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 alphaleft( {0.92 le alpha le 1} right), Hartmann number Ha left( {0 le Ha le 80} right), fin length left( {0.2 le L_{Fin} le 1} right), Darcy parameter Da left( {10^{ - 2} le Da le 10^{ - 4} } right), Rayleigh number Ra left( {10^{3} le Ra le 10^{6} } right), fusion temperature theta_{f}left( {0.05 le theta_{f} le 0.8} right), and solid volume fraction varphileft( {0 le varphi le 0.06} right) on the velocity field, isotherms, and mean Nusselt number overline{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} adjusts the strength and position of a phase change zone. The highest values of overline{Nu} are obtained when alpha = 1. An expansion in Hartmann number Ha reduces the values of overline{Nu}. Adding more concentration of nanoparticles is improving the values of overline{Nu}.
Highlights
The results indicated that the fractional time derivative changes the dual rotation between the inner fin and outer domain
It is remarked that the dual rotation between an inner fin and outer hexagonal-shaped domain is affected by the variations on a fractional time derivative α
The originality of the study is emulating the natural convection of nano-encapsulated phase change material (NEPCM) embedded in a hexagonal-shaped cavity under the impacts of a magnetic field and dual rotation between an inner fin and outer hexagonal-shaped domain
Summary
The inserted cool fin is functioning efficiently in the cooling process and adjusting the phase change zone within a hexagonal-shaped cavity. Greek symbols ζ Thermal diffusivity, m2 s−1 α Afractional time derivative β Coefficient of thermal expansion K−1 δ Heat parameter φ Nanoparticle volume fraction Ŵ Gamma function ε Porosity μ Viscosity γ A magnetic field inclination angle ν Kinematic viscosity, m2 s−1 ρ Density, kg/m3 σ Capacity ratio τ Dimensionless time θ Dimensionless temperature θf Fusion temperature ω Dimensionless angular velocity. The convection inside a complex-shaped cavity within heated fins supplied with a nano-encapsulated phase change material (NEPCM) has taken the researchers attention as an effective way to enhancement the heat and mass transfer and solving mechanical engineering problems
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