Gravity-Driven Thin Film Flow of an Ellis Fluid

Electromagnetic Trihybrid Ellis Nanofluid Flow Influenced with a Magnetic Dipole and Chemical Reaction Across a Vertical Surface

The purpose of this study is to evaluate the augmentation of thermal energy transfer in trihybrid Ellis nanofluid flow in the occurrence of magnetic dipole passes over a vertical surface. The ternary hybrid nanofluid is prepared by the dispersion of ternary nanoparticles (Al₂O₃, SiO₂, and TiO₂) in the Carreau Yasuda fluid. The velocity and heat transportation has been examined in the existence of the Darcy Forchhemier influence and heat source/sink. The phenomena of fluid flow have been mathematically designed for energy and fluid velocity in the form of a nonlinear partial differential equation (PDE)-based system. The system of PDEs is further refined to the set of ordinary differential equations via suitable similarity substitutions. The acquired dimensionless equations are numerically solved with the help of the HAM. It has been noticed that the energy contour is enhanced versus the variation of viscous dissipation and heat generation. A significant contribution of a magnetic dipole is observed to elevate the production of the thermal energy field, and an opposite trend is noticed versus the flow profile. The accumulation of Al₂O₃, SiO₂, and TiO₂ nanomaterials in the base fluid "engine oil" improves the velocity and energy profiles.

On Numerical Analysis of Carreau–Yasuda Nanofluid Flow over a Non-Linearly Stretching Sheet under Viscous Dissipation and Chemical Reaction Effects

This work reports the Carreau–Yasuda nanofluid flow over a non-linearly stretching sheet viscous dissipation and chemical reaction effects. The coupled system of non-linear partial differential equations are changed into a system of linear differential equations employing similarity equations. The spectral quasi-linearization method was used to solve the linear differential equations numerically. Error norms were used to authenticate the accuracy and convergence of the numerical method. The effects of some thermophysical parameters of interest in this current study on the non-dimensional fluid velocity, concentration and temperature, the skin friction, local Nusselt and Sherwood numbers are presented graphically. Tables were used to depict the effects of selected parameters on the skin friction and the Nusselt number.

Contact Line Instability of Gravity-Driven Flow of Power-Law Fluids

The moving contact line of a thin fluid film can often corrugate into fingers, which is also known as a fingering instability. Although the fingering instability of Newtonian fluids has been studied extensively, there are few studies published on contact line fingering instability of non-Newtonian fluids. In particular, it is still unknown how shear-thinning rheological properties can affect the formation, growth, and shape of a contact line instability. Our previous study (Hu and Kieweg, 2012) showed a decreased capillary ridge formation for more shear-thinning fluids in a 2D model (i.e. 1D thin film spreading within the scope of lubrication theory). Those results motivated this study's hypothesis: more shear-thinning fluids should have suppressed finger growth and longer finger wavelength, and this should be evident in linear stability analysis (LSA) and 3D (i.e. 2D spreading) numerical simulations. In this study, we developed a LSA model for the gravity-driven flow of shear-thinning films, and carried out a parametric study to investigate the impact of shear-thinning on the growth rate of the emerging fingering pattern. A fully 3D model was also developed to compare and verify the LSA results using single perturbations, and to explore the result of multiple-mode, randomly imposed perturbations. Both the LSA and 3D numerical results confirmed that the contact line fingers grow faster for Newtonian fluids than the shear-thinning fluids on both vertical and inclined planes. In addition, both the LSA and 3D model indicated that the Newtonian fluids form fingers with shorter wavelengths than the shear-thinning fluids when the plane is inclined; no difference in the most unstable (i.e. emerging) wavelength was observed at vertical. This study also showed that the distance between emerging fingers was smaller on a vertical plane than on a less-inclined plane for shear-thinning fluids, as previously shown for Newtonian fluids. For the first time for shear-thinning fluids, these results connect trends in capillary ridge and contact line finger formation in 2D models, LSA, and 3D simulations. The results can provide us insights on how to optimize non-Newtonian fluid properties to minimize a fingering instability in many industrial and biological applications.