5.1.1 Introduction

Chapter 4 discusses the behavior of the momentum and thermal boundary layers associated with an external flow. An external flow is broadly defined as one where the boundary layer can grow without bound; for the flat plate considered in Section 4.1, the boundary layer was never confined by the presence of another object. An internal flow is defined as one where the growth of the boundary layer is confined. Internal flows are often encountered in engineering applications (e.g., the flow through tubes or ducts) and this section discusses the qualitative behavior of internal flows. Many of the concepts that are discussed in Section 4.1 for an external flow can also be applied to internal flows in order to provide a physical understanding of their behavior.

5.1.2 Momentum Considerations

Figure 5-1(a) illustrates laminar external flow over a plate and shows, qualitatively, the momentum boundary layer and velocity distribution that results. Figure 5-1(b) illustrates laminar flow through a passage that is formed between two parallel plates; notice that at some location, the momentum boundary layer becomes bounded.

Figure 5-1: (a) Laminar external flow over a flat plate, (b) laminar internal flow between two parallel plates, and (c) the shear stress as a function of position for the external and internal flow situations.

The momentum boundary layers growing from the upper and lower plates in Figure 5-1(b) meet at some distance from the inlet; this distance is referred to as the hydrodynamic entry length, x _{fd ,}