The Euler–Euler (EE) approach derives its name from the fact that both the continuous and the dispersed phases are solved in the Eulerian frame of reference. For the fluid phase, the Eulerian frame is the natural choice and was pursued both in the particle-resolved (PR) and the Euler–Lagrange (EL) approaches. Particles are, however, inherently Lagrangian, and an Eulerian representation is possible only when the individual nature of the particles is erased. This requires that the particle-related Lagrangian quantities be suitably averaged, so that Eulerian fields of these quantities can be defined. The averaging process will allow particle volume fraction, particle velocity, and particle temperature fields to be defined as functions of space and time.

In this chapter, we investigate the problem of heat transfer from an isolated rigid sphere subjected to a cross flow of different temperature. This thermal problem is analogous to the flow problem considered earlier, and the interest here is to establish an expression for heat transfer in terms of the undisturbed ambient flow, which must now be characterized both in terms of relative velocity and temperature difference. We will start our investigation with rigorous analytical results in the Stokes and the small Péclet number regime.

The Eulerian representation of the continuous phase is natural, where quantities such as fluid velocity u(x,t) represent the average velocity of all the fluid molecules within a suitably chosen volume for continuum description. In the previous section, we considered filtering of these flow quantities over a suitably chosen length scale that is much larger than the size of the individual particles.

Tidal range generation, tidal stream generation and wave power are discussed. The tidal energy resource is described, together with the use of harmonic constituents to predict the height of the tide and velocity of the tidal flow at a location. The principles of tidal range generation are discussed and ebb generation is illustrated. The main components of a tidal range scheme are explained as well as the potential environmental impact of any large tidal range scheme. Tidal barrages are compared with tidal lagoons. The generation of electricity from tidal streams is discussed and examples of the tidal stream resource provided. Tidal stream turbines are described and compared with wind turbines using axial momentum theory. Simple water wave theory is summarized and the use of the wave height and wave period to describe of the wave power resource is described. Prototyped devices for wave power generation are described and the power that would be generated by a wave power device wave climate is shown. The chapter is supported by 8 examples, 15 questions with answers and full solutions in the accompanying online material. Further reading and online resources are identified.

In this chapter we will consider in detail the interaction of an isolated rigid particle with the surrounding continuous-phase flow. In the low Reynolds number limit, the problem can be solved analytically. At finite Reynolds number, one must resort to numerical simulations. Nevertheless, in both cases, by simultaneously solving the Navier–Stokes equations for the fluid, equations of rigid-body motion for the particle, and coupling them with no-slip and no-penetration boundary conditions, we can obtain complete details of the flow around the particle.

From the range of topics and the depth of physics that were discussed in the previous chapters, it is quite clear that multiphase flow is a challenging subject even at the level of an individual particle. But clearly we need to move forward and begin to consider more complex multiphase-flow physics. Toward this goal, we will progress beyond an isolated particle in an unbounded medium in two different ways. First, in this chapter we will consider the problem of an isolated particle in an ambient flow, but in the presence of a nearby wall.

The second edition of this popular textbook has been extensively revised and brought up-to-date with new chapters addressing energy storage and off-grid systems. It provides a quantitative yet accessible overview of the renewable energy technologies that are essential for a net-zero carbon energy system. Covering wind, hydro, solar thermal, photovoltaic, ocean and bioenergy, the text is suitable for engineering undergraduates as well as graduate students from other numerate degrees. The technologies involved, background theory and how projects are developed, constructive and operated are described. Worked examples demonstrate the simple calculation techniques used and engage students by showing them how theory relates to real applications. Tutorial chapters provide background material supporting students from a range of disciplines, and there are over 150 end-of-chapter problems with answers. Online resources, restricted to instructors, provide additional material, including copies of the diagrams, full solutions to the problems and examples of extended exercises.

In this chapter our attention will primarily be restricted to the dispersed phase. Clearly the continuous phase is also important, but in this chapter we will discuss the state or evolution of the continuous phase only as needed in the context of characterizing the state of the dispersed phase. Consider the case of a turbulent multiphase flow with a random distribution of monosized spherical particles (or droplets or bubbles) within it. Imagine taking pictures of the particle distribution in an experiment (i.e., in one realization) without recording the details of the flow surrounding the particles.

Photosynthesis takes carbon dioxide from the atmosphere and stores the carbon in the biomass of plants and trees. This carbon is released when the biomass is converted to energy but the overall cycle of growing biomass through photosynthesis and converting it to useful energy can be considered to produce limited net emissions of greenhouse gases. The processes by which biomass is converted into energy are described, including the thermochemical processes of combustion and gasification of solid biomass, the biochemical processes of anaerobic digestion, and alcoholic fermentation and the extraction of oil from plants. Combustion of biomass to generate electricity is described and the gasification of biomass is discussed. Anaerobic digestion to produce biogas and the alcoholic fermentation of crops to produce biofuel are described. The production of biodiesel by the extraction and purification of vegetable oil from plants is also described. The chapter is supported by 5 examples, 16 questions with answers and full solutions in the accompanying online material. Further reading and online resources are identified.

We have completed our discussion of the drag force, where the term “drag” has been used to represent the force on a particle that is in the direction of ambient flow as seen in a frame of reference attached to the particle (i.e., drag is the force component along the direction of relative velocity). But there are many situations where the force on the particle is not only directed along the ambient flow, but also has a component that is perpendicular to the direction of ambient flow. In this case, the particle not only experiences a “drag” force, but also is subjected to a “lift” force.

The solar heating of buildings, the solar heating of water and solar thermal electricity generation are discussed. The importance of solar energy in determining the temperature of buildings is emphasized. The circuit representation of low-temperature heat transfer is used to estimate the heat loss and solar gain in buildings. The use of degree-days to predict the long-term performance of a building is illustrated and the behaviour of glass in capturing solar energy is described. The principles of solar water heating using a flat-plate or evacuated-tube solar collector is shown and the performance of a flat-plate solar collector is analysed. The use of selective absorber surfaces to improve the performance of a solar thermal system is discussed. High-temperature concentrated solar thermal systems are described with particular applications for electricity generation. Parabolic trough and Fresnel lens linear collectors are described as well as solar power tower schemes. The chapter is supported by 4 examples, 13 questions with answers and full solutions in the accompanying online material. Further reading and online resources are identified.

Collisions among particles, droplets, and bubbles and their growth through coagulation is vital in the understanding of many multiphase problems. Similarly, particles, droplets, and bubbles can also breakup into smaller fragments and daughter droplets and bubbles. For example, it is now well established that collisions and coagulation of droplets play a central role in the formation of precipitation-size raindrops in a cloud (Mason, 1969; Yau and Rogers, 1979; Sundaram and Collins, 1997; Shaw, 2003; Grabowski and Wang, 2013).