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

doi:10.16183/j.cnki.jsjtu.2023.018

Abstract

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

CLC Number:

TK311

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.

Figures/Tables 13

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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