Many complex biological systems, such as blood and polymeric materials, can be approximated as single constituent homogeneous fluids whose properties can change because of the chemical reactions that take place. For instance, the viscosity of such fluids could change because of the chemical reactions and the flow. Here, I investigate the pulsatile flow of a chemically-reacting fluid whose viscosity depends on the concentration of a species (constituent) that is governed by a convection-reaction-diffusion equation and the velocity gradient, which can thicken or thin the fluid. I study the competition between the chemical reaction and the kinematics in determining the response of the fluid. The solutions to the equations governing the steady flow of a chemicallyreacting, shear-thinning fluid are obtained analytically. The solution for the velocity exhibits a parabolic-type profile reminiscent of the Newtonian fluid profile, if the fluids are subject to the same boundary conditions. The full equations associated with the fluid undergoing a pulsatile flow are studied numerically. A comparison of the shear-thinning/chemical-thinning fluid to the shear-thinning/chemicalthickening fluid using a new non-dimensional parameter–the competition number (CN) shows that both the shear-thinning effects and the chemical-thinning/thickening effects play a vital role in determining the response of the fluid. For the parameter values chosen, the effects of chemical-thinning/thickening dominate the majority of the domain, while the effects due to shear-thinning are dominant only in a small region near the boundary.

A numerical study of flow of power law fluid in an elbow bend has been carried out. The motivation behind this study is to analyze the velocity profiles, especially the pattern of the secondary flow of power law fluid in a bend as there are several important technological applications to which such a problem has relevance. This problem especially finds applications in the polymer processing industries and food industries where the fluid needs to be pumped through bent pipes. Hence, it is very important to study the secondary flow to determine the amount of power required to pump the fluid. This problem also finds application in heat exchangers.

A numerical study of flow of power law fluid in an elbow bend has been carried out. The motivation behind this study is to analyze the velocity profiles, especially the pattern of the secondary flow of power law fluid in a bend as there are several important technological applications to which such a problem has relevance. This problem especially finds applications in the polymer processing industries and food industries where the fluid needs to be pumped through bent pipes. Hence, it is very important to study the secondary flow to determine the amount of power required to pump the fluid. This problem also finds application in heat exchangers.

We examine the boundary-layer flow of generalised Newtonian fluids. A specific member of this class of non-Newtonian fluids, namely the Ostwald-de Waele or power-law fluid, is studied in some detail. We show, through the numerical solution of the governing equations, that this empirical model of fluids encountered in physical and industrial situations is of limited benefit when considering the boundary-layer flow of such a fluid. We then develop and employ a Carreau viscosity model in the same context and show that the numerical marching scheme has better convergence behaviour than was the case for power-law fluids. We also investigate the boundary-layer flow of a Newtonian fluid over a thin film of non-Newtonian fluid, described by a Carreau fluid model, by focusing specifically on similarity-type solutions. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1456589 / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2009

Title: Incompressible fluids with temperature dependent visco- sity, numerical analysis and computational simulations Author: RNDr. Oldřich Ulrych Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., DSc. Abstract: Flows of incompressible fluids connected with significant exchange of ther- mal and mechanical energy and with material moduli varying with the temperature and the shear rate, are described by the balance equations for linear momentum and energy, complemented by suitable constitution equations for the Cauchy stress and the heat flux. Assuming sufficient smoothness of quantities involved, the energy balance equation exhibits several equivalent formulations. However, within the context of weak solution, these formulations are, in general, not equivalent. This thesis is based on the existence theory for the generalized Navier-Stokes-Fourier system describing planar flow of fluids with a shear and temperature dependent vis- cosity. We specify parameters of a generalized power-law model under which weak formulations of balance equations are meaningful and both considered formulations of the energy balance equation are equivalent. Supported by the existence theory, we propose and numerically solve several problems pursuing the aim to systematically compare the...