  The present theory considers the transient evolution of the temperature and
fuel mass fraction distributions, and it can determine the critical heating
power and minimum ignition energy for successful ignition. The flame initiation
process subject to central heating can be approximately decomposed into four
stages, i.e., the fast establishment of the ignition kernel, the
ignition-energy-supported flame kernel propagation, unsteady transition of the
flame kernel, and quasi-steady spherical flame propagation. Comparison between
present transient theory and previous quasi-steady theory indicates that the
unsteady effects directly lead to the appearance of flame kernel establishing
stage and considerably affect the subsequent flame kernel development by
lowering the flame propagation speed. Time scale analysis is conducted, and it
is found that the transient formulation completely degenerates to the
quasi-steady theory either in the neighborhood of stationary flame ball or as
approaching the planar flame. Previous quasi-steady theory shows that the
critical heating power for successful ignition is proportional to the cube of
the critical flame radius. However, the critical heating power predicted by the
present transient formulation deviates this scaling law, which can be
attributed to the unsteady thermal conduction from heating center to the flame
front. Furthermore, in the transient formulation the central heating with
finite duration is considered and the minimum ignition energy is obtained. For
the first time, the memory effect that persistently drives flame propagation
subsequent to central heating switching-off is examined. It is found that as
the heating power grows, the memory effect becomes increasingly important and
it can greatly reduce the minimum ignition energy.
