The time‐fractional ISPH method for fin circular rotation on MHD bioconvection flow of oxytactic microorganisms and NEPCM within a hexagonal‐shaped cavity

This work investigates the bioconvection flow of oxytactic microorganisms and nanoparticle‐enhanced phase change material (NEPCM) within a hexagonal‐shaped cavity containing a rotated cross fin, utilizing the incompressible smoothed particle hydrodynamics (ISPH) method based on a time‐fractional derivative. The study considers the circular rotation of an inner cross fin and the presence of two rectangular heat sources on the plane walls inside the hexagonal cavity. The novelty of this work is its integration of a hexagonal‐shaped cavity with a rotated cross fin and the use of a time‐fractional derivative in the ISPH method to analyze bioconvection flow, offering new insights into the interaction between microorganism motion and heat transfer dynamics in complex geometries. The effects of Darcy, Hartmann, Lewis, Peclet, Rayleigh, and bioconvection Rayleigh numbers on isotherms, heat capacity ratio, microorganism density, velocity fields, and average Nusselt number are analyzed. The key findings demonstrate the significant impact of Rayleigh and bioconvection Rayleigh numbers in enhancing heat distribution and velocity fields, thereby significantly influencing microorganism motion. Due to Lorentz forces, the velocity field decreases by with an increase in the Hartmann number from 0 to 50. The resistance of the nanofluid's velocity becomes apparent as the Darcy number decreases. Increasing Lewis and Péclet numbers cause the microorganisms to shift towards the cavity's boundaries.