Abstract
This study examines the effects of magnetic-field-dependent (MFD) viscosity on the boundary layer flow of a non-Newtonian sodium alginate-based Fe3O4Fe3O4<math><mi>F</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></math> nanofluid over an impermeable stretching surface. The non-Newtonian Casson and homogeneous nanofluid models are utilized to derive the governing flow and heat transfer equations. Applying Lie group transformations to dimensional partial differential equations yields nondimensional ordinary differential equations, which are then numerically solved using the spectral quasi-linearization technique. The analysis primarily focuses on the impacts of the MFD viscosity parameter, nanoparticle volume fraction of Fe3O4Fe3O4<math><mi>F</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></math>, and magnetic parameters on the flow and heat transfer characteristics. The local skin friction and heat transfer rate behaviors influenced by viscosity changes due to the magnetic field are discussed. It is found that MFD viscosity significantly impacts flow and thermal energies, enhancing skin friction coefficients and reducing Nusselt numbers in the boundary layer region.