We describe an elementary model of one-dimensional unsteady forward sm
oldering, purged of all unnecessary physics. Following work of Dosanjh
and Pagni, a late time solution is constructed, characterized by two
reaction fronts-an exothermic oxidation front, an unusual kind of diff
usion flame; and an endothermic pyrolysis front. It is shown that the
flame temperature and the ratio of the speeds of the two fronts relati
ve to the solid are independent of the blowing rate, in agreement with
data obtained by Ohlemiller and Lucca. The structure of the oxidation
front is described in the context of one-step Arrhenius kinetics, and
it is shown that leakage of solid reactant through the front is possi
ble, but not leakage of oxygen. An elementary pyrolysis structure is a
lso examined which reduces to the frontal model in a certain limit, an
d clarifies its nature.