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Natural convection of nanofluid in a U-shaped enclosure emphasizing on the effect of cold rib dimensions

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Abstract

Natural convection characteristics in an enclosure having U-shape that contains nanofluid are studied by extensively examining the effect of aspect ratio. The three outer walls of cavity are at isothermal high temperature, and facing inner walls are at a uniform low temperature. Computations are performed to explore the effect of the aspect ratios of cold wall to hot walls of the U-shaped cavity in the horizontal and vertical directions on the velocity and temperature characteristics in the cavity. The impact of various Rayleigh numbers and nanoparticle volume fractions of CuO is also studied. The computational results showed that all the considered parameters have a considerable influence on the heat transfer performance. Furthermore, the augmentation in heat transfer rate introduced by nanoparticles is more profound for larger vertical aspect ratios and low Rayleigh numbers. In addition, a noticeable relationship between the contribution of nanoparticles and the two different aspect ratios studied in this work is observed. Furthermore, the influence of vertical aspect ratio on the heat transfer is more pronounced compared to the horizontal aspect ratio, i.e., increasing the height of the cold wall is more effective than increasing the width of the cold wall for most of the cases. As a result of the comprehensive analysis, a correlation for mean Nusselt number including the influence of aspect ratio of cold rib, Rayleigh number and nanoparticle concentration is proposed.

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Abbreviations

ARH :

Aspect ratio of H/L

ARW :

Aspect ratio of W/L

C p :

Specific heat (J kg−1 K−1)

g :

Gravitational acceleration (m s−2)

H :

Height of the cold rib (m)

h :

Convective heat transfer coefficient (W m−2 K−1)

k :

Thermal conductivity (W m−1 K−1)

l :

Local position on the hot wall (m)

L :

Length of the hot wall of the cavity (m)

Nu:

Nusselt number

P :

Dimensionless pressure

Pr:

Prandtl number

q :

Heat flux (W m−2)

Ra:

Rayleigh number

θ :

Dimensionless temperature

u :

Horizontal component of dimensionless velocity

v :

Vertical component of dimensionless velocity

W :

Width of the cold rib (m)

α :

Thermal diffusivity (m2 s−1)

β :

Thermal expansion coefficient (K−1)

ϕ :

Nanoparticle volume fraction

µ :

Dynamic viscosity (Pa s)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

c:

Cold

eff:

Effective

f:

Fluid

h:

Hot

nf:

Nanofluid

l:

Local

p:

Particle

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Authors and Affiliations

  1. Mechanical Engineering Department, Engineering Faculty, Kocaeli University, 41001, Kocaeli, Turkey

    Çağatay Yıldız, Müslüm Arıcı & Hasan Karabay

  2. ENS-Cachan, LMT, CNRS, Université Paris Saclay, 61 Avenue du Président, 94235, Wilson, France

    Rachid Bennacer

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  1. Çağatay Yıldız
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Yıldız, Ç., Arıcı, M., Karabay, H. et al. Natural convection of nanofluid in a U-shaped enclosure emphasizing on the effect of cold rib dimensions. J Therm Anal Calorim 146, 801–811 (2021). https://doi.org/10.1007/s10973-020-10023-3

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