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Natural convection of nanoliquid from elliptic cylinder in wavy enclosure under the effect of uniform magnetic field: numerical investigation

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Abstract

In the current article, a three-dimensional numerical simulation is conducted to scrutinize the steady laminar natural convective flow and transfer of heat between a cold wavy porous enclosure and a hot elliptic cylinder. Alumina nanoparticles are dispersed in the water to enhance the heat exchange process. The nanofluid flow is taken as laminar and incompressible, while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The influences of different governing parameters such as nanoparticles volume fraction (ϕ), angle of rotation (α), Darcy number (Da), Hartmann number (Ha), and Rayleigh number (Ra) on the fluid flow, temperature (T) filed and average Nusselt number are presented. The results exhibit that the heat transfer is enhanced when either of Ra, Da and ϕ is raised. The permeability increment achieved a 12.73% enhancement in the heat transfer rate. Also, when \(\mathrm{Ha}\) is altered from 0 to 100, a reduction in values of the Nusselt number is given up to 22.22%. Furthermore, the optimal inclination angle for the convective process is α = 45°.

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Abbreviations

Cp:

Heat capacitance (J kg −1 °C −1)

B :

Magnetic induction

Da:

Darcy number

K :

Permeability (m2)

k :

Thermal conductivity (W m−1 K−1)

k eff :

Effective thermal conductivity (W m−1 K−1)

Nu:

Nusselt number

P :

Dimensionless pressure

p :

Pressure (Pa)

Pr:

Prandtl number

Ra:

Rayleigh number

T :

Temperature (K)

u, v, w :

Nondimensional velocity components

U, V, W :

Dimensionless velocity magnitude

N :

Undulation number

φ :

Solid volume fraction

α :

Heat diffusion coefficient (m2 s−1)

β :

Thermal diffusion coefficient (k−1)

ε :

Porosity

μ :

Dynamic viscosity (kg m−1 s−1)

μ eff :

Effective dynamic viscosity (kg m−1 s−1)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Fluid density (kg m−3)

θ :

Nondimensional temperature

c :

Cold

eff:

Effective

f :

Fluid

h :

Hot

s :

Solid

hnf:

Hybrid nanofluid

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Authors and Affiliations

  1. Laboratoire de Physique Quantique de La Matière Et Modélisation Mathématique (LPQ3M), Université Mustapha Stambouli de Mascara, Mascara, Algeria

    Abed Mourad, Abderrahmane Aissa & Mohammed Sahnoun

  2. Department of Physics, Faculty of Sciences, University of 20 Août 1955-Skikda, 2100, Skikda, Algeria

    Fateh Mebarek-Oudina

  3. Mechanical Engineering Department, College of Engineering, Prince Mohammad Bin Fahd University, Al Khobar, 31952, Saudi Arabia

    Weal. Al-Kouz

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  1. Abed Mourad
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  2. Abderrahmane Aissa
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  4. Weal. Al-Kouz
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  5. Mohammed Sahnoun
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Correspondence to Weal. Al-Kouz.

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Mourad, A., Aissa, A., Mebarek-Oudina, F. et al. Natural convection of nanoliquid from elliptic cylinder in wavy enclosure under the effect of uniform magnetic field: numerical investigation. Eur. Phys. J. Plus 136, 429 (2021). https://doi.org/10.1140/epjp/s13360-021-01432-w

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