Heat Transfer
Offering complex and timely real-world problems that are inherently interesting, this book provides engineers with the capability, tools, and confidence to solve real-world heat transfer problems.
TABLE OF CONTENTS Heat Transfer
1.2: Steady-State 1-D Conduction without Generation
1.2 Steady-State 1-D Conduction without Generation
1.2.1 Introduction
Chapters 1 through 3 examine conduction problems using a variety of conceptual, analytical, and numerical techniques. We will begin with simple problems and move eventually to complex problems, starting with truly one-dimensional (1-D), steady-state problems and working finally to two-dimensional and transient problems. Throughout this book, problems will be solved both analytically and numerically. The development of an analytical or a numerical solution is accomplished using essentially the same steps regardless of the complexity of the problem; therefore, each class of problem will be solved in a uniform and rigorous fashion. The use of computer software tools facilitates the development of both analytical and numerical solutions; therefore, these tools are introduced and used side-by-side with the theory.
1.2.2 The Plane Wall
In general, the temperature in a material will be a function of position ( x, y, and z, in Cartesian coordinates) and time ( t). The definition of steady-state is that the temperature is unchanging with time. There are certain idealized problems in which the temperature varies in only one direction (e.g., the x-direction). These are one-dimensional (1-D), steady-state problems. The classic example is a plane wall (i.e., a wall with a constant cross-sectional area, A c, inthe x-direction) that is insulated around its edges. In order for the temperature distribution to be 1-D, each face of the wall must be subjected to a uniform boundary condition. For example, Figure 1-4 illustrates a plane...
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