Thermal and Bioconvective Modeling and Analysis of Unsteady Cu‐Water Nanofluid Flow through Porous Media with Gyrotactic Microorganisms

ABSTRACT This study examined unsteady boundary layer flow of a nanofluid over an expanding sheet embedded in a Darcy porous medium, containing gyrotactic microorganisms. The model includes often‐overlooked factors like heat source effects, unsteadiness, buoyancy, slip conditions, and nanoparticle radius. The bvp4c technique in MATLAB is utilized to solve the governing PDEs numerically once converted into ODEs by utilizing similarity transformations. The findings indicate that while a higher volume fraction of nanoparticles raises temperature and thermal conductivity, it decreases velocity because of increased viscosity. Unsteadiness reduces surface temperature and enhances heat transmission. Larger nanoparticle radii, acting through relative viscosity, increase velocity and decrease temperature. In contrast to thermal buoyancy, which increases fluid motion and thickens the momentum boundary layer, permeability makes flow and convective transport difficult. Shear stress and heat transport are considerably changed by velocity and thermal slip. Larger bioconvection Schmidt numbers decrease the dispersion of microorganisms; thermophoresis and Brownian motion aid in their movement. Additionally, the skin friction coefficient increases as velocity slip increases, whereas the Nusselt number decreases with increased slip and porous resistance but improves in unsteady conditions. The work provides fresh perspectives on bioconvective systems, renewable energy, and thermal control.