Calculation Method of 3D Transient Temperature Fields in Functionally Graded Materials Subjected to Annular Heat Source

doi:10.19596/j.cnki.1001-246x.8764

Abstract

Abstract:

In order to solve the complex and time-consuming problem of 3D transient heat conduction analysis of functionally gradient materials subjected to annular heat source, a semi-analytical method for the heat conduction of exponentially graded materials with an annular heat source is developed through Fourier-Laplace frequency response functions, numerical Laplace inversion and two-dimensional discrete Fourier inversion, which is compared with 3D Fourier transform method in literature and FEM to verify the reliability of the proposed method. Based on the semi-analytical method, the temperature and temperature gradient response, as well as the sensitivity of their peaks under annular and Gaussian heat sources are compared. Case studies show that the temperature and temperature gradient distribution have different responses to the inner and outer diameter of the annular heat source and the material gradient indices. Compared with Gaussian heat sources, annular heat sources have the relatively uniform temperature and temperature gradient fields. Changing the inner and outer diameter of the annular heat source can adjust the temperature peak and temperature gradient peak.

Key words: annular heat source, functionally graded material, 3D transient heat conduction, semi-analytical method

CLC Number:

TG151.1

Xuefeng SUO, Denghui HE, Huadong WANG, Wei CAO. Calculation Method of 3D Transient Temperature Fields in Functionally Graded Materials Subjected to Annular Heat Source[J]. Chinese Journal of Computational Physics, 2024, 41(3): 367-379.

Figures/Tables 19

Fig.1 Three dimensional heat conduction model of graded material with moving heat source

Fig.2 Power density distribution of annular Gaussian heat source

Fig.3 Procedure of algorithm for 3D temperature field

Fig.4 Variation of the maximum temperature with time

Fig.5 Temperature distributions along X axis (t=2 s)

Table 1 Predicted results from the present method and 3D-FFT method

Duration time t₀/s	T_max/℃ (Fig. 4, t=10 s)			T/℃ (Fig. 5, t=3 s, X=0)			CPU t/s
Duration time t₀/s	3D-FFT	Present study	Deviation	3D-FFT	Present study	Deviation	3D-FFT	Present study
t₀=1	-32.69	8.33	125.48%	459.90	462.63	0.59%	61.28	171.63
t₀=2	24.30	46.65	91.97%	319.11	315.35	1.49%	60.05	173.62
t₀=3	99.76	109.76	10.02%	194.97	197.33	1.21%	60.89	172.56

Fig.6 Finite element model of annular heat source heating

Fig.7 Variation of the maximum temperature with time

Fig.8 Temperature distributions along X axis (t=0.2 s)

Table 2 Comparisons of predicted results from the present method and FEM

Duration time t₀/s	T_max/℃ (Fig. 7, t=0.5 s)			T/℃ (Fig. 8, t=0.2 s, X=0)			CPU t/s
Duration time t₀/s	FEM	3D-FFT	Present study	FEM	3D-FFT	Present study	FEM	3D-FFT	Present study
t₀=0.1	63.64	59.87	62.50	173.52	170.98	184.39	1 623.42	49.63	120.36
t₀=0.2	110.60	101.57	106.83	108.35	104.21	118.96	1 931.85	51.26	122.44
t₀=0.3	108.04	98.69	105.84	68.36	63.03	72.85	1 736.64	51.31	123.56

Fig.9 Temperature distributions and gradients along X axis at t=1 s

Fig.10 Temperature distributions in XZ plane (a) Gaussian heat source; (b) annular heat source

Fig.11 Temperature gradient distributions in XY and XZ plane (a) Gaussian heat source; (b) annular heat source

Fig.12 Influence of inner and outer diameter of annular heat source on the maximum temperature (a)inner radius; (b) outer radius

Fig.13 Influence of inner and outer diameter of annular heat source on temperature along X axis (a)inner radius; (b) outer radius

Fig.14 Influence of inner and outer diameter of annular heat source on temperature gradient distributions along X axis (a)inner radius; (b) outer radius

Fig.15 Influence of material gradient index on the maximum temperature

Fig.16 Influence of material gradient index on temperature distributions along X and Z axes (a) X axis; (b) Z axis

Fig.17 Influence of material gradient index on temperature gradient distributions along X axis at (a) z=0.0 mm and (b) z=0.10 mm

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