There is an ever-increasing interest in understanding the behavior of nanofluids, some of which can behave as non-Newtonian fluids due to their microstructure or higher volume fraction loading of nanoparticles. Nanofluids have also been found to possess enhanced thermophysical properties such as thermal conductivity, thermal diffusivity, viscosity, and convective heat transfer coefficients compared to those of base fluids such as oil or water. Nanofluids may have the potential to significantly increase heat transfer rates in a variety of areas such as industrial cooling applications, nuclear reactors, the transportation industry, micro-electromechanical systems, electronics and instrumentation, and biomedical applications. Layi Fagbenle, in Applications of Heat, Mass and Fluid Boundary Layers, 2020 14.2.5 Non-Newtonian nanofluid boundary layer transfer Overview of non-Newtonian boundary layer flows and heat transfer Living plants also circulate fluids through xylem and phloem cells that convey water and minerals from the roots to the leaves, and sugars and other products of photosynthesis from the leaves to the rest of the plant. Models of steady and unsteady flow in straight tubes having appropriate properties are reasonably successful in explaining many features of human blood circulation. Both the protein content and the presence of red blood cells contribute to the shear thinning character of blood. The flexibility of the large arteries partially smoothes the pressure pulses produced by the heart's rhythmic pumping. The branched geometry of the blood vessels minimizes flow resistance while providing a large surface area at the capillary level for the exchange of oxygen, nutrients, and wastes that are carried to or from the body's tissues. It is a branched network of flexible-wall vessels through which a non-Newtonian fluid flows in an unsteady manner. The human circulatory system illustrates some of the many challenges associated with understanding and modeling biological fluid flows. Ayyaswamy, in Fluid Mechanics (Sixth Edition), 2016 Abstractīiofluid mechanics is a vast field that involves fluid motion inside and outside living organisms. For application, analytical solutions are used to verify numerical simulation results. The analytical solutions and resulting procedure can be regarded as an extension of Buckley–Leverett theory to non-Newtonian displacement. A practical procedure is presented for calculating saturations for non-Newtonian fluid displacement. Then, it analyzes displacement of a Newtonian fluid by a power-law fluid, a Bingham fluid by a Newtonian fluid, and non-Newtonian fluids in a radial system. A Buckley–Leverett solution for displacement of Newtonian and non-Newtonian fluids is presented. The first portion of this chapter is devoted to discussion of non-Newtonian fluids and rheological models, followed by governing equations for immiscible flow of non-Newtonian fluids. It presents Buckley–Leverett type solutions for non-Newtonian fluid flow in porous media. This chapter discusses extension of Buckley–Leverett theory to analyzing immiscible flow of non-Newtonian fluids through porous media. Yu-Shu Wu, in Multiphase Fluid Flow in Porous and Fractured Reservoirs, 2016 Abstract Immiscible Displacement of Non-Newtonian Fluids Finally, the finite element solution to non-Newtonian fluid flow problems is presented using the Galerkin method along with an iterative method for the solution. The stream function–vorticity formulation, coupled with the variational approach, is used to derive the finite element equations. An iterative solution is given for solving full Navier–Stokes equations. The velocity–pressure formulation, based on the Galerkin method, is outlined by developing the finite element equations. Because no universally accepted variational principle is available for solving Navier–Stokes equations, the pseudovariational principle, given by Olson, is used to present the finite element solution, based on an 18 degrees of freedom–conforming triangular element. The stream function formulation is outlined using a variational approach. The solution methods are based on the use of the stream function formulation, which treats the stream function as an unknown, the velocity–pressure formulation with velocity components and the pressure as unknowns, and the stream function–vorticity formulation with the stream function and vorticity as unknowns. The basic equations governing two-dimensional steady incompressible Newtonian flow and its boundary conditions are stated in terms of the pressure, velocity, and velocity gradient, along with possible solution methods. The solutions to viscous and non-Newtonian fluid flow problems are presented. Rao, in The Finite Element Method in Engineering (Sixth Edition), 2018 Abstract
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