The aim of this dissertation is to construct a virtual element method (VEM) for models in magneto-hydrodynamics (MHD), an area that studies the behavior and properties of electrically conducting fluids such as a plasma. MHD models are a coupling of the Maxwell’s equations for electromagnetics and models for fluid flow....
In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of...
Because of competition from abroad, the U. S. Steel
industry has begun research into the processes involved
with electric arc steelmaking. This paper addresses the
mathematical background of these furnaces and the electro-magneto-
hydrodynamical effects used to melt the large
quantities of steel. A classical approach to the
derivation of...
An experimental investigation was carried out to
determine the thermodynamics and fluid mechanics of the
pipe flow of magnetic fluids. A water-based magnetic
fluid was synthesized in the laboratory and its relative
viscosity and magnetic properties were determined
as a function of temperature. A "thermomagnetic pump"
was built and tested...
The effect of a non-uniform magnetic field on the coupled transport of momentum and heat is studied for the case of laminar pipe flow of a magnetically susceptible ferrofluid. The momentum and heat transport equations are complemented with the necessary electromagnetic terms and used to develop a computer simulation of...