Mathematical Modeling for Complex Fluids and Flows Mathematical Modeling for Complex Fluids and Flows provides researchers and engineering practitioners encountering fluid flows with state of the art knowledge in continuum concepts and associated fluid dynamics. In doing so it supplies the means to design mathematical models of these flows that adequately express the engineering physics involved. It exploits the implicit link between the turbulent flow of classical Newtonian fluids and the laminar and turbulent flow of non Newtonian fluids such as those required in food processing and polymeric flows. The book develops a descriptive mathematical model articulated through continuum mechanics concepts for these non Newtonian viscoelastic fluids and turbulent flows. Each complex fluid and flow is examined in this continuum context as well as in combination with the turbulent flow of viscoelastic fluids. Some details are also explored via kinetic theory especially viscoelastic fluids and their treatment with the Boltzmann equation. Both solution and modeling strategies for turbulent flows are laid out using continuum concepts including a description of constructing polynomial representations and accounting for non inertial and curvature effects. Ranging from fundamental concepts to practical methodology and including discussion of emerging technologies this book is ideal for those requiring a single source assessment of current practice in this intricate yet vital field. 1. Introduction 2. Tensor Analysis Invariants and Representations 3. Kinematics and Dynamics 4. Constitutive Equations: General Principles 5. Non Newtonian and Viscoelastic Fluids 6. Turbulent Flows 7. The Boltzmann Equation 8. Properties of the Hermite Polynomials Table of symbols References.