The heat transfer in the laminar boundary layer of a heated plate in flow at high speed can be obtained by integration of the conventional differential equations of the boundary layer, so long as the material values can be regarded as constant. This premise is fairly well satisfied at speeds up to about twice the sonic speed and at not excessive temperature rise of the heated plate. The general solution of the equation includes Pohlhausen's specific cases of heat transfer to a plate at low speeds and of the plate thermometer. The solution shows that the heat transfer coefficient at high speed must be computed with the same equation as at low speed, when it is referred to the difference of the wall temperature of the heated plate in respect to its "natural temperature." Since this fact follows from the linear structure of the differential equation describing the temperature field, it is equally applicable to the heat transfer in the turbulent boundary layer.
Equations are given for the elastic behavior of initially curved sheets in which the deflections are not small in comparison with the thickness, but at the same time small enough to justify the use of simplified formulas for curvature. These equations are solved for the case of a sheet with circular cylindrical shape simply supported along two edges parallel to the axis of the generating cylinder. Numerical results are given for three values of the curvature and for three ratios of buckle length to buckle width. The computations are carried to buckle deflections of about twice the sheet thickness. It was concluded that initial curvature may cause an appreciable increase in the buckling load but that, for edge strains which are several times the buckling strain, the initial curvature causes a negligibly small change in the effective width.