University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 17 1 2026 03 01 Variational Formulation of Thermal Explosion Problem with Internal Heat Generation 1 11 115407 10.22052/ijmc.2025.256937.2017 EN Igor Donskoy Melentiev Energy Systems Institute SB RAS‎, ‎130 Lermontova st.‎, ‎Irkusk‎, ‎Russian Federation‎, ‎664033 Journal Article 2025 05 26 ‎The article considers the problem of thermal stability in plane symmetry with an exothermic chemical reaction and constant heat release‎. ‎The dependence of the critical reactivity on the intensity of heat release is investigated‎. ‎Differential and variational formulations are considered; for the latter‎, ‎an approximate analytical solution is given that relates the parameters of the problem for critical conditions‎. ‎A simple Rayleigh-Ritz procedure results in a set of equations expressing the temperature distribution in terms of polynomials‎. ‎The ignition boundary can be found through second derivatives of the integral‎, ‎which can be evaluated using some simplifications that are typical for combustion theory‎. ‎The results are reduced to simple approximations that can be used to estimate the ignition limits in systems with combined heat release‎. https://ijmc.kashanu.ac.ir/article_115407_b3c20ca8f0a17e9f4bc4334da49725cb.pdf