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Comparison of Nusselt number and stream function in tall and narrow enclosures in the mixed convection of hybrid nanofluid

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Abstract

In this research, the average Nusselt number in tall and narrow enclosures in the presence of mixed convection of a water-based nanofluid (H2O–Cu–TiO2) is determined and compared. The effect of quantities such as Richardson number of 0.01–100, the volume fractions of 0–2% and geometric shape of the enclosure on average Nusselt number and maximum value of flow function is numerically investigated. The FVM and SIMPLER algorithm are used for resolving the nonlinear equations. According to numerical results, for all the Richardson number and two tall and narrow enclosures, the average Nusselt number rises with growing the nanoparticles volume fractions. Comparison of the tall and narrow enclosures shows that for obtaining the highest heat transfer, by growing the nanoparticles volume fractions under similar conditions, it is better to use tall enclosures for large Richardson number and narrow enclosures for small Richardson number. The highest enhancement of the average Nusselt number with increasing the nanoparticles volume fractions for narrow enclosures was 10.44% at the Ri = 0.01. Whereas in the tall enclosures, the highest increase in the average Nusselt number was 14.51% at Ri = 100. For all the Richardson number and two tall and narrow enclosures, the maximum flow function value of the nanoparticles increases with increasing volume fractions. This increase in small Richardson number is greater than in large Richardson number.

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Abbreviations

c P :

Specific heat at constant pressure (J kg−1 K−1)

g :

Gravitational acceleration (m s−2)

H :

Cavity height (m)

k :

Thermal conductivity (W m−1 K−1)

Nu:

Nusselt number

P :

Pressure (Pa)

Re:

Reynolds number

Ri:

Richardson number

Pr:

Prandtl number

T :

Temperature (K)

u :

Velocity component (x)

v :

Velocity component (y)

U :

Dimensionless velocity (X)

V :

Dimensionless velocity (Y)

α :

Thermal diffusivity (m2 s−1)

β :

Coefficient of thermal expansion (K−1)

ρ :

Density (kg m−3)

θ :

Dimensionless temperature

υ :

Kinematic viscosity (m2 s−1)

φ :

Volume fraction of nanoparticles

ψ :

Stream function (m2 s−1)

Ψ :

Dimensionless stream function

avg:

Average

c:

Cold

h:

Hot

nf:

Nanofluid

np:

Nanoparticle

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Acknowledgements

This work was financially supported by the Key project of the National Social Science Foundation of the year 2018 (18AJY013); The 2017 National Social Science Foundation Project (17CJY072); The 2018 planning project of philosophy and social science of Zhejiang Province (18NDJC086YB); The 2018 Fujian Social Science Planning Project (FJ2018B067); The Planning Fund Project of Humanities and Social Sciences Research of the Ministry of Education in 2019 (19YJA790102).

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Authors and Affiliations

  1. Institute of Applied Economics, Yango University, Fuzhou, 350015, China

    Shu-Rong Yan & Xiao-Xiao Tian

  2. Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

    Rasool Kalbasi

  3. Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran

    Ansar Parvin

  4. Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Arash Karimipour

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  1. Shu-Rong Yan
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Correspondence to Arash Karimipour.

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Yan, SR., Kalbasi, R., Parvin, A. et al. Comparison of Nusselt number and stream function in tall and narrow enclosures in the mixed convection of hybrid nanofluid. J Therm Anal Calorim 143, 1599–1609 (2021). https://doi.org/10.1007/s10973-020-09809-2

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