ZFK equation
Reaction–diffusion equation / From Wikipedia, the free encyclopedia
ZFK equation, abbreviation for Zeldovich–Frank-Kamenetskii equation, is a reaction–diffusion equation that models premixed flame propagation. The equation is named after Yakov Zeldovich and David A. Frank-Kamenetskii who derived the equation in 1938 and is also known as the Nagumo equation.[1][2] The equation is analogous to KPP equation except that is contains an exponential behaviour for the reaction term and it differs fundamentally from KPP equation with regards to the propagation velocity of the traveling wave. In non-dimensional form, the equation reads
with a typical form for given by
where is the non-dimensional dependent variable (typically temperature) and
is the Zeldovich number. In the ZFK regime,
. The equation reduces to Fisher's equation for
and thus
corresponds to KPP regime. The minimum propagation velocity
(which is usually the long time asymptotic speed) of a traveling wave in the ZFK regime is given by
whereas in the KPP regime, it is given by