  Avrami's model describes the kinetics of phase transformation under the
assumption of spatially random nucleation. In this paper we provide a
quasi-exact analytical solution of Avrami's model when the transformation takes
place under continuous heating. This solution has been obtained with different
activation energies for both nucleation and growth rates. The relation obtained
is also a solution of the so-called Kolmogorov-Johnson-Mehl-Avrami
transformation rate equation. The corresponding non-isothermal
Kolmogorov-Johnson-Mehl-Avrami transformation rate equation only differs from
the one obtained under isothermal conditions by a constant parameter, which
only depends on the ratio between nucleation and growth rate activation
energies. Consequently, a minor correction allows us to extend the
Kolmogorov-Johnson-Mehl-Avrami transformation rate equation to continuous
heating conditions.
