The velocity fields associated with a variety of flows which may be described by perturbations of the Blasius solution are considered. These are flows which, for example, because of localized mass transfer, involve the initial-value problem of boundary-layer theory, or which involve a variable ratio of the viscosity-density product, or finally which involve mass transfer. The perturbation solutions are presented so that in accord with the usual linearization procedures further applications for the determination of first-order effects can be readily made. In addition, each of these perturbations involves a common differential operator whose eigenfunctions form a complete orthogonal set. Accordingly, a procedure for systematically improving each perturbation solution to obtain higher-order effects by quadrature is presented. The results of applications in several cases are given and are compared to more accurate solutions where available.

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Solutions for two types of problems involving the energy equation for flows with velocities described by the Blasius solution are presented. The first type arises in flows with arbitrary initial distributions of stagnation enthalpy and with surfaces downstream of the initial station either with constant wall enthalpy or with zero heat transfer. Exact solutions in these cases are obtained for constant ρμ, and Prandtl number of unity; they are given in terms of complete orthogonal sets of functions which can be used to obtain first- and higher-order corrections for the effects of variable ρμ, non-unity Prandtl number, and deviations of the velocity field from that described by the Blasius solution.The second type of problem pertains to flows with power-law descriptions of the wall enthalpy. Again the basic solutions are obtained for Prandtl number of unity and the effect of non-unity Prandtl number is treated as a perturbation.

An analysis of sound propagation in rarefied gases is presented. The analysis emphasizes molecular surface interactions with solid boundaries, and the feasibility of their study by acoustical means. A semiphenomenological theory is developed for the regime in which molecular-surface interactions dominate. Dispersion relations are obtained which agree with experiments.