Computational-Analysis of the Non-Isothermal Dynamics of the Gravity-Driven Flow of Viscoelastic-Fluid-Based Nanofluids Down an Inclined Plane

The paper explores the gravity-driven flow of the thin film of a viscoelastic-fluid-based nanofluids (VFBN) along an inclined plane under non-isothermal conditions and subjected to convective cooling at the free-surface. The Newton's law of cooling is used to model the convective heat-exchange with the ambient at the free-surface. The Giesekus viscoelastic constitutive model, with appropriate modifications to account for non-isothermal effects, is employed to describe the polymeric effects. The unsteady and coupled non-linear partial differential equations ( PDEs) describing the model problem are obtained and solved via efficient semi- implicit numerical schemes based on finite difference methods (FDM) implemented in Matlab. The response of the VFBN velocity, temperature, thermal-conductivity and polymeric-stresses to variations in the volume-fraction of embedded nanoparticles is investigated. It is shown that these quantities all increase as the nanoparticle volume-fraction becomes higher.