1.6.1 Introduction

The situations that were examined in Sections 1.2 through 1.5 were truly one-dimensional; that is, the geometry and boundary conditions dictated that the temperature could only vary in one direction. In this section, problems that are only approximately 1-D, referred to as extended surfaces, are considered. Extended surfaces are thin pieces of conductive material that can be approximated as being isothermal in two dimensions with temperature variations in only one direction. Extended surfaces are particularly relevant to a large number of thermal engineering applications because the fins that are used to enhance heat transfer in heat exchangers can often be treated as extended surfaces.

1.6.2 The Extended Surface Approximation

An extended surface is not truly 1-D; however, it is often approximated as being such in order to simplify the analysis. Figure 1-31 shows a simple extended surface, sometimes called a fin. The fin length (in the x-direction) is L and its thickness (in the y-direction) is th. The width of the fin in the z-direction, W, is assumed to be much larger than its thickness in the y-direction, th. The conductivity of the fin material is k. The base of the fin (at x = 0) is maintained at temperature T _b and the fin is surrounded by fluid at temperature T _? with heat transfer coefficient h.

Figure 1-31: A constant cross-sectional fin.

Energy is...