Shape factor analysis of water and aluminium oxide nanoparticles in a porous medium with slip effects

This article explores the flow of a nanofluid over a flat plate subjected to a magnetic field. The chosen nanofluid comprises Al₂O₃ nanoparticles mixed in water as the base fluid. Various nanoparticle shapes are analyzed to inspect fluid flow and thermal transfer features. The impacts of first-order velocity slip and a porous medium are also examined. The governing flow equations are nonlinear partial differential equations that are reduced into ordinary differential equations by similarity transformations, and these reduced equations are subsequently solved numerically with the bvp4c MATLAB solver. The achieved numerical outcomes are approved using an analytical approach known as the optimal auxiliary functions method. The implications of critical parameters on flow profiles and physical quantities are illustrated via graphs and tables. Different velocity curves correspond to magnetic parameter $M$ showing that fluid velocity $f^{\prime }\left(\eta \right)$ decreases, while higher inputs of nanoparticle volume fraction ${\Phi }_1$ enhance fluid velocity. Higher inputs of porosity parameter $Ps$ lead towards improved temperature distribution $\theta \left(\eta \right)$, while enhanced inputs of velocity slip parameter $S_v$ provide reduced temperature profiles. This study also suggests that heat transfer enhancement varies much more significantly than the drag reduction effect in the obtained data. Streamlines and isotherm lines are also illustrated to examine the velocity and temperature characteristics for designated nanoparticle shapes.