Exact Similar Solutions of the Laminar Boundary-Layer Equations

Abstract

The purpose of this chapter is to present comprehensive, systematic, and accurate tables of solutions to the laminar boundary-layer similarity equations for a perfect homogeneous gas. These solutions are applicable to the classical cases wherein the requirements for similarity are satisfied exactly. The solutions may be used in applying local similarity methods to cases that do not meet the exact requirements for similar flows. In particular, the sensitivity of the numerical values of the wall derivatives (which govern heat transfer and skin friction) and the values of the integral thickness parameters to changes in the similarity variables may be accurately determined. For many physical situations, relaxing one or more of the conditions required for exact similarity will not lead to large errors when the local similar solutions are used to estimate boundary-layer properties. Solutions are included to illustrate the effects of the leading-edge sweep, the mass transfer at the surface, pressure gradient, the wall temperature, the free-stream Mach number, local external-flow velocity, the Prandtl number, and the viscosity-temperature law of the fluid. The tables include most of the numerical solutions obtained by previous authors. Section II presents the similarity equations in their general form, including the equation for species concentration. Section III gives a concise guide to the solutions of this chapter. Section IV presents the numerical method of computation used in this program. The concept of local similarity is discussed in Section V, where criteria are presented for judging the applicability of similar solutions in situations where the similarity parameters vary. The analysis is extended to large positive values of the pressure-gradient parameter β in Section VI.