Stability of heated boundary layers

A three-dimensional linear stability analysis is presented for two-dimensional boundary layer flows. The method of multiple scales is used to derive the amplitude and the wave number modulation equations, which take into account the nonparallelism of the basic flow. The zeroth-order eigenvalue problem is numerically integrated to calculate the quasi-parallel growth rates which are then integrated together with the nonparallel growth rates along the characteristics of the wave number modulation equations to evaluate the n-factors. The most critical frequency is defined to be the one that yields the n-factor corresponding to transition in the shortest possible distance. This definition is used to evaluate the critical frequency for the Blasius boundary layer, a wedge flow, and an axisymmetric boundary layer. The effect of three-dimensional disturbances is evaluated and found to be less critical than two-dimensional disturbances. The effect of heating the boundary layer is evaluated for the Blasius, Falkner-Skan, and axisymmetric boundary layers.