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The hypersonic strong-interaction regime for the flow of a viscous, heat-conducting compressible fluid past a flat plate is analysed using the Navier–Stokes equations as a basis. It is assumed that the fluid is a perfect gas having constant specific heats, a constant Prandtl number σ, whose numerical value is of order one, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied as the free-stream Mach numberM, the free-stream Reynolds number based on the plate lengthRL, and the interaction parameterx= {(γM2)2+ω/RL}½, go to infinity.Through the use of asymptotic expansions and matching, it is shown that, for (1−ω) > 0, three distinct layers for which similarity exists make up the region between the shock wave and the plate. The behaviour of the flow in these three layers is analysed.

Asymptotic expansion techniques are used, in the limit of large Reynolds number, to study the structure of fully turbulent shear layers. The relevant Reynolds number characterizes the ratio of the local turbulent stress to the local laminar stress, so that a relatively thick outer defect layer, in which, to lowest order, there is a balance between turbulent stress and convection of momentum, may be distinguished from a relatively thin wall layer, in which, to lowest order, there is a balance between turbulent and laminar stresses. The two cases examined are channel (or pipe) flow and two-dimensional boundary-layer flow with an applied pressure gradient, upstream of any separation. Attention, for these two cases, is confined to the flow of incompressible constant property fluids. Closure is effected through the introduction of an eddy-viscosity model formulated with sufficient generality for most existing models to be special cases. Results are carried to higher orders of approximation to indicate what properties for the friction velocity, integral thicknesses, and velocity profiles, and what conditions for similarity are implied by current eddy-viscosity closures.

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The steady one-dimensional isobaric combustion of a gaseous premixture of fuel and oxidant under a direct one-step irreversible Arrhenius-type exothermic chemical reaction is studied analytically for constant, but general, Lewis-Sernenov number. Limit-process expansions are used to obtain solutions in the physically interesting limit of activation temperature large relative to the hot-boundary temperature. The eigenvalue or critical flow speed for an adiabatic system is established as a function of departure from stoichiometry. It is emphasized that, for relatively small departures from stoichiometry, the bimolecular system behaves as a monopropellant decomposition, to lowest order of approximation, because the richer reactant is effectively undepleted. The porous-disk-type flameholder for a flat-flame burner is modeled as a (nonadiabatic) heat source (supercritical flow speed) or heat sink (subcritical flow speed). The flame stand-off distance and the amount of departure of the hot-boundary temperature from the adiabatic flame temperature are obtained as functions of flow speed and stoichiometry. It is noted that for a I/ol/distributed heat source/sink, the heat transfer to/from the flameholder is a unique function of flow speed, provided only that the heat transfer is less than that derived from combustion of the premixture. The reliability of evidence for two flame speeds for spatially distributed heat losses is critically reviewed.