Boundary Layer Problems in Applied Mechanics

Abstract

This chapter provides an introduction to boundary layer, presents a simple characterization of the boundary layer problem, and discusses varying detail of the analysis of several isolated problems, which fall into this category. The term “boundary layer” has become most closely associated with the phenomena arising when a fluid flows past an obstacle at high Reynolds number. There is a large and interesting variety of physical problems whose analysis is most appropriately carried out by invoking the ideas that are associated with boundary layer problems. The various boundary layer problems discussed are the ocean current problem, heat transfer problem, convection problem, and the relaxation oscillations of the van der Pol oscillator. Other problems discussed are elasticity problems and flow of a viscous fluid past an obstacle problem. The chapter also discusses the solution of the boundary layer problem that takes place in two steps. First, one finds an interior solution by integrating the system of equations, then one changes the scale of the normal coordinate to the boundary and the scale of any other functions whose size is not known in such a manner that a system of equations of the appropriate order is retained.