A finite-difference solution of similar nonequilibrium boundary layers.

Abstract

The solution of nonequilibrium boundary-layer problems by forward integration techniques becomes progressively more difficult as the dimensionless reaction rate constant K (ratio of flow time to reaction time) increases. With these methods the solutions grow exponentially in a distance of order K~, so that the initial values of the derivatives must be guessed nearly exactly if a solution is to be found for K ^>> 1. The method proposed circumvents this difficulty by treating the two-point boundary-value problem directly rather than as an initial-value problem. The differential equations are linearized with respect to the principal variable about an appropriate initial guess satisfying the boundary conditions. The resulting uncoupled, second-order linear equations are put into finite-difference form and are solved by matrix inversion. Temperature, velocity, and concentration profiles are obtained by successively solving the linearized equations in sequence until convergence (to the solution of the nonlinear equations) is reached. The specific case treated is the stagnationpoint dissociation of nitrogen. For conditions given, at K = 10~, the flow was effectively frozen, and by K = 10, equilibrium was substantially attained.