Abstract
The time-fractional derivative based on the Grunwald–Letnikove derivative of the 2D-ISPH method is applying to emulate the dual rotation on MHD natural convection in a hexagonal-shaped cavity suspended by nano-encapsulated phase change material (NEPCM). The dual rotation is performed between the inner fin and outer hexagonal-shaped cavity. The impacts of a fractional time derivative
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\begin{document}$$\alpha$$\end{document}
α
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\begin{document}$$\left( {0.92 \le \alpha \le 1} \right)$$\end{document}
0.92
≤
α
≤
1
, Hartmann number Ha
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\begin{document}$$\left( {0 \le Ha \le 80} \right)$$\end{document}
0
≤
H
a
≤
80
, fin length
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\begin{document}$$\left( {0.2 \le L_{Fin} \le 1} \right)$$\end{document}
0.2
≤
L
Fin
≤
1
, Darcy parameter Da
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\begin{document}$$\left( {10^{ - 2} \le Da \le 10^{ - 4} } \right)$$\end{document}
10
-
2
≤
D
a
≤
10
-
4
, Rayleigh number Ra
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\begin{document}$$\left( {10^{3} \le Ra \le 10^{6} } \right)$$\end{document}
10
3
≤
R
a
≤
10
6
, fusion temperature
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\begin{document}$$\theta_{f}$$\end{document}
θ
f
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\begin{document}$$\left( {0.05 \le \theta_{f} \le 0.8} \right)$$\end{document}
0.05
≤
θ
f
≤
0.8
, and solid volume fraction
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\begin{document}$$\varphi$$\end{document}
φ
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\begin{document}$$\left( {0 \le \varphi \le 0.06} \right)$$\end{document}
0
≤
φ
≤
0.06
on the velocity field, isotherms, and mean Nusselt number
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Nu
¯
are discussed. The outcomes signaled that a dual rotation of the inner fin and outer domain is affected by a time-fractional derivative. The inserted cool fin is functioning efficiently in the cooling process and adjusting the phase change zone within a hexagonal-shaped cavity. An increment in fin length augments the cooling process and changes the location of a phase change zone. A fusion temperature
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θ
f
adjusts the strength and position of a phase change zone. The highest values of
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Nu
¯
are obtained when
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\begin{document}$$\alpha = 1$$\end{document}
α
=
1
. An expansion in Hartmann number
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\begin{document}$$Ha $$\end{document}
Ha
reduces the values of
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. Adding more concentration of nanoparticles is improving the values of
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.