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Natural Convection and Surface Radiation Heat Transfer in a Square Cavity with an Inner Wavy Body

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Abstract

An in-house CFD code has been developed to address the coupling between natural convection and surface radiation in irregular geometries encountered in cooling electronic components. In the current numerical study, the discrete ordinate methods with the concept of blocked-off region are used in order to investigate the conjugate natural convection and surface radiation in an enclosure containing a wavy inner circular cylinder. The validity of the numerical code is ascertained by comparing our results with previously published results dealing with the limiting case of a smooth circular cylinder enclosed in a cavity. Extensive computations have been performed to study in detail the effect of the Rayleigh number (\(10^{3} \le {\text{Ra}} \le 10^{7}\)), the inner and outer surface emissivities (\(0 \le \upvarepsilon_{{{\text{E}}\,{\text{or I}}}} \le 1\)), the undulations number (\(4 \le {\text{N}} \le 1 2\), their amplitude (\(0 \le {\upalpha} \le 1\)) and the average radius of the wavy circular cylinder (\(0.05 \le {\text{R}}_{ 0} \le 0.25\)) on the flow structure as well as on the convective and radiative heat transfer characteristics. The obtained results showed that the amplitude and the average radius have more significant effect on the total heat transfer rate than the undulations number of the wavy wall.

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Abbreviations

g:

Gravitational acceleration, m·s−2

H:

Height of the cavity, m

I:

Dimensionless intensity

k:

Thermal conductivity, W·m−1K−1

L:

Width of the cavity, m

N:

Undulations number

Nu:

Nusselt number

P:

Pressure, Pa

Pl:

Planck number

Pr:

Prandtl number

Ra:

Rayleigh number

T:

Temperature, K

TR :

Temperature ratio

U, V:

Velocity components

x, y:

Cartesian coordinates, m

X, Y:

Dimensionless Cartesian coordinates

α:

Thermal diffisuvity, m2·s−1, undulations amplitude

β:

Thermal expansion coefficient, \({\text{K}}^{ - 1}\)

\({{\Delta {\mathbf{T}}}}\) :

Temperature difference, \({\text{K}}\)

δ:

Kronecker symbol

ε:

Emissivity of the radiative surface

θ:

Dimensionless temperature

\({\upsigma }\) :

Stefan-Boltzmann constant, W·K−4·m−2

\({{\upnu }}\) :

Kinematic viscosity, m2·s−1

ρ:

Density, kg·m−3

τ:

Time, s, optical thickness

\({{\upxi }}\) :

Direction cosines

ω:

Scattering albedo

B:

Black body

C:

Cold, convective

E:

External

H:

Hot

i, j:

Directions

I:

Internal

L:

Local

max:

Maximum

min:

Minimum

R:

Radiative

S:

Surface

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  1. LMFE, Department of Physics, Faculty of Sciences Semlalia, Cadi Ayyad University, B.P. 2390, Marrakesh, Morocco

    L. El Moutaouakil, M. Boukendil, Z. Zrikem & A. Abdelbaki

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  1. L. El Moutaouakil
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El Moutaouakil, L., Boukendil, M., Zrikem, Z. et al. Natural Convection and Surface Radiation Heat Transfer in a Square Cavity with an Inner Wavy Body. Int J Thermophys 41, 109 (2020). https://doi.org/10.1007/s10765-020-02688-7

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