This paper studies a system of partial differential equations modelling the behaviour of a reverse flow reactor. For the parameters appropriate for the oxidation of ammonia on a Pt/Al2O3 catalyst in a typical laboratory set-up, the reactor may be split into regions where approximate formulas that determine its behaviour are deduced. Numerical calculations are presented and can be used to compare with the analytical formulas. The physical insight gained from the asymptotic analysis suggests a new switching strategy which is the subject of numerical experiments. The switching strategy is found to be efficient at minimising the ammonia exiting the reactor after reversal.