620-342 Industrial & Applied Mathematics

620-331.

This subject introduces the basic principles governing flow and transport processes within continuous media. It develops vector and tensor methods needed to formulate these principles mathematically; and also introduces the concept of a constitutive equation. Students should develop the ability to select a constitutive equation and correctly pose relevant boundary-value problems; to solve transport and flow problems in simple geometries; to identify valid approximate analyses; and to interpret solutions in physical terms. This subject demonstrates the potential for mathematical modelling of flow and transport processes which arise in manufacturing, mineral exploitation and other areas of science and technology. It also shows the intimate connection between continuum mechanical problems and fundamental mathematical problems.

Introduction to continuum mechanics topics include the continuum approximation, Eulerian and Lagrangian viewpoints, streamlines, conservation of mass, Cauchy equation of motion, constitutive equation for stress tensor, Cartesian tensors and dyadic notation, and hydrostatics. Incompressible ideal fluids topics include Euler equations, Bernoulli's theorem, potential flow, persistence of irrotationality, and d'Alembert's paradox. Incompressible viscous fluids topics include Navier-Stokes equations, dynamical similarity, exact solutions. Special flows topics include creeping flow, Stokes drag, thin film flows, Hele-Shaw flow, lubrication, laminar boundary layer flow, flow past a plate, and boundary layer separation.

Up to 24 pages of written assignments and a 3-hour end-of-semester written examination.