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Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
A generalized Newtonian fluid is described by a constitutive equation in which the viscosity is only a function of the magnitude of the second invariant of the stress or the shear rate. Common empiricisms for the function η(γ˙) or η(τ) (where τ is the magnitude or second invariant of τij) are summarized in TABLE 37.1. The generalized Newtonian fluid is best suited to describing steady state shear flows or small deviations from such flows as long as the Deborah number is sufficiently low. Like the Newtonian fluid, it cannot describe normal stress effects or time-dependent elastic effects. In elongational flows and in rapidly changing flows, the generalized Newtonian models should not be used
Rheology of Polymer Coatings
Published in Sanjay Mavinkere Rangappa, Jyotishkumar Parameswaranpillai, Suchart Siengchin, Polymer Coatings, 2020
Finally, in generalized Newtonian fluids the viscosity is constant, the shear stress is a discrete or punctual function of the shear strain rate, and the internal stress state does not depend on the shear strain history.
Bioconvective Carreau nanofluid flow with magnetic dipole, viscous, and ohmic dissipation effects subject to Arrhenius activation energy
Published in Numerical Heat Transfer, Part A: Applications, 2023
Generally fluids are categorized as Newtonian, non-Newtonian, and generalized Newtonian fluids. Obeying Newton’s law of viscosity, fluids referred as Newtonian fluids. Fluids having nonlinear viscosity interaction with shear rate are categorized to be non-Newtonian fluids. Fluids in which viscosity varies with shear rate are considered as generalized Newtonian fluids. In such fluids Newton’s viscosity law was modified empirically and allowed the viscosity to change with rate of shear. Carreau [1] proposed a model which was the combination of Newtonian and power law properties that accurately predicts viscosity for extremely high or low shear rates. Carreau model reduces the obstruction of the Power-law model also widely acceptable in technological processes and chemical engineering.
Qualitative analysis of magnetohydrodynamics Powell–Eyring fluid with variable electrical conductivity
Published in International Journal of Modelling and Simulation, 2023
Sradharam Swain, Suman Sarkar, Bikash Sahoo, Oluwole D. Makinde
Over the last three decades, studies of non-Newtonian viscosity have attracted current scientists due to the large-scale of applications in modern chemical and biochemical industries such as the aerodynamic extrusion of plastic sheets, liquid films in condensation process, paper production, crystal glowing, glass-blowing, paints and manufacturing of rubber sheets, etc. The generalized Newtonian fluids viscosity varies upon shear rate. The variation in the viscosity over two or three orders of magnitudes for certain fluids should be addressed while lubrication problems are studied. Hence, one of the fundamental adjustments to Newton’s law of viscosity established experimentally is to enable the viscosity to differ from the shear rate. These various fluids are typically called generalized Newtonian fluids studied in Bird et al. [1]. The most important generalized Newtonian fluid is the power-law fundamental relations. However, there is a drawback in the power-law viscosity concept that it is unable to accurately estimate the viscosity for shear rates that are either extremely small or incredibly high. Considering such drawbacks of the power-law viscosity model, particularly for extremely low and very shear rates, we have taken a new model named Powell–Eyring model [2]. The Powell–Eyring model overcomes the limitations of the power-law viscosity model mentioned above and is gaining popularity in modern chemical and biochemical engineering industries. It highlights a particular area with a linear relationship between apparent viscosity and shear rate. Therefore, this model finds a power-law region. Moreover, it indicates a finite viscosity as the shear rate reaches zero.