Introduction to Convective Heat Transfer

4Integral Methods in Convective Heat Transfer

4.1 Introduction

When electronic computers were not available, the integral method of solving boundary layer problems was very popular. If the solution procedure becomes tedious, it is very useful to use approximate methods. The integral method is one such method. The integral method is capable of handling arbitrary variations of free stream velocity U_∞(x) and surface temperature T_w(x). If the exact solution is not known or difficult to obtain, then the integral method is very useful. Fortunately, an integral method due to von Karman is available, as discussed in [1]. The integral method is used very often in heat transfer because of its simplicity. It applies to both the laminar and turbulent flows. However, the basic laws are satisfied in average sense, and naturally, the integral method gives approximate solutions. The accuracy of the solution depends on the assumed velocity and temperature profiles. The assumed velocity and temperature profiles can range from linear to more complex forms. The sophisticated functions are better able to capture the characteristics of velocity and temperature profiles. The undetermined coefficients of these velocity and temperature profiles are selected so that the boundary conditions are satisfied. It is true that the integral method is considerably less accurate than its differential counterpart, but the success it has enjoyed in many engineering applications justifies the usage of the method. ...