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摘要

利用格子玻尔兹曼方法(lattice Boltzmann method, LBM)对倾斜多孔介质方腔内Al ₂O ₃-H ₂O纳米流体的自然对流进行数值模拟, 考虑了孔隙率(0.3 ≤ $\epsilon $ ≤ 0.9)、瑞利数(10 ³≤ Ra≤ 10 ⁶)、纳米颗粒体积分数(0 ≤ ϕ≤ 0.04)和倾斜角(0° ≤ γ≤ 120°)等因素的影响, 研究了正弦温度分布边界条件下倾斜多孔介质方腔内纳米流体的自然对流传热机理. 结果表明: 若 $\epsilon $ 和 γ保持不变时, 随着 Ra数的增大, 热壁面处的平均努塞尔数( Nu _ave数)呈现出先减小后增大的趋势; 对于给定的 Ra数, 当 γ= 0°时, 随着孔隙率的增大, 热壁面处 Nu _ave数逐渐增大, 当 γ= 40°, 80°和120°时, Nu _ave数在 $\epsilon $ = 0.7左右时达到最大值; 若 $\epsilon $ 和 Ra数保持不变, 当 γ= 40°时, 方腔内的自然对流换热效率最强, 当 γ= 80°时热壁面自然对流换热效率被削弱. 最后, 研究了纳米颗粒体积份数的影响, 当方腔施加一定倾角时, 热壁面处的 Nu_ave数随着纳米颗粒体积分数的增大而增大.

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Abstract

In this work, numerical simulation of nature convection of Al ₂O ₃-H ₂O nanofluid in an inclined square porous enclosure is investigated to analyze the influence of different physical parameters on fluid flow and heat transfer via the lattice Boltzmann method. Due to stable chemical properties and low price in the dispersion system, Al ₂O ₃-H ₂O nanofluid is widely used in the field of industrial heat transfer enhancement, which is the focus of present work. When the nanofluid is transport in a porous media, the Darcy-Brinkman-Forchheimer model is usually used to describe the porous media effects on nanofluid flow. Compared with uniform thermal boundary condition, the natural convection of nanofluids with non-uniform thermal boundary condition has not received much attention. In this paper, the sinusoidal boundary condition is applied to the left side wall to analyze the heat transfer mechanism of Al ₂O ₃-H ₂O nanofluid in the inclined square porous enclosure. The effect of porosity (0.3 ≤ $\epsilon $ ≤ 0.9), Rayleigh number (10 ³≤ Ra≤ 10 ⁶), volume fraction of nanoparticle (0 ≤ ϕ≤ 0.04), tilt angle (0° ≤ γ≤ 120°) on the heat transfer performance are systematically investigated. Numerical results show that the non-uniform boundary condition can affect the heat transfer performance on Al ₂O ₃-H ₂O nanofluid with different physical quantities, which is different from the uniform boundary condition. When γ= 0° and Rais fixed, the Nu _avenumber (average Nusselt number) at the heated wall increases with porosity. When γ= 40°, 80° or 120°, the Nu _avereaches its maximum value at $\epsilon $ = 0.7. In addition, if $\epsilon $ and Raare fixed, the results show that the heat transfer performance is most efficient at γ= 40° whereas it is weakened at γ= 80°. Moreover, when different inclination angles are applied to the square cavity, the Nu _aveincreases slightly with an augmentation of ϕ. In all, compared with the uniform temperature boundary condition, the effect of volume fraction of nanoparticles on the enhanced heat transfer is not significant, therefore, to improve the heat transfer performance of nanofluids with given ϕand Ra, it is necessary to take advantage of the improvement of effective thermal conductivity for the nanofluids in porous media and the perturbation influence of inclination angles on the system together with using appropriate porosity and square cavity tilt angle to intervene the flow.

Keywords:

nanofluids/
nature convection/
non-equilibrium temperature distribution/
lattice Boltzmann method

作者及机构信息

张贝豪,
郑林

通信作者:郑林,lz@njust.edu.cn

基金项目:国家自然科学基金(批准号: 51876092, 51506097)资助的课题

Authors and contacts

Corresponding author:Zheng Lin,lz@njust.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 51876092, 51506097)

文章全文: translate this paragraph

参考文献

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施引文献

下载: 全尺寸图片幻灯片

物性参数	H₂O	Al₂O₃	Glass fiber^[23,24]
ρ/kg·m^–3	997.1	397	1650
C_p/J·kg^–1·K^–1	4179	765	750
k/W·m^–1·K^–1	0.613	25	1.2
β/K^–1	21 × 10^–5	1.89 × 10^–5	—
d_s/nm	—	47	—

下载: 导出CSV

热物性参数	计算表达式
纳米流体粘度	$\mu {}_{nf} = \dfrac{{{\mu _f}}}{{{{\left( {1 - \phi } \right)}^{2.5}}}}$
纳米流体密度	${\rho _{nf}} = \left( {1 - \phi } \right){\rho _f} + \phi {\rho _s}$
纳米流体热容	${\left( {\rho {C_p}} \right)_{nf}} = \left( {1 - \phi } \right){\left( {\rho {C_p}} \right)_f} + \phi {\left( {\rho {C_p}} \right)_s}$
纳米流体热扩散系数	${\alpha _{nf}} = \dfrac{{{k_{nf}}}}{{{{\left( {\rho {C_p}} \right)}_{nf}}}}$
纳米流体热膨胀系数	${\left( {\rho \beta } \right)_{nf}} = \left( {1 - \phi } \right){\left( {\rho \beta } \right)_f} + \phi {\left( {\rho \beta } \right)_s}$
纳米流体导热系数	${k_{nf}} = \dfrac{{{k_p} + 2{k_f} - 2\left( {{k_f} - {k_p}} \right)\phi }}{{{k_p} + 2{k_f} + 2\left( {{k_f} - {k_p}} \right)\phi }}{k_f}$
多孔介质有效导热系数	${k_m} = \left( {1 - \epsilon} \right){k_p} + {\epsilon k_{nf}}$

下载: 导出CSV

	不同网格数下的Nu_ave数
	80 × 80	100 × 100	120 × 120	140 × 140
Nu_ave数	8.528	8.670	8.744	8.785
误差/%	3.39%	1.70%	0.83%	0.36%

下载: 导出CSV

Ra数	文献[27]	本文结果	误差/%
10³	1.116	1.123	0.63
10⁴	2.238	2.266	1.25
10⁵	4.509	4.556	1.04
10⁶	8.817	8.744	0.83

下载: 导出CSV

NO.	Da数	Ra数	文献[34]	本文结果	误差/%
1	10^–2	10⁴	1.530	1.497	2.16
2	10^–2	10⁵	3.555	3.441	3.09
3	10^–2	5 × 10⁵	5.740	5.694	0.87

下载: 导出CSV

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