Some problems concerning the mathematical theory of non-isothermal kinetics. II. primary isothermal differential kinetic equations (PIDKEs)

Abstract

Following earlier work, this paper deals with some new aspects concerning the mathematical theory of non-isothermal kinetics. After a short introduction which emphasizes that in non-isothermal kinetics the temperature T and time t are dependent variables, one of the main problems of non-isothermal kinetics, which involves the derivation of adequate non-isothermal differential kinetic equations, is discussed. The derivation of such equations from isothermal differential kinetic equations using the “classical” transformation (change), i.e. expressing T as a function of t or vice versa is shown to be equivalent to the postulation of some “primary isothermal differential kinetic equations” (PIDKEs). After a discussion concerning the model of infinitesimal isothermal portions (MIIP) in connection with PIDKEs. a non-isothermal kinetic treatment of the nucleation and nuclei growth is suggested. A short discussion of the non-isothermal integration of the Johanson-Mehl-Avrami-Yerofeyev-Kolmogorov (JMAYK) equation completes the paper.