Effect of dual-rotation on MHD natural convection of NEPCM in a hexagonal-shaped cavity based on time-fractional ISPH method

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 $$\alpha$$ α $$\left( {0.92 \le \alpha \le 1} \right)$$ 0.92 ≤ α ≤ 1 , Hartmann number Ha $$\left( {0 \le Ha \le 80} \right)$$ 0 ≤ H a ≤ 80 , fin length $$\left( {0.2 \le L_{Fin} \le 1} \right)$$ 0.2 ≤ L Fin ≤ 1 , Darcy parameter Da $$\left( {10^{ - 2} \le Da \le 10^{ - 4} } \right)$$ 10 - 2 ≤ D a ≤ 10 - 4 , Rayleigh number Ra $$\left( {10^{3} \le Ra \le 10^{6} } \right)$$ 10 3 ≤ R a ≤ 10 6 , fusion temperature $$\theta_{f}$$ θ f $$\left( {0.05 \le \theta_{f} \le 0.8} \right)$$ 0.05 ≤ θ f ≤ 0.8 , and solid volume fraction $$\varphi$$ φ $$\left( {0 \le \varphi \le 0.06} \right)$$ 0 ≤ φ ≤ 0.06 on the velocity field, isotherms, and mean Nusselt number $$\overline{Nu}$$ 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 $$\theta_{f}$$ θ f adjusts the strength and position of a phase change zone. The highest values of $$\overline{Nu}$$ Nu ¯ are obtained when $$\alpha = 1$$ α = 1 . An expansion in Hartmann number $$Ha $$ Ha reduces the values of $$\overline{Nu}$$ Nu ¯ . Adding more concentration of nanoparticles is improving the values of $$\overline{Nu}$$ Nu ¯ .