It is predicted that, at a temperature difference a little less than that at which motion starts according to linear stability theory, a steady hexagonal convective pattern will develop from finite-amplitude instabilities in a horizontal layer of fluid heated from below. This is because the first disturbances to start growing must be the triplet of two-dimensional ‘rolls’ which form angles of 60° with each other and whose amplitudes and phases first fall in certain critical ranges. The growth of these disturbances stabilizes all other disturbances and is such that ultimately the right phases and amplitudes occur to give hexagonal cells. If the temperature difference is increased somewhat beyond its critical value, the hexagonal pattern becomes unstable and a two-dimensional roll pattern is predicted. In an intermediate temperature range, rolls are unstable but transport more heat than hexagons. ‘Free–free’ boundary conditions, a viscosity which varies with temperature, and a fixed disturbance wave-number are assumed in this extension of the work of Palm (1960) and Segel & Stuart (1962). Other theoretical results and some experimental results are compared with the present predictions.

Consideration is given to the flow of an elastico-viscous liquid in a curved pipe under a pressure gradient. The cross-section of the pipe is an ellipse, the axes of which are in an arbitraty position with respect to the radius of curvature of the pipe. The method of solution is an extension of that used by Dean (1927) and by Thomas & Walters (1963) in their consideration of flow through a curved pipe of circular cross-section.

It is shown that the liquid elements move along the pipe in two sets of spirals. When the axes of the ellipse are in an asymmetrical position the streamline projections on the cross-section of the pipe are strongly dependent on the elasticity in the liquid. This is not so when the axes are in a symmetrical position. However, in this case, the pitch of the spirals is strongly dependent upon the elasticity of the liquid.

It is also shown that the flux through the pipe is independent of the curvature of the pipe to first order in the curvature.

The flow round an elliptic cylinder immersed in a finite volume of fluid and influenced by an electric field is determined, under the boundary conditions arising from electrosmosis at the surface of the cylinder. This is a problem in slow viscous flow with difficult boundary conditions, and is solved by numerical analysis, using the relaxation method. After the flow pattern has been determined, the mechanical action on the cylinder is calculated. An experimental application based on the theoretical results is suggested as a method for the determination of electrokinetic potentials.

A highly rarefied gas, initially in equilibrium, is compressed by an infinite plane piston. The resulting flow is considered when the gas is unbounded and also when the gas is bounded by a second stationary wall. In the first case, the density ahead of the piston is analysed for specularly and diffusely reflecting surfaces. In the second case, the average temperature of the gas is found as a function of the wall separation for specularly reflecting surfaces. This (non-equilibrium) temperature is compared with that generated in the corresponding continuum flow which involves multiple shock wave reflexion. It is shown that, for a given average density gradient, the free molecule temperatures are very much higher than the continuum temperatures.

This paper is concerned with deducing the most important features of the steady separated flow past a circular cylinder in the limit of vanishing viscosity. First of all, it is shown that the experimental results reported in an earlier article cannot be reconciled with the notion that, as the Reynolds number Re is increased, the flow becomes inviscid everywhere and that viscous effects remain confined within infinitesimally thin shear layers. In contrast, the limiting solution is visualized as exhibiting three essential features: a viscous, closed ‘wake bubble’ of finite width but with a length increasing linearly with Re in which inertial and viscous effects are everywhere of equal order of magnitude; an outer inviscid flow; and, separating the two regions, a diffuse viscous layer covering large sections of the external field. Further properties of this asymptotic solution include: a finite form drag, a negative rear pressure coefficient at the rear stagnation point of the cylinder, and a Nusselt number for heat transfer which becomes independent of Re along the non-wetted portion of the cylinder surface. This model is shown to be consistent with all the experimental data presently available, including some new heat transfer results that are presented in this paper.

An approximate technique is also proposed which takes into account the asymptotic character of the flow in the vicinity of the cylinder and which predicts the pressure distribution around the cylinder in good agreement with the experiments.