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A novel treatment of fractional-time derivative using the incompressible smoothed particle hydrodynamics (ISPH) method is introduced to simulate the bioconvection flow of nano-enhanced phase change materials (NEPCM) in a porous hexagonal cavity. The fractional-time derivative is based on the Caputo style, which reflects the fractional order behavior in complex systems. In this work, the circular rotation of the embedded four-pointed star and the motion of oxytactic microorganisms in a hexagonal cavity are conducted. Due to the significance of fractional derivatives in handling real physical problems with more flexibility than conventional derivatives, the present scheme of the ISPH method is developed to solve the fractional-time derivative of the bioconvection flow in a porous hexagonal cavity. This study implicates the variations of a fractional-time derivative, a parametric of an inner four-pointed star, and the pertinent physical parameters on the behavior of a bioconvection flow of a nanofluid in a hexagonal-cavity containing oxytactic microorganisms. The presence of microorganisms has a significant role in many biological, engineering, and medical phenomena. From the present numerical investigation, it is well mentioned that the computational time of the transient processes can be reduced by applying a fractional-time derivative. The variable sizes of an inner four-pointed star enhance the bioconvection flow in a hexagonal cavity.

A novel treatment of fractional-time derivative using the incompressible smoothed particle hydrodynamics (ISPH) method is introduced to simulate the bioconvection flow of nano-enhanced phase change materials (NEPCM) in a porous hexagonal cavity. The fractional-time derivative is based on the Caputo style, which reflects the fractional order behavior in complex systems. In this work, the circular rotation of the embedded four-pointed star and the motion of oxytactic microorganisms in a hexagonal cavity are conducted. Due to the significance of fractional derivatives in handling real physical problems with more flexibility than conventional derivatives, the present scheme of the ISPH method is developed to solve the fractional-time derivative of the bioconvection flow in a porous hexagonal cavity. This study implicates the variations of a fractional-time derivative, a parametric of an inner four-pointed star, and the pertinent physical parameters on the behavior of a bioconvection flow of a nanofluid in a hexagonal-cavity containing oxytactic microorganisms. The presence of microorganisms has a significant role in many biological, engineering, and medical phenomena. From the present numerical investigation, it is well mentioned that the computational time of the transient processes can be reduced by applying a fractional-time derivative. The variable sizes of an inner fourpointed star enhance the bioconvection flow in a hexagonal cavity. [ABSTRACT FROM AUTHOR]