design

试验编号	因素1	因素2	因素3
1	1	5	7
2	2	10	3
3	3	4	10
4	4	9	6
5	5	3	2
6	6	8	9
7	7	2	5
8	8	7	1
9	9	1	8
10	10	6	4
11	11	11	11

表8 尾鳍结构微通道均匀设计

Table 8 Uniform design table for MC-T

试验编号	$D t / W c h$	$b t / W c h$	$α t$ /(°)	$R t o t$ /(K/W)	$W p$ /(W)
1	0.40	0.129	156	0.767	0.0044
2	0.42	0.159	132	0.798	0.0042
3	0.44	0.123	174	0.698	0.0047
4	0.46	0.153	150	0.682	0.0045
5	0.48	0.117	126	0.688	0.0045
6	0.50	0.147	168	0.665	0.0049
7	0.52	0.111	144	0.679	0.0048
8	0.54	0.141	120	0.649	0.0047
9	0.56	0.105	162	0.586	0.0056
10	0.58	0.135	138	0.641	0.0051
11	0.60	0.165	180	0.606	0.0061

表8 尾鳍结构微通道均匀设计

Table 8 Uniform design table for MC-T

试验编号	$D t / W c h$	$b t / W c h$	$α t$ /(°)	$R t o t$ /(K/W)	$W p$ /(W)
1	0.40	0.129	156	0.767	0.0044
2	0.42	0.159	132	0.798	0.0042
3	0.44	0.123	174	0.698	0.0047
4	0.46	0.153	150	0.682	0.0045
5	0.48	0.117	126	0.688	0.0045
6	0.50	0.147	168	0.665	0.0049
7	0.52	0.111	144	0.679	0.0048
8	0.54	0.141	120	0.649	0.0047
9	0.56	0.105	162	0.586	0.0056
10	0.58	0.135	138	0.641	0.0051
11	0.60	0.165	180	0.606	0.0061

表9 热阻及泵功多元二次回归方程系数值

Table 9 Coefficients of multivariate quadratic regression equations for Rtot and Wp

系数	MC-T
系数	$R t o t$	$W p$
$a 0$	1.9605	0.0148
$a 1$	-3.4258	-0.0165
$a 2$	1.212×10^-3	-0.1758
$a 3$	-2.969×10^-3	5.31×10^-5
$a 11$	4.6921	-7.045×10^-3
$a 22$	-10.5677	0.1775
$a 33$	-4.09×10^-3	3.28×10^-5
$a 12$	1.3994	0.5492
$a 13$	0.0355	-4.135×10^-4
$a 23$	-1.7×10^-6	-1.62×10^-8

表9 热阻及泵功多元二次回归方程系数值

Table 9 Coefficients of multivariate quadratic regression equations for Rtot and Wp

系数	MC-T
系数	$R t o t$	$W p$
$a 0$	1.9605	0.0148
$a 1$	-3.4258	-0.0165
$a 2$	1.212×10^-3	-0.1758
$a 3$	-2.969×10^-3	5.31×10^-5
$a 11$	4.6921	-7.045×10^-3
$a 22$	-10.5677	0.1775
$a 33$	-4.09×10^-3	3.28×10^-5
$a 12$	1.3994	0.5492
$a 13$	0.0355	-4.135×10^-4
$a 23$	-1.7×10^-6	-1.62×10^-8

表10 尾鳍结构微通道Pareto优化解集

Table 10 Pareto optimized solution set for MC-T

序号	$D t / W c h$	$b t / W c h$	$α t$ /(°)	$W p$ /W	$R t o t$ /(K/W)
1	0.400	0.140	120.00	0.0147	0.652
2	0.405	0.139	124.36	0.0150	0.631
3	0.409	0.139	130.28	0.0153	0.609
4	0.413	0.136	132.32	0.0156	0.598
5	0.420	0.137	134.77	0.0158	0.586
6	0.423	0.137	137.00	0.0160	0.578
7	0.440	0.138	133.14	0.0162	0.572
8	0.428	0.134	141.58	0.0165	0.562
9	0.470	0.138	134.14	0.0170	0.546
10	0.480	0.137	135.10	0.0172	0.536
11	0.464	0.137	148.69	0.0175	0.523
12	0.468	0.137	155.99	0.0179	0.513
13	0.513	0.137	141.85	0.0183	0.502
14	0.551	0.125	142.22	0.0189	0.479
15	0.554	0.121	146.30	0.0193	0.469
16	0.566	0.119	154.31	0.0201	0.456
17	0.574	0.117	157.30	0.0205	0.450
18	0.600	0.121	163.78	0.0210	0.445
19	0.599	0.108	161.88	0.0219	0.439
20	0.600	0.105	163.78	0.0225	0.438

表10 尾鳍结构微通道Pareto优化解集

Table 10 Pareto optimized solution set for MC-T

序号	$D t / W c h$	$b t / W c h$	$α t$ /(°)	$W p$ /W	$R t o t$ /(K/W)
1	0.400	0.140	120.00	0.0147	0.652
2	0.405	0.139	124.36	0.0150	0.631
3	0.409	0.139	130.28	0.0153	0.609
4	0.413	0.136	132.32	0.0156	0.598
5	0.420	0.137	134.77	0.0158	0.586
6	0.423	0.137	137.00	0.0160	0.578
7	0.440	0.138	133.14	0.0162	0.572
8	0.428	0.134	141.58	0.0165	0.562
9	0.470	0.138	134.14	0.0170	0.546
10	0.480	0.137	135.10	0.0172	0.536
11	0.464	0.137	148.69	0.0175	0.523
12	0.468	0.137	155.99	0.0179	0.513
13	0.513	0.137	141.85	0.0183	0.502
14	0.551	0.125	142.22	0.0189	0.479
15	0.554	0.121	146.30	0.0193	0.469
16	0.566	0.119	154.31	0.0201	0.456
17	0.574	0.117	157.30	0.0205	0.450
18	0.600	0.121	163.78	0.0210	0.445
19	0.599	0.108	161.88	0.0219	0.439
20	0.600	0.105	163.78	0.0225	0.438

图23 尾鳍结构微通道(MC-T)Pareto优化解集和5个聚类点

Fig.23 Pareto optimized solution set and five clustering points

图24 优化解与未优化解对比

Fig.24 Comparison of optimized and unoptimized solution

表11 MC-T优化前后的结果对比

Table 11 Comparison of results before and after optimization

项目		$D t / W c h$	$b t / W c h$	$α t$ /(°)	$R t o t$ /(K/W)	$W p$ /W
优化前		0.6	0.12	180	0.576	0.00560
点1	优化后	0.405	0.139	120.37	0.786	0.00398
点1	模拟值	0.405	0.139	120.37	0.773	0.00404
点2	优化后	0.437	0.132	120.91	0.744	0.00416
点2	模拟值	0.437	0.132	120.91	0.756	0.00398
点3	优化后	0.476	0.135	121.01	0.698	0.00438
点3	模拟值	0.476	0.135	121.01	0.703	0.00456
点4	优化后	0.511	0.133	146.96	0.649	0.00483
点4	模拟值	0.511	0.133	146.96	0.633	0.00497
点5	优化后	0.554	0.112	174.99	0.592	0.00558
点5	模拟值	0.554	0.112	174.99	0.604	0.00534

表11 MC-T优化前后的结果对比

Table 11 Comparison of results before and after optimization

项目		$D t / W c h$	$b t / W c h$	$α t$ /(°)	$R t o t$ /(K/W)	$W p$ /W
优化前		0.6	0.12	180	0.576	0.00560
点1	优化后	0.405	0.139	120.37	0.786	0.00398
点1	模拟值	0.405	0.139	120.37	0.773	0.00404
点2	优化后	0.437	0.132	120.91	0.744	0.00416
点2	模拟值	0.437	0.132	120.91	0.756	0.00398
点3	优化后	0.476	0.135	121.01	0.698	0.00438
点3	模拟值	0.476	0.135	121.01	0.703	0.00456
点4	优化后	0.511	0.133	146.96	0.649	0.00483
点4	模拟值	0.511	0.133	146.96	0.633	0.00497
点5	优化后	0.554	0.112	174.99	0.592	0.00558
点5	模拟值	0.554	0.112	174.99	0.604	0.00534

参考文献 38

1	于仓仓, 云和明, 崔云杰, 等. 菱形微通道圆盘热沉流动传热的数值模拟研究及优化[J]. 节能, 2022, 41(4): 31-37.
	Yu C C, Yun H M, Cui Y J, et al. Numerical simulation rsearch and optimization of flow and heat transfer in diamond microchannel disk heat sink[J]. Energy Conservation, 2022, 41(4): 31-37.
2	吉亚萍, 云和明, 郭训虎. 电子元件冷却的场协同分析[J]. 煤气与热力, 2019, 39(6): 20-26.
	Ji Y P, Yun H M, Guo X H. Field synergy analysis of electronic components cooling[J]. Gas & Heat, 2019, 39(6): 20-26.
3	王宁. 仿生蛛网型微通道散热器结构研究及参数优化[D]. 太原: 中北大学, 2022.
	Wang N. Research on structure and parameter optimization of bionic cobweb micro-channel radiator[D]. Taiyuan: North University of China, 2022.
4	Tuckerman D B, Pease R F W. High-performance heat sinking for VLSI[J]. IEEE Electron Device Letters, 1981, 2(5): 126-129.
5	Wang G L, Chen T, Tian M F, et al. Fluid and heat transfer characteristics of microchannel heat sink with truncated rib on sidewall[J]. International Journal of Heat and Mass Transfer, 2020, 148: 119142.
6	Li F, Ma Q M, Xin G M, et al. Heat transfer and flow characteristics of microchannels with solid and porous ribs[J]. Applied Thermal Engineering, 2020, 178: 115639.
7	陆卓群, 谢志辉, 王蓉, 等. 单侧内肋阵微通道复合热沉的流动和传热性能分析与构形设计[J]. 工程热物理学报, 2022, 43(11): 2841-2851.
	Lu Z Q, Xie Z H, Wang R, et al. Flow and heat transfer performance analysis and constructal design of hybrid microchannel heat sink with single-sided internal fin array[J]. Journal of Engineering Thermophysics, 2022, 43(11): 2841-2851.
8	Hsieh S S, Hsieh Y C, Hsu Y C, et al. Low Reynolds numbers convective heat transfer enhancement in roughened microchannels[J]. International Communications in Heat and Mass Transfer, 2020, 112: 104486.
9	李金星, 潘治良, 李平. 端部圆角结构提升带针肋微通道热沉均温性[J]. 科学通报, 2018, 63(1): 108-116.
	Li J X, Pan Z L, Li P. Improvement of temperature uniformity in microchannel with pin-fin based on endwall fillet structure[J]. Chinese Science Bulletin, 2018, 63(1): 108-116.
10	郭勇, 朱传勇, 郭雯, 等. 扰流结构微通道流动沸腾换热特性的数值研究[J]. 工程热物理学报, 2022, 43(5): 1296-1303.
	Guo Y, Zhu C Y, Guo W, et al. Numerical study on heat transfer characteristics of flow boiling in microchannel with turbulence structure[J]. Journal of Engineering Thermophysics, 2022, 43(5): 1296-1303.
11	李艺凡, 王志鹏. 带有周期性扰流结构的微通道内流动与传热特性[J]. 化工进展, 2022, 41(6): 2893-2901.
	Li Y F, Wang Z P. Flow and heat transfer characteristics in microchannels with periodic fluid disturbance structures[J]. Chemical Industry and Engineering Progress, 2022, 41(6): 2893-2901.
12	Pan M Q, Wang H Q, Zhong Y J, et al. Experimental investigation of the heat transfer performance of microchannel heat exchangers with fan-shaped cavities[J]. International Journal of Heat and Mass Transfer, 2019, 134: 1199-1208.
13	范贤光, 黄江尧, 许英杰. 凹槽型微通道传热与流动性能的数值分析[J]. 半导体光电, 2020, 41(2): 232-236, 241.
	Fan X G, Huang J Y, Xu Y J. Numerical analysis on heat transfer and flow characteristics of grooved microchannel[J]. Semiconductor Optoelectronics, 2020, 41(2): 232-236, 241.
14	Zhou F, Zhou W, Qiu Q F, et al. Investigation of fluid flow and heat transfer characteristics of parallel flow double-layer microchannel heat exchanger[J]. Applied Thermal Engineering, 2018, 137: 616-631.
15	王兆奇, 李孟山, 胡海涛, 等. 双排对折型微通道换热器仿真模型开发[J]. 化工学报, 2021, 72(S1): 113-119.
	Wang Z Q, Li M S, Hu H T, et al. Development of simulation model for double row folded microchannel heat exchanger[J]. CIESC Journal, 2021, 72(S1): 113-119.
16	陈超伟, 王鑫煜, 辛公明. 多孔鳍歧管微通道流动传热特性研究[J]. 制冷学报, 2022, 43(3): 62-70.
	Chen C W, Wang X Y, Xin G M. Flow and heat transfer characteristics in manifold microchannel with porous fins[J]. Journal of Refrigeration, 2022, 43(3): 62-70.
17	谢文远, 吕晓辰, 李龙, 等. 分级歧管微通道阵列散热器流动与散热特性研究[J]. 航天器工程, 2020, 29(4): 99-107.
	Xie W Y, Lv X C, Li L, et al. Flow and thermal characteristics research on hierarchical manifold microchannel heat sink array[J]. Spacecraft Engineering, 2020, 29(4): 99-107.
18	陈涛, 王桂莲, 吴永进, 等. 交错内肋微通道的流动和传热特性研究[J]. 热能动力工程, 2022, 37(9): 128-135.
	Chen T, Wang G L, Wu Y J, et al. Study on flow and heat transfer characteristics of microchannels with staggered internal ribs[J]. Journal of Engineering for Thermal Energy and Power, 2022, 37(9): 128-135.
19	Chen Y P, Deng Z L. Gas flow in micro tree-shaped hierarchical network[J]. International Journal of Heat and Mass Transfer, 2015, 80: 163-169.
20	Xia C H, Fu J Z, Lai J T, et al. Conjugate heat transfer in fractal tree-like channels network heat sink for high-speed motorized spindle cooling[J]. Applied Thermal Engineering, 2015, 90: 1032-1042.
21	Mills Z G, Warey A, Alexeev A. Heat transfer enhancement and thermal-hydraulic performance in laminar flows through asymmetric wavy walled channels[J]. International Journal of Heat and Mass Transfer, 2016, 97: 450-460.
22	Yu C M, Liu M F, Zhang C H, et al. Bio-inspired drag reduction: from nature organisms to artificial functional surfaces[J]. Giant, 2020, 2: 100017.
23	宋善鹏, 于志家, 刘兴华, 等. 超疏水表面微通道内水的传热特性[J]. 化工学报, 2008, 59(10): 2465-2469.
	Song S P, Yu Z J, Liu X H, et al. Heat transfer characteristics of water flowing in microchannels with super-hydrophobic inner surface[J]. Journal of Chemical Industry and Engineering (China), 2008, 59(10): 2465-2469.
24	Shen X, Zhai Y L, Guo W J, et al. Optimization and thermodynamic analysis of rib arrangement and height for microchannels with sharkskin bionic ribs[J]. Numerical Heat Transfer Part A-Applications, 2023, 84(1): 54-70.
25	Li P, Guo D Z, Huang X Y. Heat transfer enhancement, entropy generation and temperature uniformity analyses of shark-skin bionic modified microchannel heat sink[J]. International Journal of Heat and Mass Transfer, 2020, 146: 118846.
26	Gao Q Y, Zou H B, Li J. Numerical investigations of heat transfer and fluid flow characteristics in microchannels with bionic fish-shaped ribs[J]. Processes, 2023, 11(6): 1861.
27	Ling H J, Wang Z D. Investigation on thrust force conversion method of oscillating caudal fin based on wake vortex field structure[J]. Applied Bionics and Biomechanics, 2021, 2021: 5561268.
28	Xie F R, Zuo Q Y, Chen Q L, et al. Designs of the biomimetic robotic fishes performing body and/or caudal fin (BCF) swimming locomotion: a review[J]. Journal of Intelligent & Robotic Systems, 2021, 102(1): 13.
29	Zhang X, Su Y M, Wang Z L. Numerical and experimental studies of influence of the caudal fin shape on the propulsion performance of a flapping caudal fin[J]. Journal of Hydrodynamics, 2011, 23(3): 325-332.
30	Shah R K, London A L. Other doubly connected ducts[M]∥Laminar Flow Forced Convection in Ducts. New York: Academic Press, 1978: 341-353.
31	Li Z G, Huai X L, Tao Y J, et al. Effects of thermal property variations on the liquid flow and heat transfer in microchannel heat sinks[J]. Applied Thermal Engineering, 2007, 27(17): 2803-2814.
32	刘文竹, 云和明, 王宝雪, 等. 基于场协同和耗散的微通道拓扑优化研究[J]. 化工学报, 2023, 74(8): 3329-3341.
	Liu W Z, Yun H M, Wang B X, et al. Microchannel topology optimization based on field synergy and entransy[J]. CIESC Journal, 2023, 74(8): 3329-3341.
33	赵光攀, 向立平, 罗振兵, 等. 不同结构形式微通道热沉的传热性能[J]. 化学工程, 2023, 51(11): 7-12.
	Zhao G P, Xiang L P, Luo Z B, et al. Heat transfer performance of microchannel heat sinks with different structures[J]. Chemical Engineering (China), 2023, 51(11): 7-12.
34	Wang J Y, Yan W, Sang T, et al. Aeroelastic response and structural improvement for heavy-duty truck cab deflectors[C]∥SAE Technical Paper Series. PA, United States: SAE International, 2019.
35	张国秋, 王文璇. 均匀试验设计方法应用综述[J]. 数理统计与管理, 2013, 32(1): 89-99.
	Zhang G Q, Wang W X. A citation review on the uniform experimental design[J]. Journal of Applied Statistics and Management, 2013, 32(1): 89-99.
36	杜双奎. 试验优化设计与统计分析[M]. 2版. 北京: 科学出版社, 2020.
	Du S K. Experimental Design and Statistical Analysis[M]. 2nd ed. Beijing: Science Press, 2020.
37	Yan Y F, Yan H Y, Yin S Y, et al. Single/multi-objective optimizations on hydraulic and thermal management in micro-channel heat sink with bionic Y-shaped fractal network by genetic algorithm coupled with numerical simulation[J]. International Journal of Heat and Mass Transfer, 2019, 129(15): 468-479.
38	Yao P T, Zhai Y L, Li Z H, et al. Thermal performance analysis of multi-objective optimized microchannels with triangular cavity and rib based on field synergy principle[J]. Case Studies in Thermal Engineering, 2021, 25: 100963.

[1]	王金山, 王世学, 朱禹. 冷却表面温差对高温质子交换膜燃料电池性能的影响[J]. 化工学报, 2024, 75(5): 2026-2035.
[2]	李怡菲, 董新宇, 王为术, 刘璐, 赵一璠. 微肋板表面干冰升华喷雾冷却传热数值模拟[J]. 化工学报, 2024, 75(5): 1830-1842.
[3]	刘帆, 张芫通, 陶成, 胡成玉, 杨小平, 魏进家. 歧管式射流微通道液冷散热性能[J]. 化工学报, 2024, 75(5): 1777-1786.
[4]	李静, 张方芳, 王帅帅, 徐建华, 张朋远. 凹腔结构对正丁烷部分预混火焰可燃极限的影响[J]. 化工学报, 2024, 75(5): 2081-2090.
[5]	谢磊, 徐永生, 林梅. 不同截面肋柱-软尾结构单相流动传热比较[J]. 化工学报, 2024, 75(5): 1787-1801.
[6]	关朝阳, 黄国庆, 张一喃, 陈宏霞, 杜小泽. 泡沫铜导离气泡强化流动沸腾换热实验研究[J]. 化工学报, 2024, 75(5): 1765-1776.
[7]	王文雅, 张玮, 楼小玲, 钟若菲, 陈冰冰, 贠军贤. 纳米纤维素嵌合型晶胶微球的多微管成形与模拟[J]. 化工学报, 2024, 75(5): 2060-2071.
[8]	赵金鹏, 张永民, 兰斌, 罗节文, 赵碧丹, 王军武. 气固鼓泡床结构双流体传热模型及其模拟验证[J]. 化工学报, 2024, 75(4): 1497-1507.
[9]	吉笑盈, 郑园, 李晓鹏, 杨振, 张维, 邱诗蕊, 张倩颖, 罗沧海, 孙东鹏, 陈东, 李东亮. 微流控可控制备液滴、颗粒和胶囊及其应用[J]. 化工学报, 2024, 75(4): 1455-1468.
[10]	谷世良, 谭博仁, 程全中, 姚玮洁, 董志鹏, 许峰, 王勇. 轴流泵式混合室内水力学特征的数值模拟[J]. 化工学报, 2024, 75(3): 815-822.
[11]	陈彦松, 阮达, 刘渊博, 郑通, 张帅帅, 马学虎. 微通道换热器拓扑结构优化与性能研究[J]. 化工学报, 2024, 75(3): 823-835.
[12]	徐百平, 梁瑞凤, 喻慧文, 吴桂群, 肖书平. 双螺杆挤出机强化三角形转子作用下的腔内分布混合模拟[J]. 化工学报, 2024, 75(3): 858-866.
[13]	陈饶, 赵鑫, 陈戴欣, 姜圣坤, 廉应江, 王金波, 杨梅, 陈光文. 微反应器内甲苯连续二硝化制备二硝基甲苯[J]. 化工学报, 2024, 75(3): 867-876.
[14]	邓志诚, 许世峰, 王淇冬, 王家瑞, 王斯民. 浸没燃烧处理高盐高化学需氧量废水过程与能耗分析[J]. 化工学报, 2024, 75(3): 1000-1008.
[15]	屠楠, 刘晓群, 王驰宇, 方嘉宾. 连续进出料鼓泡流化床停留时间分布的相似准则研究[J]. 化工学报, 2024, 75(2): 543-552.