We introduce solutions to the diffusion equation (Fick’s second law), which arises from Fick’s first law and continuity. Diffusion into semi-infinite half spaces as well as problems in finite spaces and the approach to equilibrium are addressed and solutions are given. The second part of the chapter describes fundamental, atomic scale aspects of diffusion in the solid state.

The powerful methods of dimensional analysis are introduced via the pi-theorem. The reader discovers that many of the results obtained in Chapters 3 and 4 can be arrived at using dimensional analysis alone. These include drag and pipe flow. Dynamical similarity is explained.

In this chapter we study the idealised, inviscid fluid. The central formula is Bernoulli’s equation, and its consequences are explored in a number of examples. Next we look at flow which is irrotational (vortex free) and develop potential theory, which in two dimensions can be treated very elegantly using complex analysis and the Cauchy–Riemann equations.

This chapter is mostly about solid mechanics: Cauchy stress, finite and infinitesimal strain, rotation. Velocity and acceleration are developed in both inertial and non-inertial fames. This is central to the education of the physicist and engineer, but the development leads to a derivation of the Navier–Stokes equations, which are central to fluid dynamics.

The equations of fluid dynamics and energy balance are arrived at from the starting point of the powerful Reynolds transport theorem. After writing down the four conservation laws – mass, energy, linear and angular momentum – their consequences when inserted into the transport equation are revealed, in particular Cauchy’s equations of motion, Navier–Stokes equations and the equation of energy balance. A number of prevalent examples are given, including Stokes’s formulae and the Darcy law. The chapter concludes with the theory of the boundary layer.

Here we begin fluid dynamics with the science of fluids at rest. This includes planetary science aspects of atmospheric and oceanic pressure, the forced and free vortex. Here also are introduced the three basic differential operators: grad, div and curl, which will be used throughout the book.

Heat transfer by conduction, convection and radiation are given a brief treatment. The connection with the previous chapter is emphasised since both involve the ‘heat equation’. The application of boundary conditions to the one-dimensional heat dissipation in a slab is presented. This chapter makes contact with Chapter 4 through a discussion of heat transfer across the boundary layer.

An introduction to the broad subject with a graphical outline of the fundamental equations to be encountered is presented. The reader is informed of any necessary mathematical prerequisites and the structure of the notation to be used is explained.

This chapter puts together fluid mechanics and heat and mass flow to describe chemical and materials processing in which diffusion and convection are combined. After setting up the central equations, special cases are introduced which can be described by equations in closed form; solutions are given.

In this chapter, we explore the basics of fluid mechanics. We will think about how to describe fluids and look at the kinds of things they can do.

Unusually, and a little defensively, the title of this chapter highlights what we won’t talk about, rather than what we will. Fluids have a property known as viscosity. This is an internal friction force acting within the fluid as diferent layers rub together. It is crucially important in many applications. In spite of its importance, we will start our journey into the world of fluids by ignoring viscosity altogether. Such flows are called inviscid. This will allow us to build intuition for the equations of fluid mechanics without the complications that viscosity brings. Moreover, the flows that we find in this section will not be wasted work. As we will see later, they give a good approximation to viscous flows in certain regimes where the more general equations reduce to those studied here.