Cu-water Williamson nano-fluid in EMHD flow over an exponentially expanding sheet embedded in a Darcy–Forchheimer porous medium considering viscous dissipation

In this broadside, the unsteady magnetohydrodynamic (MHD) stream of a Williamson nano-fluid (WNF) established in a porous media has been considered, incorporating the belongings of heat generation/absorption, thermal radiation, and heat source. The commanding nonlinear partial differential equations (PDEs), which describe the motion, energy, and concentration fields, have been derived under appropriate assumptions. By using similarity transformations, these equations were turn into a system of ordinary differential equations (ODEs), which was resolved numerically using a Chebyshev spectral collocation method implemented in Mathematica. The study emphasizes the impact of various physical factors, such as Darcy–Forchheimer drag, Williamson factor, magnetic field strength, thermal radiation, and nanoparticle concentration, on the distributions of velocity, temperature, and concentration. Graphical illustrations and tables were used to display the behavior of these distributions in response to changes in the relevant parameters. The study’s outcomes demonstrate that enhancing the Williamson parameter reduces the velocity while increasing the fluid’s temperature. Additionally, the concentration distribution was found to decrease with higher nanoparticle volume fractions. The results of this investigation can serve as a useful reference for industrial processes involving non-Newtonian nano-fluids subjected to magnetic fields in porous media environments.