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Thermo-magnetic convection analysis of magnetite ferrofluid in an arc-shaped lid-driven electronic chamber with partial heating

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Abstract

The present paper investigates a magnetic source’s thermal and flow impacts on mixed convection conditions in a novel arc-shaped lid-driven cavity problem. The examined cavity consists of a square enclosure of length (L) with two arc-shaped vertical plates, and it is filled with Fe3O4/water ferrofluid. For this purpose, an in-house solver has been developed within the OpenFOAM® libraries based on the finite-volume method to solve the governing equations. In this regard, different parameters were implemented, which include various magnetic numbers (0 ≤ Mn ≤ 100), Richardson numbers (0.04 ≤ Ri ≤ 40), solid volume fractions (0 ≤ ϕ ≤ 0.05), and the dimensionless wide length of the arc (b* = b/L) varies from 0 to 0.15. The outcomes revealed that applying the magnetic source in the vicinity of the heater causes the appearance of a recirculation zone which boosts the diffusion phenomena. At Ri = 0.04, with the actions of the magnetic field, arc-shaped walls, and suspending magnetite nanoparticles, heat transfer enhancement can reach up to 338.35%. However, the heat transfer rate diminishes when the kelvin force is considered at Ri = 40. Finally, these outcomes are followed by developing two new correlations of the NuM versus Ri, ϕ, Mn, and b*.

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Abbreviations

\(b\) :

Dimensional wide length of the arc (m)

b* :

Dimensionless wide length of the arc

\({\text{Ec}}\) :

Eckert number

\({\varvec{F}}_{{\mathbf{K}}}\) :

Kelvin force (N  m−3)

\(g\) :

Gravity (m  s−2)

\({\text{Gr}}\) :

Grashof number

\(H\) :

Magnetic field (N m−1 A−1)

\(k\) :

Thermal conductivity (W m−1 K−1)

\(L\) :

Cavity length (m)

\(M\) :

Magnetization (N m−1 A−1)

\({\text{Mn}}\) :

Magnetic number

\({\text{Nu}}\) :

Nusselt number

\(p\) :

Pressure (N m−2)

\(P\) :

Dimensionless pressure

Pr:

Prandtl number

\({\text{Re}}\) :

Reynolds number

\({\text{Ri}}\) :

Richardson number

\(T\) :

Temperature (K)

\(u\) :

\(v\), Dimensional velocities (m s−1)

\(U, V\) :

Dimensionless velocities

\(u_{0}\) :

Uniform top wall velocity (m s−1)

\(x, y\) :

Coordinates (m)

\(X, Y\) :

Dimensionless coordinates

\(\alpha\) :

Diffusivity (m2 s−1)

\(\beta\) :

Thermal expansion coefficient (K−1)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\rho\) :

Density (kg m−3)

\(\theta\) :

Dimensionless temperature

\(\phi\) :

Volume fraction

c:

Cold

f:

Fluid

L:

Local

h:

Hot

M:

Mean variable

nf:

Nanofluid

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Authors and Affiliations

  1. Applied Energetics and Pollution Laboratory, Department of Mechanical Engineering, Faculty of Sciences Technology, Frères Mentouri Constantine1 University, 25000, Constantine, Algeria

    Zakaria Korei, Farid Berrahil & Smail Benissaad

  2. Department of Mechanical and Electro-Mechanical Engineering, Science and Technology Institute, University Center Abdelhafid Boussouf, 43000, Mila, Algeria

    Farid Berrahil

  3. Laboratoire de Mécanique et Systèmes Energétiques Avancés, Ecole Nationale Polytechnique de Constantine, BP75, A, Nouvelle Ville Ali Mendjli, 25000, Constantine, Algeria

    Abdelkader Filali

  4. Chemical Engineering Department, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK

    Abdelkader Filali

  5. Department of Mathematics and Computer Science, Science and Technology Institute, University Center Abdelhafid Boussouf, 43000, Mila, Algeria

    Aissa Boulmerka

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  1. Zakaria Korei
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Korei, Z., Berrahil, F., Filali, A. et al. Thermo-magnetic convection analysis of magnetite ferrofluid in an arc-shaped lid-driven electronic chamber with partial heating. J Therm Anal Calorim 148, 2585–2604 (2023). https://doi.org/10.1007/s10973-022-11894-4

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