In many practical situations of interest to combustion, high-speed gas flow prevails. Examples are flame stabilization by bluff bodies within the combustion chamber of a gas turbine, accidental or intentional explosion of a combustible by a hot metal particle or projectile, thermal protection of reentry vehicles by ablative heat shields, and the burning of solid and liquid surfaces in an oxidizing gas stream.

When such a high-speed flow is adjacent to either a solid surface or another flow with slower velocity, a transition region exists. Across this region, the flow velocity, and possibly also temperature and concentration, will change from their respective freestream values to either satisfy the boundary conditions required at the solid surface or approach the freestream values of the slower flow. For fluids with small viscosity µ, the transition region is thin and the normal gradient across it, ∂u/∂y, is large such that despite the small µ, the shear stress, τ = µ∂u/∂y, may assume large values. Thus if the characteristic dimensions over which properties change appreciably in the x- and y-directions are ℓ and δ respectively, then the existence of a boundary layer is implied by the condition δ/ℓ ≪ 1. Furthermore, since for gases the diffusive transport processes of heat, mass, and momentum occur at comparable rates, we expect that the boundary-layer thicknesses for these three processes also should not differ too much from each other.