Convection Heat Transfer

Adrian Bejan

• Publisher: Wiley
• Year: 2013
• ISBN:
  9781118330081
• Edition: 4
• Topic: Physical Sciences
• Subtopic: Thermodynamics

A new edition of the bestseller on convection heat transfer

A revised edition of the industry classic, Convection Heat Transfer, Fourth Edition, chronicles how the field of heat transfer has grown and prospered over the last two decades. This new edition is more accessible, while not sacrificing its thorough treatment of the most up-to-date information on current research and applications in the field.

One of the foremost leaders in the field, Adrian Bejan has pioneered and taught many of the methods and practices commonly used in the industry today. He continues this book's long-standing role as an inspiring, optimal study tool by providing:

• Coverage of how convection affects performance, and how convective flows can be configured so that performance is enhanced
• How convective configurations have been evolving, from the flat plates, smooth pipes, and single-dimension fins of the earlier editions to new populations of configurations: tapered ducts, plates with multiscale features, dendritic fins, duct and plate assemblies (packages) for heat transfer density and compactness, etc.
• New, updated, and enhanced examples and problems that reflect the author's research and advances in the field since the last edition
• A solutions manual

Complete with hundreds of informative and original illustrations, Convection Heat Transfer, Fourth Edition is the most comprehensive and approachable text for students in schools of mechanical engineering.

Chapter 1

Fundamental Principles

Convective heat transfer, or simply, convection, is the study of heat transport processes effected by the flow of fluids. The very word convection has its roots in the Latin verbs convecto-are and conv

ho-v

h

re [1],¹ which mean to bring together or to carry into one place. Convective heat transfer has grown to the status of a contemporary science because of our need to understand and predict how a fluid flow acts as a “carrier” or “conveyor belt” for energy and matter.

Convective heat transfer is clearly a field at the interface between two older fields: heat transfer and fluid mechanics. To study the interdisciplinary is valuable, but it must come after one possesses the disciplines, not the other way around. For this reason, the study of any convective heat transfer problem must rest on a solid understanding of basic heat transfer and fluid mechanics principles. The objective in this chapter is to review these principles in order to establish a common language for the more specific issues addressed in later chapters.

Before reviewing the foundation of convective heat transfer methodology, it is worth reexamining the historic relationship between fluid mechanics and heat transfer. Especially during the past 100 years, heat transfer and fluid mechanics have enjoyed a symbiotic relationship in their development, a relationship where one field was stimulated by the curiosity and advance in the other field. Examples of this symbiosis abound in the history of boundary layer theory and natural convection. The field of convection grew out of this symbiosis, and if we are to learn anything from history, important advances in convection will continue to result from this symbiosis. Thus, the student and the future researcher would be well advised to devote equal attention to fluid mechanics and heat transfer literature.

1.1 Mass Conservation

The first principle to review is undoubtedly the oldest: It is the conservation of mass in a closed system or the “continuity” of mass through a flow (open) system. From engineering thermodynamics, we recall the mass conservation statement for a control volume [2]:

1.1

where M_cv is the mass that is trapped instantaneously inside the control volume (cv), while the

's are the mass flow rates associated with flow into and out of the control volume. In convective heat transfer, we are usually interested in the velocity and temperature distribution in a flow region near a solid wall; hence, the control volume to consider is the infinitesimally small Δx Δy box drawn around a fixed location (x, y) in a flow field. In Fig. 1.1, as in most of the problems analyzed in this book, the flow field is two-dimensional (i.e., the same in any plane parallel to the plane of Fig. 1.1). In a three-dimensional flow field, the control volume would be the parallelepiped Δx Δy Δz. Taking u and

as the local velocity components at point (x, y), the mass conservation equation (1.1) requires that

1.2

or, dividing through by the constant size of the control volume (Δx Δy),

1.3

Figure 1.1 Mass conservation and systems of coordinates.

In a three-dimensional flow, an analogous argument yields

1.4

where w is the velocity component in the z direction. The local mass conservation statement (1.4) can also be written as

1.5

or

1.6

In expression (1.6), v is the velocity vector (u,

, w), and D/Dt represents the “material derivative” operator,

1.7

Of particular interest to classroom and fundamental treatment of the convection problem is the wide class of flows in which temporal and spatial variations in density are negligible relative to the local variations in velocity. For this class, the mass co...