Critical conditions of ignition and extinction are studied theoretically fo
r the case of a heterogeneous exothermic reaction proceeding on the uniform
ly accessible surface of a channel or a pore. Particular emphasis is placed
on the thermal-hysteresis effect of the reaction tan ignition temperature
in excess of the extinction temperature), which ensures stability of the re
action against changes in the external conditions. A model for the process
is proposed and substantiated. It permits one to analyze the main regularit
ies of the thermal reaction regime with allowance for the distribution of h
eat flows from the reaction zone to the reaction medium and the channel wal
l. The dependence of the critical conditions of ignition and extinction on
the rate constants of heat release, the reaction order, and the thermal and
geometric characteristics of the system is established. A rule is proposed
that permits evaluating the effect of heat losses on the critical phenomen
a and the thermal hysteresis of a reaction on a cooled surface in the case
where the critical conditions for the reaction on an adiabatic surface are
known.