Longwave modeling of thin film flow of a generalized second-grade fluid down a slanted plate

• Published in: International journal of non-linear mechanics 2023-03, Vol.149, p.104327, Article 104327
• Main Authors: T., Mahesh, Panda, Satyananda
• Format: Article
• Language: English
• Subjects: Finite volume method; Generalized second-grade fluid; Long-wavelength approximation; Thin liquid film
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2022.104327

The free surface dynamics of a thin film of a generalized second-grade fluid flowing down a slanted plate subjected to the action of gravity have been studied. A nonlinear evolution equation for the dynamics of the thin liquid film is derived using the long-wavelength approximation. The model allows to investigate the impact of fluid rheology and geometrical parameters on the thin film’s height. The nonlinear dynamics equation is implicitly approximated on a uniform grid by applying the finite volume discretization method, which uses upwind discretization of the flux function and first-order discretization of the time differential term. The investigation reveals that the free surface deformation trends are similar for the Newtonian and non-Newtonian fluids but the non-Newtonian fluid properties substantially influenced the size and shape of the deformation. It is also found that the shear-thinning fluid moves faster down to the plate compared to the Newtonian and shear-thickening fluid. •An evolution equation for the dynamics of the thin liquid film of the generalized-second grade fluid is derived.•The numerical solutions are obtained using the finite volume method•The non-Newtonian fluid’s properties significantly impact the deformation’s size and shape.•The higher plate inclination angle results in a higher deformation height for both shear-thinning and thickening liquid.•The fluid’s normal stress coefficient is investigated concerning the shear-dependent viscosity and its effects on the deformation of the film height.