University of Colorado at Boulder
Boulder, Colorado, U. S. A.
Similarity reduction procedures that often lead to asymptotic solutions of partial differential equations in fluid dynamics are reviewed. We show how in some instances the governing equations may be used to find parameter space limitations on solutions or to determine unknown boundary conditions. New results for cross-flow in boundary layers and boundary layer flow over irregular leading edges are presented. Natural convection boundary layers resulting from point and line heat sources adjacent to inclined walls are discussed both for Newtonian fluids and in porous media. Here similarity solutions of the first or second kind appear depending on whether the boundary conditions at the solid wall are adiabatic or isothermal. Matching procedures for flows naturally encompassing two different similarity solutions are discussed briefly.