Interplay of steady/unsteady Jeffrey EMHD nanofluid flow formation in a vertical channel with induced magnetic field

This study explores the electro-magneto-hydrodynamic (EMHD) flow, heat and mass transfer of a Jeffrey nanofluid between two horizontal plates under the combined influence of electroosmotic flow (EOF), velocity slip, and an induced magnetic field. The base fluid is water with dispersed copper (Cu) nanoparticles. The governing nonlinear partial differential equations are solved using a finite difference method (FDM), complemented by an analytical approach via the method of undetermined coefficients. The results show that nanofluid velocity increases with higher Grashof numbers and permeability parameter, driven by buoyancy and porous medium effects. A magnetic field lowers fluid velocity but enhances the induced magnetic field near the lower wall; velocity slip reduces wall shear stress but increases velocity farther from the boundary; the Prandtl number improves heat transfer by reducing thermal diffusivity; the Darcy number facilitates flow through porous media; and an increase in Reynolds number sharpens the velocity profile and slightly enhances heat and mass transfer. These findings offer important insights into the coupled dynamics of EMHD nanofluid flow with potential applications in microfluidic and biomedical fields.