Fast calculation of radiative heat transfer coefficient between diffuse and non-diffuse surfaces

Fubing Li; Qi You; Junmin Leng; Linhao Yang

doi:10.3788/IRLA20230611

Infrared and Laser Engineering, Volume. 53, Issue 3, 20230611(2024)

Fast calculation of radiative heat transfer coefficient between diffuse and non-diffuse surfaces

Fubing Li, Qi You, Junmin Leng, and Linhao Yang

School of Information and Communication Engineering, Beijing Information Science and Technology University, Beijing 102206, China

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Figures & Tables(15)

Fig. 1. Monte-Carlo method for calculating radiative heat transfer coefficient

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Fig. 2. (a) The representation of reflected light by diffuse surface in Monte-Carlo method; (b) Fast method

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Fig. 3. Fast calculation method for calculating the radiative heat transfer coefficient of non-diffuse surface element i

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Fig. 4. (a) Illustration of 3D geometry model and its surface ID; (b) Illustration of random positions and direction vectors for emitted rays

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Fig. 5. Fast calculation of radiative heat transfer coefficient for model with diffuse and specular surfaces

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Fig. 6. (a) Comparison of computational time between Monte-Carlo method and Fast method when the inner surface reflectivity of the cube is ρ=0.4; (b) ρ=0.8

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Fig. 7. L-shape unenclosed cavity model

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Fig. 8. (a) Comparison of computational time between Monte-Carlo method and Fast method when the inner surface reflectivity of the L-shape cavity is ρ=0.4; (b) ρ=0.8

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Fig. 9. Illustration of the average number of ray-tracing times

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Table 1. Radiative heat transfer coefficient for the inner surfaces of the cube (Monte-Carlo method)

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Table 1. Radiative heat transfer coefficient for the inner surfaces of the cube (Monte-Carlo method)

Facet	1(AA'B'B)	2(BB'C'C)	3(CC'D'D)	4(DD'A'A)	5(A'B'C'D')	6(ABCD)	Integrality
1	0.05897	0.17917	0.21741	0.18131	0.18132	0.18116	0.99934
2	0.17956	0.05924	0.18051	0.21850	0.18032	0.18122	0.99934
3	0.21776	0.18120	0.04888	0.18594	0.18307	0.18249	0.99934
4	0.18201	0.21647	0.18750	0.04936	0.18190	0.18212	0.99934
5	0.17921	0.17974	0.18220	0.18333	0.07049	0.20437	0.99934
6	0.17872	0.17926	0.18274	0.18213	0.20545	0.07105	0.99934

Table 2. Radiative heat transfer coefficient for the inner surfaces of the cube (Fast method)

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Table 2. Radiative heat transfer coefficient for the inner surfaces of the cube (Fast method)

Facet	1(AA'B'B)	2(BB'C'C)	3(CC'D'D)	4(DD'A'A)	5(A'B'C'D')	6(ABCD)	Integrality	MAE
1	0.05937	0.18057	0.21859	0.18222	0.17886	0.17975	0.99934	1.29227‰
2	0.18068	0.05972	0.18135	0.21884	0.17903	0.17972	0.99934	0.93054‰
3	0.22136	0.18010	0.04669	0.18631	0.18214	0.18324	0.99985	1.48970‰
4	0.18218	0.22024	0.18636	0.04688	0.18098	0.18323	0.99985	1.59877‰
5	0.17933	0.18143	0.18179	0.18329	0.06566	0.20834	0.99985	1.84531‰
6	0.18179	0.18012	0.18301	0.18145	0.20777	0.06570	0.99985	2.09184‰

Table 3. MAE and integrality of radiative heat transfer coefficient for L-shape cavity model (Fast method)

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Table 3. MAE and integrality of radiative heat transfer coefficient for L-shape cavity model (Fast method)

Facet	ρ=0.4		ρ=0.8
Facet	MAE	Integrality	MAE	Integrality
1	1.11640‰	0.98594	0.61132‰	0.85933
2	1.29494‰	0.94656	2.29617‰	0.77797
3	0.55498‰	0.79605	1.91049‰	0.64609
4	1.19067‰	0.79290	1.34883‰	0.64261
5	6.59430‰	0.97410	4.82850‰	0.80405
6	0.98649‰	0.98910	0.64184‰	0.85692
7	0.64990‰	0.93160	0.56992‰	0.76133
8	1.33612‰	0.65359	1.32864‰	0.41103
9	5.29473‰	0.94401	5.60488‰	0.77703
10	1.45282‰	0.79286	1.44651‰	0.65081
11	1.03800‰	0.79272	1.53688‰	0.64366
12	2.62882‰	0.94494	3.66704‰	0.77457
13	5.80383‰	0.98413	4.92681‰	0.84846

Table 4. Ratio of average-tracking-times for a single ray emitted from the non-diffuse surface calculated with Fast method compared to Monte-Carlo method

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Table 4. Ratio of average-tracking-times for a single ray emitted from the non-diffuse surface calculated with Fast method compared to Monte-Carlo method

ρ	C_d
ρ	1/6	2/6	3/6	4/6	5/6
0.1	0.813	0.653	0.520	0.413	0.333
0.2	0.672	0.461	0.330	0.250	0.200
0.3	0.615	0.397	0.277	0.208	0.167
0.4	0.520	0.307	0.208	0.156	0.125
0.5	0.446	0.248	0.167	0.125	0.100
0.6	0.341	0.178	0.119	0.089	0.071
0.7	0.247	0.125	0.083	0.063	0.050
0.8	0.161	0.081	0.054	0.040	0.032
0.9	0.076	0.038	0.025	0.019	0.015

Table 5. Ratio of consumed time for all the surfaces using Fast method compared with Monte-Carlo method

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Table 5. Ratio of consumed time for all the surfaces using Fast method compared with Monte-Carlo method

ρ	C_d
ρ	1/6	2/6	3/6	4/6	5/6
0.1	0.844	0.769	0.760	0.804	0.889
0.2	0.727	0.641	0.665	0.750	0.867
0.3	0.679	0.598	0.638	0.736	0.861
0.4	0.600	0.538	0.604	0.719	0.854
0.5	0.539	0.499	0.583	0.708	0.850
0.6	0.451	0.452	0.560	0.696	0.845
0.7	0.373	0.417	0.542	0.688	0.842
0.8	0.301	0.387	0.527	0.680	0.839
0.9	0.230	0.359	0.513	0.673	0.836

Table 6. Theoretical and measured values of the computation time ratio between Fast method and Monte-Carlo method when ρ=0.8
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Table 6. Theoretical and measured values of the computation time ratio between Fast method and Monte-Carlo method when ρ=0.8
C_d 1/6 2/6 3/6 4/6 5/6
Theoretical 0.301 0.387 0.527 0.680 0.839
Measured 0.331 0.384 0.524 0.695 0.846

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Fubing Li, Qi You, Junmin Leng, Linhao Yang. Fast calculation of radiative heat transfer coefficient between diffuse and non-diffuse surfaces[J]. Infrared and Laser Engineering, 2024, 53(3): 20230611

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Paper Information

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Received: Oct. 31, 2023

Accepted: --

Published Online: Jun. 21, 2024

The Author Email:

DOI:10.3788/IRLA20230611

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Radiative heat transfer coefficient for the inner surfaces of the cube (Monte-Carlo method)

Table 1. Radiative heat transfer coefficient for the inner surfaces of the cube (Monte-Carlo method)

Table 2. Radiative heat transfer coefficient for the inner surfaces of the cube (Fast method)

Table 2. Radiative heat transfer coefficient for the inner surfaces of the cube (Fast method)

Table 3. MAE and integrality of radiative heat transfer coefficient for L-shape cavity model (Fast method)

Table 3. MAE and integrality of radiative heat transfer coefficient for L-shape cavity model (Fast method)

Table 4. Ratio of average-tracking-times for a single ray emitted from the non-diffuse surface calculated with Fast method compared to Monte-Carlo method

Table 4. Ratio of average-tracking-times for a single ray emitted from the non-diffuse surface calculated with Fast method compared to Monte-Carlo method

Table 5. Ratio of consumed time for all the surfaces using Fast method compared with Monte-Carlo method

Table 5. Ratio of consumed time for all the surfaces using Fast method compared with Monte-Carlo method

Table 6. Theoretical and measured values of the computation time ratio between Fast method and Monte-Carlo method when ρ=0.8

Table 6. Theoretical and measured values of the computation time ratio between Fast method and Monte-Carlo method when ρ=0.8