Igor G. Donskoy

Melentiev Energy Systems Institute Siberian Branch of the Russian Academy of Sciences

The paper proposes approximate variational principles for the classical thermal explosion problem and its modifications (including cases where the high activation energy approximation does not hold). Variational problems are solved using a one-parameter test function and the Ritz method (for polynomial approximation of the solution). The results of the calculations make it possible to determine the dependence of the critical conditions on the parameters of the problem: the intensity of heat transfer at the inner boundary, forced convection, and viscous dissipation.

thermal explosion, inverse variational problem, critical conditions, numerical methods