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Effect of double rotating cylinders on the MHD mixed convection and entropy generation of a 3D cubic enclosure filled by nano-PCM

Abstract

In this manuscript, phase change material (PCM) including the nanoparticles is considered in a 3D cubic enclosure to investigate the mixed convection of heat transfer under the magnetic field effect. Double rotating cylinders also are located in the middle of the enclosure to study the effect of their angular velocity in different conditions. Governing equations are solved by Galerkin Finite Element Method (GFEM) and were confirmed by previous studies. As main outcomes, results with enhanced angular velocity, both the average temperature and cumulative energy were significantly decreased. Furthermore, unaltered fluidity (\(\hbox {Ha}=0\)) imposes greater entropy, but this tendency reverses when the Hartman number (Ha) rises, resulting in minimum entropy trends.

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Data Availability

This manuscript has associated data in a data repository. [Authors’ comment: All data included in this manuscript are available upon request by contacting with the corresponding author.]

Abbreviations

r:

Radius of the cylinder, [m]

h:

Dimensional length of the heated wall (m)

p:

Static pressure \((\hbox {N/m}^{2})\)

Pr:

Prandtl number

X,Y:

Dimensionless coordinate

T:

Local temperature (\(^{^{\circ }}\hbox {K}\))

u:

Velocity in the x-direction (m/s)

v:

Velocity in the y-direction (m/s)

U,V:

Dimensionless velocity

\(C_{ps}\) :

solid PCM-specific heat (kJ/kgK)

\(C_{pl}\) :

liquid PCM-specific heat (kJ/kgK)

L:

latent heat of fusion of the PCM (kJ/kg)

\(\hbox {T}_{\mathrm{m}}\) :

PCM melting temperature (K)

\(\upalpha \) :

Thermal diffusivity (\(\hbox {m}^{2}/\hbox {s}\))

\(\beta \) :

Coefficient of thermal expansion (\(1/^{{\circ }}\hbox {K}\))

\(\theta \) :

Dimensionless temperature

\(k_{ls}\) :

solid  PCM  thermal  conductivity \((\hbox {W/m}\cdot \hbox {K})\)

\(k_{l}\) :

liquid  PCM  thermal  conductivity \((\hbox {W/m}\cdot \hbox {K})\)

\(\rho _{l}\) :

liquid  PCM  density \(\left( \mathrm {kg/}\mathrm {m}^{\mathrm {3}} \right) \)

\(\rho _{s}\) :

solid  PCM  density \(\left( \mathrm {kg/}\mathrm {m}^{\mathrm {3}} \right) \)

\(\upnu \) :

Kinematic viscosity (\(\hbox {m}^{2\, }/\hbox {s}\))

\(\upmu \) :

Dynamic viscosity (kg/ms)

\(\Omega \) :

angular rotational speed of the cylinder, [rad/s]

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Abderrahmane, A., Hatami, M., Younis, O. et al. Effect of double rotating cylinders on the MHD mixed convection and entropy generation of a 3D cubic enclosure filled by nano-PCM. Eur. Phys. J. Spec. Top. (2022). https://doi.org/10.1140/epjs/s11734-022-00586-7

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  • DOI: https://doi.org/10.1140/epjs/s11734-022-00586-7