Introduction to Convective Heat Transfer

7Laminar External Boundary Layers: Momentum and Heat Transfer

7.1 Introduction

In this section, the search for a similarity method is the main concern. With the similarity variable, the partial differential equation of the physical problem is expected to be transformed into an ordinary differential equation. After the original work of Blasius [1] on the boundary layer problem of flat plate, Goldstein [2] studied the problem in depth. Following a different approach, Sedov [3] developed a method to find a similarity variable using dimensional analysis. The similarity method is discussed in several books such as [4–8]. Later, Arpaci and Larsen [9] presented a method to search for a similarity variable. Their method is based on dimensional analysis, and this method will be used in this book as much as possible. Details of the method are discussed by Arpaci and Larsen, and a brief outline will be given here:

1. (1) The dependent and independent variables are made dimensionless in terms of characteristic properties. If there is no characteristic property, arbitrarily selected reference quantities are used.
2. (2) All the arbitrarily selected reference quantities are eliminated successively by employing the mathematical and physical principles. The mathematical principle states the invariance of the number of dependent and independent variables of a mathematical expression under any transformation. On the other hand, the physical principle concerns with the dimensional homogeneity of a ...