Computational Analysis of Shear Banding in Simple Shear Flow of Viscoelastic Fluid-Based Nanofluids Subject to Exothermic Reactions

Abstract

We investigated the shear banding phenomena in the non-isothermal simple-shear flow of a viscoelastic-fluid-based nanofluid (VFBN) subject to exothermic reactions. The polymeric (viscoelastic) behavior of the VFBN was modeled via the Giesekus constitutive equation, with appropriate adjustments to incorporate both the non-isothermal and nanoparticle effects. Nahme-type laws were employed to describe the temperature dependence of the VFBN viscosities and relaxation times. The Arrhenius theory was used for the modeling and incorporation of exothermic reactions. The VFBN was modeled as a single-phase homogeneous-mixture and, hence, the effects of the nanoparticles were based on the volume fraction parameter. Efficient numerical schemes based on semi-implicit finite-difference-methods were employed in MATLAB for the computational solution of the governing systems of partial differential equations. The fundamental fluid-dynamical and thermodynamical phenomena, such as shear banding, thermal runaway, and heat transfer rate (HTR) enhancement, were explored under relevant conditions. Important novel results of industrial significance were observed and demonstrated. Firstly, under shear banding conditions of the Giesekus-type VFBN model, we observed remarkable HTR and Therm-C enhancement in the VFBN as compared to, say, NFBN. Specifically, the results demonstrate that the VFBN are less susceptible to thermal runaway than are NFBN. Additionally, the results illustrate that the reduced susceptibility of the Giesekus-type VFBN to the thermal runaway phenomena is further enhanced under shear banding conditions, in particular when the nanofluid becomes increasingly polymeric. Increased polymer viscosity is used as the most direct proxy for measuring the increase in the polymeric nature of the fluid.

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

“…The superscript ( Ã ) denotes dimensional variables. The variables and parameters are otherwise similar to those described in [1][2][3].…”

“…The current study builds on the investigations in [1][2][3] and extends these investigations to free-surface, gravity-driven, thin-film flows with convective heat exchange at the free-surface. Additionally and alternatively, the current work extends the combined (particle-free) fluid-dynamics studies in [25] and [29] to the inclusion of solid nanoparticles and hence raising the cited works to nanofluid-dynamics.…”

“…of nanofluids are well documented in the literature and summarized by the cited references. Noting the fundamental importance of the rheology of the base fluid to the modern applications of nanofluids, the studies, say in [1][2][3] focus attention on non-Newtonian (specifically polymeric) base-fluids under various flow conditions. The widespread importance of non-Newtonian fluids, both the Generalized Newtonian Fluids (GNF) as well as the polymeric (viscoelastic) fluids, in contemporary application is quite straightforward for example [1][2][3]6,8,[25][26][27][28][29][30][31][32][33][34].…”

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,…”