Some Steady and Unsteady Flow Problems Involving Newtonian and Non-Newtonian Fluids

Abstract

The ability of electromagnetic fields to influence fluid flow has long been known and used with val'ying degrees of success. The equations governing the How consist of the Navier-Stokes equations of fluid motion coupled with Ma.-xwell's equations of electro-magnetics and material constitutive relations. The study of these flows is Electro-Magneto-Fluid Dynamics (EMFD). The field of EMFD has traditionally been divided into Bows influenced only by electric fields and electric charges, and flows influenced only by magnetic fields and without electric charges. The former are called Electrohyclroclynamic (EHD) flows and the latter Magnetohydroclynantic (MHD) flows , However, the full system of equations in each case has, up until recently, been far too compie..-x to solve generally. The Navier-Stokes equations alone become complex when analysis of flows in more dimensions is taken into account. Moreover, the governing equations become much complicated when hydrodynamic flows of realistic interest are desired ( that is, turbulent, chemically reacting, multiconstituent, and/or non-Newtonian fluids). Coupled with Maxwell 's equations, the complexity of the system is raised by orders of magnitude. The field is too vast to exhaustively cover the subject, so the intent is to provide some analytical solutions of the field. To accomplish this, chapters two and five provide the analytic solutions of velocity fields for MHD flows. Effort is made to provide a physical understanding of the field material interactions causing magnetization. Chapter two contains a general developed formula for any periodic disk oscillations. Asymptotic analysis has also been carried out to determine the viscous solutions for the larg time. Besides the engineering applications, the presented analysis in this chapter possesses geophysical applications. The contents of chapter two have been published in Mathematical and Computer Modelling...