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 [Formula: see text] [Formula: see text] , Hartmann number Ha [Formula: see text] , fin length [Formula: see text] , Darcy parameter Da [Formula: see text] , Rayleigh number Ra [Formula: see text] , fusion temperature [Formula: see text] [Formula: see text] , and solid volume fraction [Formula: see text] [Formula: see text] on the velocity field, isotherms, and mean Nusselt number [Formula: see text] 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 [Formula: see text] adjusts the strength and position of a phase change zone. The highest values of [Formula: see text] are obtained when [Formula: see text] . An expansion in Hartmann number [Formula: see text] reduces the values of [Formula: see text] . Adding more concentration of nanoparticles is improving the values of [Formula: see text] .