Applied Magnetofluid Dynamics: Modelling and Computation discusses a selection of advanced topics in linear and nonlinear flows of electrically-conducting fluids. It uses a differential equation model-building approach to study such phenomena, including in each chapter details of mathematical formulations, literature reviews, analytical and numerical solution procedures and interpretation. Many complex phenomena, not previously considered in other textbooks in magneto-fluid dynamics (MFD) are considered. These include resonance, magnetic squeeze films, non-Newtonian magneto-hydrodynamics and magneto-heat transfer from conical and rotating bodies. Applications of the models discussed range from magnetic materials processing to physiological flows and aerospace engineering. Complex variables, asymptotic methods, element free Galerkin methods, finite differences, MAPLE, homotopy, finite element, local nonsimilarity and network simulation methods are all described in detail.