基于组合边界条件的固体材料热扩散系数测试方法

doi:10.16183/j.cnki.jsjtu.2023.018

上海交通大学学报 ›› 2024, Vol. 58 ›› Issue (8): 1201-1210.doi: 10.16183/j.cnki.jsjtu.2023.018

基于组合边界条件的固体材料热扩散系数测试方法

陈清华¹^,²^,³(), 吴佳乐¹, 陆育¹, 季家东¹^,²^,³, 刘萍¹^,²^,³

1.安徽理工大学机械工程学院,安徽淮南 232001
2.安徽理工大学环境友好材料与职业健康研究院, 安徽芜湖 241003
3.安徽理工大学矿山智能装备与技术省重点实验室,安徽淮南 232001

收稿日期:2023-01-16 修回日期:2023-04-12 接受日期:2023-05-22 出版日期:2024-08-28 发布日期:2024-08-27
作者简介:陈清华(1978-),教授,从事材料热物性、传热传质学等领域的研究; E-mail: ahhnds@163.com.
基金资助:
国家自然科学基金(52175070);安徽理工大学环境友好材料与职业健康研究院研发专项基金(ALW2021YF12)

Testing Method for Thermal Diffusivity of Solid Materials Based on Combined Boundary Conditions

CHEN Qinghua¹^,²^,³(), WU Jiale¹, LU Yu¹, JI Jiadong¹^,²^,³, LIU Ping¹^,²^,³

1. School of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001, Anhui, China
2. Environmental Friendly Materials and Occupational Health Research Institute, Anhui University of Science and Technology, Wuhu 241003, Anhui, China
3. Key Laboratory of Mine Intelligent Equipment and Technology, Anhui University of Science and Technology, Huainan 232001, Anhui, China

Received:2023-01-16 Revised:2023-04-12 Accepted:2023-05-22 Online:2024-08-28 Published:2024-08-27

摘要/Abstract

摘要：

提出了一种组合边界条件下结合传热反问题思想测算固体材料热扩散系数的方法.建立了正问题理论模型,基于有限体积法和交替方向隐式方法的思想利用MATLAB软件对正问题温度场进行数值求解,利用共轭梯度法结合软件编程求解反问题,反演得到材料的热扩散系数.设计了实验方案并搭建了完整的测试系统,利用测试装置对亚克力板(PMMA)、硼硅玻璃(Pyrex7740)、大理石3种材料进行了综合实验,结果表明导热系数测试结果与文献值的最大相对偏差为3.45%,小于5%,验证了测试方法和装置的可行性与准确性.进一步对PMMA热扩散系数实验的不确定度进行了分析,得到扩展不确定度为4.86%,处于较低水平,说明实验数据可靠,测试方法科学.

关键词: 固体材料, 对流边界, 组合边界, 热扩散系数, 传热反问题

Abstract:

A method for measuring the thermal diffusivity of solid materials under combined boundary conditions in combination with the idea of inverse heat transfer problem is proposed. Based on the idea of the finite volume method and the alternating direction implicit method, MATLAB software is used to numerically solve the temperature field of the forward problem. The conjugate gradient method in combination with software programming is used to solve the inverse problem, and the thermal diffusion coefficient of the material is obtained by inversion. Based on the test principle, an experimental scheme is designed and a complete test system is built. The structure design, selection, and machining of the device equipment for constructing three types of boundary conditions and collecting temperature data are performed. The main program of each functional module of the software part is programmed and debugged in LabVIEW software. The comprehensive experiments of acrylic plate (PMMA), borosilicate glass (Pyrex7740) and marble are conducted by using the test device. The results show that the maximum relative deviation between the thermal conductivity test results and the literature values is 3.45%, less than 5%, which verifies the feasibility and accuracy of the test method and device. The uncertainty of PMMA thermal diffusion coefficient experiment is further analyzed, and the expanded uncertainty is 4.86%, which is at a low level, indicating that the experimental data are reliable and the test method is scientific.

Key words: solid materials, convection boundary, combined boundary, thermal diffusion coefficient, inverse heat transfer problem

中图分类号:

TK311

陈清华, 吴佳乐, 陆育, 季家东, 刘萍. 基于组合边界条件的固体材料热扩散系数测试方法[J]. 上海交通大学学报, 2024, 58(8): 1201-1210.

CHEN Qinghua, WU Jiale, LU Yu, JI Jiadong, LIU Ping. Testing Method for Thermal Diffusivity of Solid Materials Based on Combined Boundary Conditions[J]. Journal of Shanghai Jiao Tong University, 2024, 58(8): 1201-1210.

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t/s	T/℃					α×10⁷/ (m²·s^-1)	λ/ [W·(m·K)^-1]	Δλ/%
t/s	测点1	测点2	测点3	测点4	测点5	α×10⁷/ (m²·s^-1)	λ/ [W·(m·K)^-1]	Δλ/%
100	29.0	29.4	29.8	30.3	30.9	1.168	0.188 6	1.46
120	30.0	30.6	30.9	31.5	32.3	1.229	0.198 4	3.66
140	31.1	31.8	32.1	32.7	33.5	1.214	0.196 0	2.40
160	32.1	32.8	33.2	33.7	34.5	1.206	0.194 7	1.72
180	33.1	33.7	34.2	34.7	35.4	1.192	0.192 5	0.57
200	33.9	34.6	35.1	35.5	36.2	1.163	0.187 8	1.88
220	34.6	35.4	35.8	36.3	37.1	1.166	0.188 3	1.62
240	35.3	36.1	36.5	37.0	37.7	1.155	0.186 5	2.56
平均值						1.186	0.191 6

t/s	T/℃			α×10⁷/ (m²·s^-1)	λ/[W· (m·K)^-1]	Δλ/ %
t/s	测点1	测点2	测点3	α×10⁷/ (m²·s^-1)	λ/[W· (m·K)^-1]	Δλ/ %
24	29.9	30.4	31.1	13.830	2.976	4.53
32	32.0	32.6	33.2	13.595	2.925	2.74
40	33.6	34.2	34.7	13.386	2.881	1.19
48	35.0	35.6	36.1	13.289	2.860	0.46
56	36.1	36.7	37.2	13.135	2.826	0.74
64	37.1	37.7	38.2	13.036	2.805	1.48
68	37.6	38.2	38.6	12.661	2.724	4.32
76	38.4	39.9	39.5	12.934	2.783	2.25
平均值				13.228	2.847

t/s	T/℃			α×10⁷/ (m²·s^-1)	λ/[W· (m·K)^-1]	Δλ/ %
t/s	测点1	测点2	测点3	α×10⁷/ (m²·s^-1)	λ/[W· (m·K)^-1]	Δλ/ %
26	28.6	28.7	28.9	6.943	1.181	3.87
30	30.1	30.3	30.5	6.765	1.151	1.23
34	31.3	31.5	31.9	6.646	1.158	1.85
38	32.4	32.7	33.1	6.710	1.147	0.88
42	33.5	33.8	34.2	6.649	1.131	0.53
46	34.4	34.7	35.2	6.624	1.127	0.88
50	35.3	35.6	36.1	6.639	1.114	2.02
54	36.2	36.4	36.8	6.545	1.111	2.29
平均值				6.679	1.137

材料	ρ/(kg·m^-3)	c/[J·(kg·℃)^-1]	α×10⁷/(m²·s^-1)	λ/[W· (m·K) ^-1]		Δλ/%
材料	ρ/(kg·m^-3)	c/[J·(kg·℃)^-1]	α×10⁷/(m²·s^-1)	计算值	文献值^[19-20]	Δλ/%
PMMA	1 170	1 380	1.193	0.193	0.194	0.72
Pyrex7740	2 250	740.2	6.833	1.138	1.1	3.45
大理石	2 634.2	816.9	13.205	2.842	2.8	1.50

实验次数	A类标准不确定度	α×10⁷/ (m²·s^-1)	残差	残差平方
1	4.825×10^-3	1.203	0.001 4	1.96×10^-6
2		1.231	0.029 4	8.64×10^-4
3		1.217	0.015 4	2.37×10^-4
4		1.184	-0.017 6	3.1×10^-4
5		1.190	-0.011 6	1.35×10^-4
6		1.205	0.003 4	1.16×10^-5
7		1.212	0.010 4	1.08×10^-4
8		1.198	-0.003 6	1.3×10^-5
9		1.184	-0.017 6	3.1×10^-4
10		1.192	-0.009 6	9.22×10^-5

基于组合边界条件的固体材料热扩散系数测试方法

Testing Method for Thermal Diffusivity of Solid Materials Based on Combined Boundary Conditions

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