A continuation of both ME201 and ME203 in which both classical calculus techniques and the computer implementation of numerical methods are discussed. Partial differential equations of mathematical physics: wave, diffusion, Laplace, Poisson equations. Boundary and initial conditions. Separation of variables, transforms, and numerical methods. Applications will emphasize the role of partial differential equations in understanding the behaviour of physical systems.

Introduction to heat transfer mechanisms. The formulation and solution of steady and transient heat conduction. Radiant heat transfer including exchange laws and view factors. Introductory convective heat transfer.

Emphasis on applications of thermodynamics to flow processes, real fluids, evaluation of state functions of real fluids, non-reacting mixtures, reacting mixtures and equilibrium considerations.

Macroscopic approach to energy analysis. Energy transfer as work and heat, and the First Law of thermodynamics. Properties and states of simple substances. Control-mass and control-volume analyses. The essence of entropy, and the Second Law of thermodynamics. The Carnot cycle and its implications for practical cyclic devices. Introduction to heat transfer by conduction, convection and radiation. Basic formulation and solution of steady and transient problems. Issues relevant to the cooling of electrical devices.

Steady and transient heat conduction in isotropic media. Review of fundamental principles of heat conduction and boundary conditions. Introduction of the concept of thermal resistance of systems and of thermal constriction resistance. Derivation of gradient, divergence, Laplacian, conduction equation, boundary conditions and thermal resistance in general orthogonal curvilinear coordinates. Solutions of conduction equations in several coordinate systems. Introduction to finite difference and finite element formulations of the conduction equation in curvilinear coordinates.