Numerical simulation of natural convection of nanofluids in an inclined square porous enclosure by lattice Boltzmann method

Bei-Hao Zhang; Lin Zheng

doi:10.7498/aps.69.20200308

Journals >Acta Physica Sinica >Volume 69 >Issue 16 >Page 164401-1 > Article

Acta Physica Sinica
Vol. 69, Issue 16, 164401-1 (2020)

Numerical simulation of natural convection of nanofluids in an inclined square porous enclosure by lattice Boltzmann method

Bei-Hao Zhang and Lin Zheng^*

Author Affiliations

School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

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DOI: 10.7498/aps.69.20200308 Cite this Article

Bei-Hao Zhang, Lin Zheng. Numerical simulation of natural convection of nanofluids in an inclined square porous enclosure by lattice Boltzmann method[J]. Acta Physica Sinica, 2020, 69(16): 164401-1 Copy Citation Text

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Fig. 1. Schematic diagram of the physical model.

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Streamlines, isotherms contours for different : (a) = 0.3; (b) = 0.5; (c) = 0.7; (d) = 0.9.

Fig. 2. Streamlines, isotherms contours for different

: (a)

= 0.3; (b)

= 0.5; (c)

= 0.7; (d)

= 0.9.

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Fig. 3. (a) Vertical velocity distribution at X = 0; (b) horizontal velocity distribution at Y = 1 for different

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Fig. 4. (a) At the heated wall Nu_ave number; (b) local Nu number for different

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Fig. 5. Streamlines, isotherms contours for different Ra number: (a) Ra = 10³; (b) Ra = 10⁴; (c) Ra = 10⁵; (d) Ra = 10⁶.

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Fig. 6. (a) Vertical velocity distribution at X = 0; (b) horizontal velocity distribution at Y = 1 for different

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Fig. 7. (a) At the heated wall Nu_ave number; (b) local Nu number for different Ra.

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Fig. 8. Streamlines, isotherms contours for different γ number: (a) γ = 0°; (b) γ = 40°; (c) γ = 80°; (d) γ = 120°.

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Fig. 9. (a) Local temperature distribution along the Y = 0.5; (b) average velocity in the y direction & Nu_ave number at the heated wall in different γ.

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Fig. 10. (a) Local velocity in the y direction; (b) local Nu_ave number at the heated wall in different γ.

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Fig. 11. (a) Variation of Nu_ave number as a function of

in different γ at the heated wall; (b) when γ = 0°, 40°, variation of local Nu number at the heated wall in different

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Fig. 12. (a) Variation of Nu_ave number as a function of ϕ in different γ at the heated wall; (b) when γ = 0°, 40°, variation of local Nu number at the heated wall in different ϕ.

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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	—

Table 1.

Thermophysical properties of water, Al₂O₃ and glass fibers.

H₂O, Al₂O₃和玻璃纤维的热物理性质

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	${k_m} = \left( {1 - \epsilon} \right){k_p} + {\epsilon k_{nf}}$

Table 2.

Calculation formula for thermodynamic properties of nanofluids.

纳米流体的热物性参数计算公式

	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%

Table 3. Comparison of Nu_ave number with literature^[33] in different grids number.

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

Table 4. Comparison of Nu_ave number with previous literature[33].

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

Table 5. Comparison of Nu_ave number with previous literature[34].

Bei-Hao Zhang, Lin Zheng. Numerical simulation of natural convection of nanofluids in an inclined square porous enclosure by lattice Boltzmann method[J]. Acta Physica Sinica, 2020, 69(16): 164401-1

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