Application of heat-balance integral method to conjugate thermal explosion

Conjugate thermal explosion is an extension of the classical theory, proposed and studied recently by the author. The paper reports application of heat-balance integral method for developing phase portraits for systems undergoing conjugate thermal explosion. The heat-balance integral method is used as an averaging method reducing partical differential equation problem to the set of first-order ordinary differential equations. The latter reduced problem allows natural interpretation in appropriately chosen phase space. It is shown that, with the help of heat-balance integral technique, conjugate thermal explosion problem can be described with a good accuracy by the set of non-linear first-order differential equations involving complex error function. Phase trajectories are presented for typical regimes emerging in conjugate thermal explosion. Use of heat-balance integral as a spatial averaging method allows efficient description of system evolution to be developed