The boundary layers forming on the walls of an aligned cylinder in a rotating fluid in axial motion are studied theoretically. The analysis shows that the side-wall boundary layer is of the Blasius type when the Rossby number exceeds the inverse square root of the Reynolds number and is transformed to the Stewartson $\frac{1}{3}$-layer when the Rossby number is less than this value. A second thicker boundary layer is superimposed on the $\frac{1}{3}$-layer whenever the difference between the azimuthal velocities of the ambient fluid and the boundary exceeds the axial velocity. Its thickness varies according to the relative magnitudes of these velocities and yields the Stewartson ¼-layer thickness only when the ratio of the azimuthal velocity difference to the axial velocity is of order E⅙, where E is the Ekman number. A uniformly valid solution is obtained for the first case when the boundary layer is of the Blasius type.

The growth of hypersonic boundary layers over both concave and convex surfaces is described, the strong-viscous-interaction equation due to Cheng et al. (1961) for curved surfaces with sharp leading edges being solved asymptotically for small and large arguments. Both the asymptotic solution for large arguments and a numerical integration predict an oscillatory behaviour of the boundary-layer thickness on concave surfaces. A modification of Cheng's theory, as suggested by Sullivan (1968) and Stollery (1970), is also examined and compared with experimental data reported here. The experiments were conducted in air using a hypersonic gun tunnel under cold wall conditions at M∞ = 12·25. They included measurement of surface pressure, heat-transfer distributions and schlieren studies for concave and convex models.

The laminar boundary layer over the semi-infinite rigid plane y = 0, x > 0 is examined for the case when the free-stream velocity takes the form \[ U(x, t) = U_0(x) (1+\alpha_1 \sin \omega t), \] where 0 [les ] α1 < 1 and U0(x) ∝ xn, 0 [les ] n [les ] 1. The corresponding steady solution is the Falkner-Skan boundary layer with zero (n = 0) or favourable pressure gradient (n = 1 corresponds to the stagnation-point boundary layer). The skin friction, and the heat transfer from the wall when that is maintained at a uniform temperature T1 greater than the temperature T0 of the oncoming fluid, are calculated by means of two asymptotic expansions: a regular one for small values of the frequency parameter ε1(x) = ωx/U0(x) and a singular one (requiring the use of matched asymptotic expansions) for large values of ε1. The principal difference between this work and that of earlier authors is that here α1 is not required to be small. Numerical computations are made for three values of n (0, $\frac{1}{3}$, 1), three values of α1 (0·2, 0·5 and 0·8) and (in the case of the heat transfer) two values of the Prandtl number σ (0·72 and 7·1). It is demonstrated that for each n there is a value of ε1 at which the small-and the large-ε1 expansions for the skin friction overlap quite well, and that, near the overlap region, two terms of the small-ε1 expansion provide a more accurate asymptotic representation of the solution than three. It is also shown that there is no region of overlap between the small- and the large-ε1 heat-transfer expansions, except in one case (n = 1/3, σ = 0·72) where the overlap value of ε1 (= 2·0) is the same as for the skin-friction expansions. The question of the existence of eigensolutions in the large-ε1 expansion, where on physical grounds they can be expected to appear, is discussed in the appendix.

A set of constitutive equations, valid for arbitrary linear bulk flows, is derived for a dilute suspension of nearly spherical, rigid particles which are subject to rotary Brownian couples. These constitutive equations are subsequently applied to find the resulting stress patterns for a variety of time-dependent bulk flow fields. The rheological responses are found to exhibit many of the same qualitative features as have been observed in recent experimental investigations of polymeric solutions and other complex materials.