Numerical simulation study on particle orientation and anisotropic thermal conductivity in magnetic nanofluids

doi:10.11949/0438-1157.20250414

Abstract

Abstract:

Magnetic nanofluids have important applications in energy engineering due to their unique magnetically induced directional arrangement characteristics and heat transfer enhancement performance. A multi-force particle dynamics model, incorporating magnetic forces, was developed using the lattice Boltzmann method (LBM) coupled with the discrete element method (DEM). The orientation tensor was introduced to quantitatively characterize the spatial structure of particle chains under varying magnetic fields. The results show that the degree of particle alignment along the magnetic field direction increases with the strength of the applied field. Under magnetic field strengths of 200, 500, and 1000 G, the orientation tensor components in the magnetic field direction were 0.506, 0.758, and 0.972, respectively. Additionally, the thermal lattice Boltzmann method (T-LBM) was employed to simulate the thermal conductivity under magnetic field regulation. The mechanism by which the orientation tensor effectively quantifies anisotropic thermal conductivity through the characterization of the spatial configuration of particle chains was elucidated. A modified model incorporating the orientation tensor was proposed, demonstrating good predictive capability for magnetically induced anisotropic thermal conductivity.

Key words: magnetic nanofluids, particle aggregation, two-phase flow, numerical simulation, heat conduction

摘要：

磁性纳米流体因其独特的磁诱导定向排布特性与传热强化性能，在能源工程领域具有重要应用价值。利用格子Boltzmann方法（LBM）与离散单元法（DEM），建立了包括磁力的多作用力颗粒动力学模型。引入取向张量定量表征不同磁场下的颗粒链空间结构。结果表明，随着磁场强度的增大，颗粒沿磁场方向的定向排布程度逐渐提高。在200、500和1000 G的磁场强度下，磁场方向的取向张量分量分别为0.506、0.758和0.972。进一步采用热格子Boltzmann方法（T-LBM）模拟了磁场调控下的导热特性，揭示了取向张量通过表征颗粒链的空间构型来有效量化各向异性导热的机制。建立了考虑取向张量的热导率修正模型，该模型展现出了对磁诱导各向异性热导率良好的预测能力。

关键词: 磁性纳米流体, 颗粒聚集, 两相流, 数值模拟, 热传导

CLC Number:

TK 121

Shunjie WU, Rongrong CAI, A.A. Eliseev, Lizhi ZHANG. Numerical simulation study on particle orientation and anisotropic thermal conductivity in magnetic nanofluids[J]. CIESC Journal, 2025, 76(11): 5709-5719.

武顺杰, 蔡容容, Eliseev A.A., 张立志. 磁性纳米流体颗粒定向排布与各向异性导热的数值模拟研究[J]. 化工学报, 2025, 76(11): 5709-5719.

Figures/Tables 12

Fig.1 Schematic of boundary conditions

Table 1 Simulation parameters

模拟参数	数值	单位
颗粒密度 $ρ p$	5000	kg/m³
颗粒半径 $r p$	2.6×10^-8	m
Hamaker常数 $A H$	8.5×10^-20	J
颗粒体积分数φ	1.0%	—
磁场强度B	0~1000	G^①
流体密度 $ρ f$	1000	kg/m³
流体动力学黏度 $μ f$	0.001	kg/(m·s)
温度 $T$	335	K
计算域尺寸 $L 0$	3.22×10^-6	m
Zeta电势 $ψ 0$	-0.015	V

Table 1 Simulation parameters

模拟参数	数值	单位
颗粒密度 $ρ p$	5000	kg/m³
颗粒半径 $r p$	2.6×10^-8	m
Hamaker常数 $A H$	8.5×10^-20	J
颗粒体积分数φ	1.0%	—
磁场强度B	0~1000	G^①
流体密度 $ρ f$	1000	kg/m³
流体动力学黏度 $μ f$	0.001	kg/(m·s)
温度 $T$	335	K
计算域尺寸 $L 0$	3.22×10^-6	m
Zeta电势 $ψ 0$	-0.015	V

Table 2 Comparison of ETC results between T-LBM simulation and Maxwell and Bruggeman models

颗粒均匀分布的各工况纳米流体	颗粒体积分数或热导率比	有效热导率增强k_eff/k_f
颗粒均匀分布的各工况纳米流体	颗粒体积分数或热导率比	T-LBM	Maxwell	Bruggeman
不同颗粒体积分数的 SiO₂/甲醇纳米流体	0.1%	1.003	1.002	1.002
	0.5%	1.010	1.010	1.010
	1.0%	1.022	1.020	1.020
	2.0%	1.041	1.041	1.041
	5.0%	1.103	1.103	1.108
不同颗粒-基液热导率比的纳米流体	k(SiO₂)/k(H₂O) = 2.4	1.010	1.010	1.010
	k(CuO)/k(H₂O) = 16.9	1.030	1.025	1.026
	k(Fe₃O₄)/k(kerosene) = 76.9	1.038	1.029	1.030
	k(Al₂O₃)/k(methanol) = 147.9	1.039	1.030	1.030
	k(SiC)/k(H₂O) = 288.1	1.040	1.030	1.031

Fig.2 Simulation schematic of T-LBM model validation

Fig.3 Particle directional alignment under varying magnetic field intensities, with the aggregation number being the number of particles in a single chain

Fig.4 The schematic for calculating the orientation tension of aggregations

Fig.5 Orientation tensor T under varying magnetic fields, with the inset showing typical aggregation structures

Fig.6 Simulation results of ETC enhancement in x, y and z directions under different orientation tensors, along with comparison to isotropic models

Fig.7 Quantitative characterization for anisotropic heat conduction in aggregations using orientation tensor T

Fig.8 Fitting performance of the regression model

Fig.9 Comparison of model predictions of magnetic nanofluid keff/kf with reference data[8, 46]

Fig.10 Comparison of model predictions of magnetic nanofluid keff/kf with experimental data

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