Non-dimensional scales of time, temperature, length, and heat transfer may be defined as
where
;Note:
:In a typical combustion process,  so that .
:Therefore, . That is, fuel consumption time is much longer than ignition time, so fuel consumption is essentially negligible in the study of ignition.
:This is why the fuel concentration is assumed to remain the initial fuel concentration .
Substituting the non-dimensional variables in the energy equation from the introduction
Since , the exponential term can be linearized , hence
At , we have  and for ,  needs to satisfy  and