A simple model of the non-equilibrium dissociation of a gas in Couette and boundary-layer flows

Abstract

At sufficiently high temperature the oxygen and nitrogen molecules in air dissociate into atoms. Energy is required for this decomposition and, furthermore, if the temperature is not uniform, concentration gradients are formed and energy is transferred by the consequent interdiffusion of atoms and molecules. In this paper, a simple model of a gas is formulated to illustrate the effect of these processes on heat transfer in three situations: (1) in a layer of gas at rest between two walls at different temperature, (2) in Couette flow, and (3) in a laminar boundary layer on a flat plate.In the model, the law for the rate of reaction (dissociation and recombination) is of an especially simple form with the speed of reaction characterized by a single parameter. When the parameter becomes large, the gas approaches chemical equilibrium; at the other extreme, no reaction occurs within the gas.Two chemical conditions of the walls are considered, one being that the walls are catalytic (the surface reaction rate is assumed sufficiently high to hold the gas at the wall in chemical equilibrium), and the other that the walls have no effect on the reaction, i.e. they are non-catalytic.The most important of the simplifications made are: (a) The reaction rate law is put in a form in which the equilibrium concentration of atoms varies linearly with temperature. Thus, there is only one temperature at which the gas is undissociated instead of the actual range of temperature. (b) In problems (1) and (2), μ, κ, and ρD are taken to be constant. (c) In problem (3) the Lewis number is assumed to be unity. (d) Only binary mixtures of atoms and molecules are considered (so that ionization and more complex dissociation processes are not covered). (e) Coupling of irreversible flows, such as that causing thermal diffusion, is neglected. (f) Only problems in which the pressure is constant are considered.