This work adopts an incompressible smoothed particle hydrodynamics (ISPH) method for handling the bioconvection flow of nanoparticle-enhanced phase change materials (NEPCM) inside a Z-shaped containing three circular cylinders and oxytactic microorganisms. The fractional time derivative of a system of controlling equations is solved by the ISPH method. The influences of magnetic field on thermosolutal convection of NEPCM in Z-shaped cavity. The mesh-free nature of the ISPH method helps in simulating the nanofluid flow in complex geometries. The Z-shaped cavity was chosen in this work for bioconvection flow because of its uses in semiconductors in solar cells, electronic devices, biomedicine, and thermal batteries. The bioconvection flow and heat transfer of the embedded circular cylinders are significant in heat exchangers and renewable energies. The scales of physical parameters are bioconvection Rayleigh number Rab=1−1000, Lewis number Le=1−20, Hartmann number Ha=0−80, fractional-time derivative α=0.9−1, Rayleigh number Ra=103−106, the radius of embedded circular cylinders Rc=0.05−0.2, and nanoparticles’ parameter ϕ=0−0.15. The results introduced the importance of Rab in enhancing the distributions of oxytactic microorganisms, and oxygen concentrations as well as the intensity of the velocity field. The size of embedded circular cylinders is effective in adjusting the distributions of oxytactic microorganisms, oxygen concentration, and temperature inside a Z-shaped cavity. The maximum velocity field decreases by 86.79 % as nanoparticle concentration increases from 0 % to 15 % due to the resulting high viscosity of the suspension fluid. An expanded radius of embedded circular cylinders improves the values of Nu‾ and Sh‾. This research provides crucial insights into optimizing thermal management and efficiency across diverse technological applications, from electronics to renewable energy and biomedical devices.
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