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

Abstract

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. KEYWORDSSemi-implicit numerical scheme; finite difference methods; viscoelastic-fluid-based nanofluid (VFBN); nonisothermal viscoelastic flow; giesekus constitutive model; nanofluid thermal-conductivity; gravity-driven flow Nomenclature Variables and ConstantsÃ

Volume-of-Fluid Based Finite-Volume Computational Simulations of Three-Phase Nanoparticle-Liquid-Gas Boiling Problems in Vertical Rectangular Channels

“…The nano-particles and base-liquid are homogeneously mixed to form the nanofluid. The nanofluid density, heat capacity, and viscosity are calculated from a combination of the solid (nano-particle) contribution, () s , and the base-liquid contribution, () bl , see for example [33,[35][36][37][38],…”

“…The thermal conductivity for the nanofluid is empirically determined, see for example [33,[35][36][37][38]. The following empirical formula is adopted,…”

“…where ε and A 2 are thermal-conductivity parameters and ℵ is an empirically determined nano-particle shape-factor. For spherical-shaped nano-particles, ℵ = 3, [33,[35][36][37][38].…”