FIRST ORDER SLIP EFFECTS ON THE COMPRESSIBLE LAMINAR BOUNDARY LAYER OVER SLENDER BODIES OF REVOLUTION WITH ZERO PRESSURE GRADIENT

摘要

Probstein and Elliott's analysis of the transverse curvature effect on the zero pressure gradient, constant wall temperature, laminar boundary layer is extended to first order slip flow. The effect of slip and temperature jump at the wall on boundary layer flows is characterized by a slip parameter proportional to the ratio of molecular mean free path to boundary layer thickness. In first order slip flow, this parameter is small. Following Probstein and Elliott, the transverse curva¬ture effect is characterized by a transverse curvature parameter which is proportional to the ratio of boundary layer thickness to local body radius. Hence, the present solutions are obtained as double asymptotic expansions in ascending powers of the slip parameter and the transverse curvature parameter. The deter¬mination of these expansions for the same class of bodies as treated by Probstein and Elliott, namely, the bodies with local body radius proportional to arbitrary positive powers of the wetted surface length, is discussed. For several representatives of this class of bodies, the terms of the expansions up to and including the product of the first powers of the slip parameter and the transverse curvature parameter are calculated. It is found that, without pressure gradient, the first order effect of slip on skin friction is of the order of the product of the slip and the transverse curvature parameters (i.e., of the order of the ratio of mean free path to local body radius);whereas, with the exception of special cases, the first order effect of slip on heat transfer is of the order of the slip parameter alone (i.e., of the order of the ratio of the mean free path to local boundary layer thickness).