Unsteady thin film flow and heat transfer in Fe ₃ O ₄ nanofluid over an inclined stretching sheet in a porous medium

This study investigates the unsteady flow and heat transfer characteristics of a nanofluid composed of Fe3O4 (iron oxide) nanoparticles suspended in a base fluid, flowing over an inclined stretching sheet within a porous medium. The effects of magnetic fields, radiation, velocity slip, and convective boundary conditions are analyzed, along with the influence of different nanoparticle shapes (lamina, tetrahedron, and hexahedron) on heat transfer. By applying similarity transformations, the governing partial differential equations are reduced to ordinary differential equations and solved numerically. MATLAB is used to visualize velocity and temperature profiles and to tabulate skin friction coefficients and heat transfer rates. The results show that an increase in the magnetic field strength leads to a reduction in velocity, while higher porosity levels further decelerate the flow by 15%. Furthermore, increasing the Biot number (which measures convective heat transfer at the boundary) from 1.0 to 1.5 enhances heat transfer rates for lamina, tetrahedron, and hexahedron-shaped nanoparticles by 7.2%, 6.32%, and 5.79%, respectively. These results highlight that lamina-shaped nanoparticles significantly boost heat transfer rate compared to other shapes. This research provides valuable insights into nanofluid transport in porous media, with implications for energy efficiency and materials science.