Monte Carlo Method for Solving Two-Dimensional Coupled Anisotropic Conduction-Radiation Heat Transfer

doi:10.12068/j.issn.1005-3026.2025.20240040

Abstract

Abstract:

In order to study the coupled thermal conductivity-radiation heat transfer characteristics of two-dimensional anisotropic materials， a computational method was developed for solving the coupled conduction-radiation heat transfer of two-dimensional anisotropic materials based on the basic idea of random walk for a uniform discrete mesh，and the accuracy of the computational method was verified. The effects of anisotropic thermal conductivity coefficient on the heat transfer characteristics were analyzed. The results show that for a two-dimensional plate， an anisotropic thermal conductivity coefficient results in a shift of the temperature field of the plate towards the corresponding anisotropy. The anisotropy of the plate is basically unchanged when the ratio of $k 12 *$ to $k 22 *$ is the same. The increase of $k 12 *$ leads to the change of the direction of the temperature conduction in the plate when the $k 22 *$ remains constant， which makes the temperature homogeneity decrease in the plate.

Key words: anisotropy, Monte Carlo method, uniform grid, coupled heat transfer, random walk algorithm

CLC Number:

TK 124

Zi-jian GE, Zhi YI, Guo-jun LI, Lin-yang WEI. Monte Carlo Method for Solving Two-Dimensional Coupled Anisotropic Conduction-Radiation Heat Transfer[J]. Journal of Northeastern University(Natural Science), 2025, 46(9): 58-64.

Figures/Tables 10

Fig.1 Two-dimensional discrete node model

Table 1 Coefficients of nodal discrete equation

P_W	P_S	P_E	P_N	P_NE	Q_ds
$1 P k 11 ∆ x 2$	$1 P k 22 ∆ y 2$	$1 P k 11 ∆ x 2 - k 12 + k 21 ∆ x ∆ y$	$1 P k 22 ∆ y 2 - k 12 + k 21 ∆ x ∆ y$	$1 P k 12 + k 21 ∆ x ∆ y$	$Q P$

Table 1 Coefficients of nodal discrete equation

P_W	P_S	P_E	P_N	P_NE	Q_ds
$1 P k 11 ∆ x 2$	$1 P k 22 ∆ y 2$	$1 P k 11 ∆ x 2 - k 12 + k 21 ∆ x ∆ y$	$1 P k 22 ∆ y 2 - k 12 + k 21 ∆ x ∆ y$	$1 P k 12 + k 21 ∆ x ∆ y$	$Q P$

Fig.2 Geometric model of random walk

Fig.3 Flowchart of random movement of coupled proton

Fig.4 Temperature distribution curves along y-direction at x/Lx =0.5

Table 2 Dimensionless temperature T/TR at aspecific location on centerline(x/Lx=0.5,y/Ly) for different conduction-radiation parameter Ncr

N_cr	y/L_y	T/T_R
N_cr	y/L_y	DTM	LBM	本文方法
	0.3	0.737	0.738	0.736
1.0	0.5	0.630	0.631	0.630
	0.7	0.567	0.564	0.564
	0.3	0.760	0.759	0.758
0.1	0.5	0.663	0.662	0.662
	0.7	0.594	0.593	0.593
	0.3	0.790	0.788	0.785
0.01	0.5	0.725	0.722	0.726
	0.7	0.665	0.662	0.653

Fig.5 Dimensionless temperature distribution curves along y-direction at x/Lx =0.5

Table 3 Calculation conditions

计算条件	$k 12 *$	$k 22 *$
1	0.25	0.5
2	0.25	1.5
3	0.50	1.0
4	0.50	1.5

Table 3 Calculation conditions

计算条件	$k 12 *$	$k 22 *$
1	0.25	0.5
2	0.25	1.5
3	0.50	1.0
4	0.50	1.5

Fig.6 Dimensionless temperature cloud map of plate

Fig.7 Dimensionless temperature distribution curves along x-direction at y/Ly =0.5

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