We extend an earlier study of the flow arising from the injection of reactants through a lower porous wall which is stationary and from the withdrawal of products through an upper wall which is moving in its plane at arbitrary but steady speed. In addition to a variety of thermochemical parameters characterizing this flow, the key aerothermodynamic parameters are the flame location within the passage, a Reynolds number, the temperature of the upper wall, and a Mach number. With the assumed chemical model, reaction is confined to a thin reaction zone. When the Reynolds number is suitably high, the case dealt with here, we argue that adjacent to the upper wall there is a single viscous layer with an embedded reaction zone. These considerations motivate an asymptotic analysis of such a wall layer, an analysis of fundamental interest and of relevance to the development of flamelet models of chemical reaction in high-speed turbulent flows. Flows with an adiabatic upper wall and with wall cooling are considered. The analysis is applied to determine the wall temperature resulting in extinction and the alteration of the rate of creation of product by compressibility, heat transfer, and shear.