The near-exit region of confined, unsteady, momentum dominated, non-premixed, chemically reacting jets is investigated computationally using one-step chemistry. Non-premixed flame/wall interaction is manifested in the form of reaction zone broadening. Depending on the value of the stoichiometric mixture fraction, the flame zone moves into or out of the region of strong shear. For flames with large stoichiometric mixture fraction, the flame region is located in closer proximity to the isothermal wall. With increased stoichiometric mixture fraction, reaction thicknesses predicted by asymptotic theory differ from flame zone thicknesses obtained from the simulation databases.