620-342 Industrial and Applied Mathematics

Note

Students may only gain credit for one of 620-342, 618-342 (1997 Handbook).

Credit Points

Coordinator

Prerequisites

One of 620-331, 618-331 (1997 Handbook), 618-332 (1996 Handbook).

Semester

Contact

Subject Description

Students completing this subject should comprehend

• the basic principles governing flow and transport processes within continuous media;
• vector and tensor methods needed to formulate these principles mathematically;
• the concept of a constitutive equation;

have developed the ability to

• select a constitutive equation and correctly pose relevant boundary-value problems;
• solve transport and flow problems in simple geometries;
• identify valid approximate analyses;
• interpret solutions in physical terms;

and appreciate

• the potential for mathematical modelling of flow and transport processes which arise in manufacturing, mineral exploitation and other areas of science and technology;
• the intimate connection between continuum mechanical problems and fundamental mathematical problems.

Introduction to continuum mechanics: dyadic realization of tensor analysis, Eulerian and Lagrangian viewpoints, transport theorem, linear and angular momentum equations, Cauchy stress principle, existence of the stress tensor, constitutive equations. Incompressible ideal fluids: potential flow, conformal mappings, Bernoulli's theorem, Kelvin's Theorem, persistence of irrotationality, d'Alembert's paradox. Incompressible viscous fluids: Navier-Stokes equations, survey of exact solutions, dynamical similarity, low Reynolds number flow, high Reynolds number flow, unstable flows, introduction to turbulence. Extensions and applications: Selected from: interfacial instabilities, porous media flows, colloid science, linear elasticity, compressible fluids, and other areas.

Assessment

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