Double rotations between an inner wavy shape and a hexagonal-shaped cavity suspended by NEPCM using a time-fractional derivative of the ISPH method

A transient two-dimensional ISPH method based on the time-fractional derivative was applied for emulating thermosolutal convection of the nano-encapsulated phase change material (NEPCM) embedded in an annulus between an inner wavy shape and outer hexagonal-shaped cavity. The impacts of a magnetic field and double rotations amongst an inner wavy shape and outer hexagonal-shaped cavity on the heat and mass transmission of NEPCM in an annulus have been conducted. Effects of a time parameter tau (0.01 - 1), frequency parameter omega (1 - 7), fractional time derivative alpha (0.95 - 1), Darcy parameter Da (10(-2) - 10(-4)), Hartmann number Ha (0 - 100), fusion temperature theta(f) (0.05 - 0.8), and Rayleigh number Ra (10(3) - 10(5)) on the contours of temperature, heat capacity, concentration, and velocity field as well as profiles of (Nu) over bar and (Sh) over bar are investigated. The main findings signaled that the double rotations plays effectively in speed up the nanofluid movements, and changing the features of temperature, concentration, and heat capacity inside an annulus. An augmentation in a frequency parameter boosts the nanofluid speed by 128.57%. A decline in a from 1 to 0.95 enhances the maximum nanofluid velocity by 13.73%. The nanofluid movements within an annulus are reduced according to an increase in Ha and a decrease in Da. The power in the Rayleigh number enhances the nanofluid movements within an annulus.