Chapter Five can be found on the text Web site www.cambridge.org/kaviany. In Chapter 5, we begin discussion of convection heat transfer by considering an unbounded fluid stream undergoing a temperature change along the stream flow direction, where this change is caused by an energy conversion. Convection heat transfer is the transfer of heat from one point to another by a net (i.e., macroscopic) fluid motion (i.e., by currents of gas or liquid particles) given by the fluid velocity vector. The fluid motion can be void of random fluctuations, which is called a laminar flow, or it can have these random fluctuations, which is called a turbulent flow. Convection heat transfer examines themagnitude, direction, and spatial and temporal variations of the convection heat flux vector in a fluid stream. In this chapter, we examine convective heat transfer within a fluid stream without directly considering the heat transfer between the fluid and a bounding solid surface (i.e., here we consider only intramedium conduction and convection of unbounded fluid streams). In addition to the occurrence of the intramedium (i.e., bulk) convection, in many practical applications involving cooling and heating of fluids, the review of the intramedium convection allows for an introductory treatment of laminar, steady-state, uniform, one-directional fluid flow without addressing the effect of the fluid viscosity emanating from the bounding surfaces, which would require inclusion of the momentum conservation equation.

A bounded fluid stream in thermal nonequilibrium with its bounding solid surface exchanges heat, and this alters its temperature across and along the stream. That this change occurs throughout the stream is what distinguishes it from the semi-bounded streams where the far-field temperature is assumed unchanged (i.e., the change was confined to the thermal boundary layer). We now consider the magnitude, direction, and spatial and temporal variations of qu in a bounded fluid stream (also called an internal flow) that is undergoing surface-convection heat transfer qku. As in Chapter 6, initially our focus is on the fluid and its motion and heat transfer (and this is the reason for the chapter title, bounded fluid streams); later we include the heat transfer in the bounding solid. We examine qu within the fluid and adjacent to the solid surface. As in Chapter 6, at the solid surface, where uf = 0, we use qku to refer to the surface-convection heat flux vector. We will develop the average convection resistance 〈Ru〉L, which represents the combined effect of surface-convection resistance and the change in the average fluid temperature as it exchanges heat with the bounding surface.

In this introductory chapter, we discuss some of the reasons for the study of heat transfer (applications and history), introduce the units used in heat transfer analysis, and give definitions for the thermal systems. Then we discuss the heat flux vector q, the heat transfer medium, the equation of conservation of energy (with a reformulation that places q as the central focus), and the equations for conservation of mass, species, and other conserved quantities. Finally we discuss the scope of the book, i.e., an outline of the principles of heat transfer, and give a description of the following chapters and their relations. Chart 1.1 gives the outline for this chapter. This introductory chapter is partly descriptive (as compared to quantitative) in order to depict the broad scope of heat transfer applications and analyses.

Applications and History

Heat transfer is the transport of thermal energy driven by thermal nonequilibrium within amedium or among neighboringmedia. As an academic discipline, it is part of the more general area of thermal science and engineering. In a broad sense, thermal science and engineering deals with a combination of thermal science, mechanics, and thermal engineering analysis and design. This is depicted in Chart 1.2. In turn, thermal science includes thermal physics, thermal chemistry, and thermal biology.

A semi-bounded fluid stream in thermal nonequilibrium with its bounding solid surface exchanges heat by surface convection qku and this alters its temperature (and qk and qu) only in a region adjacent to the bounding surface (i.e., the farfield temperature is unchanged). In this chapter we consider a steady, semi-bounded fluid stream flowing over a solid surface (e.g., flow over a plate or a sphere) at a far-field velocity uf,∞ with the solid Ts and the far-field Tf,∞ fluid having different temperatures. We initially focus on the fluid and its motion and heat transfer adjacent to the surface (because of this focus, the chapter title, semi-bounded fluid streams, is used. Also as will be shown, there are some similarities with the transient conduction in semi-infinite solid). Later we include the heat transfer with any bounding solid (i.e., the substrate). This is also called external flow heat transfer. In Chapter 7 we will consider steady, bounded fluid streams (e.g., flow in a tube). This is also called internal flow. We are interested in the parameters and conditions influencing the surface-convection heat flux qku and its spatial variation. These parameters and conditions include the direction of the fluid flow with respect to the bounding surface (e.g., fluid flow parallel to the surface, perpendicular to the surface, or oblique), flow structure, fluid properties, liquid-gas phase change, and solid-surface conditions.

A typical one-semester course syllabus is given in the Solutions Manual. However, at the discretion of the instructor, different parts of the text can be chosen to emphasize various concepts.

Chapter 1 is, in part, descriptive (as opposed to quantitative) and introduces many concepts. Therefore, this chapter should be read for a qualitative outcome and an overview of the scope of the book. This is needed for a general discussion of heat transfer analysis before specifics are introduced. The drawing of heat flux vector tracking is initially challenging. However, once learned, it facilitates visualization of heat transfer, and then the construction of the thermal circuit diagrams becomes rather easy.

Also, to get a broad and unified coverage of the subject matter, a very general treatment of spatial temperature nonuniformity and the appropriate form of the energy equation is given in Chapter 2. This chapter gives the building blocks and the results to be used in succeeding chapters. Some of the energy conversion mechanisms may be new to students; however, they are described in the text and are easy to follow. Application of Chapter 2 materials unfolds in the chapters that follow. For example, various energy conversion mechanisms are used along with heat transfermechanisms in interesting and practical problems.

Introduction

When a fluid is locally perturbed by an impulse (for example, by an impact) or a periodic excitation (the vibration of a membrane, string, or mechanical blade), the perturbation may propagate from the source in the form of a wave. Examples include acoustic waves, surface waves, and internal waves in a stratified fluid (Lighthill, 1978). The solution of the linearized equations for small amplitude perturbations leads to a major result: the wave number k and frequency ω (or the wave speed c = ω/k) are not independent, they are related by a dispersion relation. Since this relation is obtained from linearized equations, another major result is that dispersion does not depend on the amplitude of the perturbation. However, if the amplitude exceeds some level, new effects arise that the dispersion relation of linear theory obviously does not describe. To explain these new effects it is necessary to include nonlinear terms neglected in the linear study, i.e., to develop a theory of nonlinear waves. Such waves are also referred to as finite-amplitude waves, in contrast to the waves of infinitesimal amplitude considered in a linear analysis.

The objective of the present chapter is to give an elementary account of the theory of nonlinear waves. We will show (i) how nonlinear waves can be constructed by a perturbation method (essentially the multiple-scale method presented in the preceding chapter), and (ii) how the linear stability of these waves can be studied.

Introduction

In this chapter we present an introduction to dense granular flows and their stability by discussing two classes of phenomena: avalanches on an inclined plane, and particle transport on an erodible bed sheared by a fluid flow. These granular flows lead to the appearance of surface waves, called ripples or dunes depending on whether their wavelength is of a few centimeters or a few meters (the relevance of this common distinction will be discussed later on). Owing to the difficulty – both experimental and theoretical – of studying granular media, the mechanisms responsible for these waves remain poorly understood, and so the results presented in this chapter are definitely less well established than those in the preceding chapters.

Avalanches, ripples, and dunes present serious problems for human activities. Among natural phenomena, snow and mud avalanches are well known for their destructive nature; the displacement of a sand dune by the wind – the so-called aeolian dunes – while less dramatic, can cut communication links and threaten habitation and industrial installations. Subaqueous dunes perturb navigation in rivers and shallow seas such as the North Sea, while on river bottoms such dunes increase friction and raise the water level, thereby contributing to flooding. Granular flows are also omnipresent in industry: flow and transport of coal, construction materials (cement, sand, gravel), agricultural foodstuffs, pharmaceutical materials, and sand from oilfields are some examples. Instabilities occur in the conduits used to transport these materials, giving rise to dunes which perturb the flow and may form obstructions, causing serious damage to operating equipment.

Hydrodynamic instabilities occupy a special position in fluid mechanics. Since the time of Osborne Reynolds and G. I. Taylor, it has been known that the transition from laminar flow to turbulence is due to the instability of the laminar state to certain classes of perturbations, both infinitesimal and of finite amplitude. This paradigm was first displayed in a masterful way in the studies of G. I. Taylor on the instability of Couette flow generated by the differential rotation of two coaxial cylinders. From then on, the theory of hydrodynamical instability has formed a part of the arsenal of techniques available to the researcher in fluid mechanics for studying transitions in a wide variety of flows in mechanical engineering, chemical engineering, aerodynamics, and in natural phenomena (climatology, meteorology, and geophysics).

The literature on this subject is so vast that very few researchers have attempted to write a pedagogical text which describes the major developments in the field. Owing to the enormity of the task, there is a temptation to cover a large number of physical situations at the risk of repetition and of wearying the reader with just a series of methodological approaches. François Charru has managed to avoid this hazard and has risen to the challenge. With this book he fills the gap between the classical texts of Chandrasekhar and Drazin and Reid, and the more recent book of Schmid and Henningson.

Classical instability theory essentially deals with quasi-parallel or parallel shear flows such as mixing layers, jets, wakes, Poiseuille flow in a channel, boundary-layer flow, and so on.