Introduction to Convective Heat Transfer

3Equations of Incompressible External Laminar Boundary Layers

3.1 Introduction

The concept of boundary layer theory was proposed by Prandtl in 1904. The boundary layer theory is discussed in depth by several people, such as Schlichting and Gersten [1], Rosenhead [2], and Schetz [3]. Consider heat transfer from a flat plate to a fluid stream in external flow. Assume that flat plate temperature is T_w, and free stream fluid velocity and temperature are U_∞ and T_∞, respectively. We are interested in the following:

1. The heat transfer from the plate to fluid
2. The net force exerted on the flat plate by the fluid.

We will look for answers to these questions.

3.2 Laminar Momentum Transfer

Many engineering problems in convective heat transfer can be approximated, in the limit, by the flow over a thin flat plate. Consider a thin semi‐infinite flat plate in a steady two‐dimensional stream of flow having a free stream velocity of U_∞(x). The plate is aligned with the streamlines so that there will be no disturbance in the inviscid flow. The coordinate system is located at the leading edge of the plate. At this point, it should be noted that a mirror image exists underneath our hypothetically semi‐infinite thin plate.

For some distance from the leading edge of the plate, the boundary layer is laminar. See Figure 3.1. After the laminar region, the flow field has characteristics of both the laminar and turbulent flows. This region is called the transition region. After the transition region, ...