The compressible axisymmetric laminar boundary layer is considered for very large values of the transverse curvature parameter (roughly proportional to the ratio of the Mangler value of the boundary layer displacement thickness to the local cross-sectional radius of the body). Asymptotic expansions are constructed using the method of inner-outer expansions and verified by comparison with exact numerical similarity solutions. Both finite and hypersonic Mach number inviscid flow conditions are considered. The principal results are asymptotic formulas for skin friction, heat transfer, and boundary layer displacement thickness. Existing expansions, obtained by Wei, are found to be incorrect. The viscous pressure interaction near the vertex of a pointed axisymmetric body is treated within the framework of boundary layer theory and a tangent-cone approximation. (Author).

An approximate momentum integral solution for the compressible axisymmetrix laminar boundary layer when transverse curvature effects are important is presented. Both finite and infinite inviscid Mach numbers are considered. Detailed comparisons with exact asymptotic solutions are given. The method is found, in many instances, to agree to leading order with the exact solutions as the transverse curvature becomes very large--a property that none of the existing approximate solutions for compressible flow possess. Some example calculations for a cone in supersonic and hypersonic flow are presented. Also, the method is applied to the hypersonic self-induced pressure problem for a cone. (Author).

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