This introduction to heat transfer offers advanced undergraduate and graduate engineering students a solid foundation in the subjects of conduction, convection, radiation, and phase-change, in addition to the related topic of mass transfer. A staple of engineering courses around the world for more than three decades, it has been revised and updated regularly by the authors, a pair of recognized experts in the field. The text addresses the implications, limitations, and meanings of many aspects of heat transfer, connecting the subject to its real-world applications and developing students' insight into related phenomena. Three introductory chapters form a minicourse in heat transfer, covering all of the subjects discussed in detail in subsequent chapters. This unique and effective feature introduces heat exchangers early in the development, rather than at the end. The authors also present a novel and simplified method for dimensional analysis, and they capitalize on the similarity of natural convection and film condensation to develop these two topics in a parallel manner. Worked examples and end-of-chapter exercises appear throughout the book, along with well-drawn, illuminating figures.
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In cold weather, if the air is calm, we are not so much chilled as when there is wind along with the cold; for in calm weather, our clothes and the air entangled in them receive heat from our bodies; this heat...brings them nearer than the surrounding air to the temperature of our skin. But in windy weather, this heat is prevented...from accumulating; the cold air, by its impulse...both cools our clothes faster and carries away the warm air that was entangled in them.
notes on “The General Effects of Heat”, Joseph Black, c. 1790s
6.1 Some introductory ideas
Joseph Black’s perception about forced convection (above) represents a very correct understanding of the way forced convective cooling works. When cold air moves past a warm body, it constantly sweeps away warm air that has become, as Black put it, “entangled” with the body and replaces it with cold air. In this chapter we learn to form analytical descriptions of these convective heating (or cooling) processes.
Our aim is to predict h and
, and it is clear that such predictions must begin in the motion of fluid around the bodies that they heat or cool. Once we understand these fluid motions, we can begin the process of predicting how much heat they add or remove.
Flow boundary layer
Fluids flowing past solid bodies adhere to them, so a region of variable velocity must be built up between the body and the free fluid stream, as indicated in Fig. 6.1. This region is called a boundary layer, which we abbreviate as b.l. The b.l. has a thickness, δ. The boundary layer thickness is arbitrarily defined as the distance from the wall at which the flow velocity approaches to within 1% of u∞. The boundary layer is normally very thin in comparison with the dimensions of the body immersed in the flow.1
Figure 6.1 A boundary layer of thickness δ.
The first step we must take before we can predict h is the mathematical description of the boundary layer. This was first done by Prandtl2 (see Fig. 6.2) and his students, starting in 1904, and it depended upon simplifications he could make after he recognized how thin the layer must be.
The dimensional functional equation for the boundary layer thickness on a flat surface is
where χ is the length along the surface and ρ and μ are the fluid density in kg/m3 and the dynamic viscosity in kg/m.s. We have five variables in kg, m, and s, so we anticipate two pi-groups:
Figure 6.2 Ludwig Prandtl (1875–1953). (Courtesy of Appl. Mech. Rev. [6.1])
where ν is the kinematic viscosity μ/ρ and Reχ is called the Reynolds number. It characterizes the relative influences of inertial and viscous forces in a fluid problem. The subscript on Re—χ in this case—tells what length it is based upon.
We discover shortly that the actual form of eqn. (6.1) for a flat surface, where u∞ remains constant, is
