Generalized second-grade fluid flow over a tilted plate with bump topography

The long-wave theory is used to model the thin film flow of a generalized second-grade fluid (GSGF) down a tilted plate with a bump topography. The derived single non-linear partial differential equation for the film thickness describes the surface wave generated by the bump, which disturbs the uniform flow. The model involves the non-Newtonian and geometrical parameters that investigate the wave’s shape and amplitude. The model equation is strongly non-linear due to the GSGF’s constitutive equations, and it is solved numerically using the finite volume method, where the flux function is approximated implicitly using the upwind scheme. The simulation reveals that the bump creates the surface wave, it splits and propagates, and its shape and size are influenced by the bump’s height and the non-Newtonian fluid properties.