An explicit time accurate predictor-corrector scheme, similar to MacCormack's, has been used to simulate unsteady nonequilibrium laminar chemically-reacting diffusion-reaction generated flows. A zonal approach, along with nonstructured boundaries, allows computation of internal and external flow with the same computer code. Results for equilibrium flows generated by dissociating, vibrationally relaxing nitrogen in a rectangular chamber are presented. The unsteady flows were generated strictly by the chemical reactions and concentration gradients.