[1] D. A. Frank-Kamenetskii, Diffusion and Heat Exchange in Chemical Kinetics, Princeton Univ. Press, 2015.
[2] I. G. Dik, Thermal-explosion degeneration limits in a system with an additional heat source, Combust. Explos. Shock Waves. 16 (1980) 126–129, https://doi.org/10.1007/BF00756256.
[3] V. N. Vilyunov, E. A. Nekrasov and I. G. Dik, Critical conditions for thermal explosion in the presence of a supplementary heat source, Combust. Explos. Shock Waves. 14 (1978) 172–175,
https://doi.org/10.1007/BF00788373.
[4] A. P. Aldushin, Macrokinetic analysis of refractory compound synthesis using the electrothermal explosion method, Adv. Mater. Technol. 2 (2019) 3–7.
[5] A. D. Margolin, Thermal explosion with constant distributed heat source, Zhurnal Fizicheskoj Khimii 37 (4) (1963) 887–888. (in Russ.)
[6] M. J. Frankel, Thermal explosion theory in an external field, J. Appl. Phys. 50 (1979) 4412-4414.
[7] S. A. Bostandzhiyan, I. S. Gordopolova and V. A. Shcherbakov, Modeling of an electrothermal explosion in gasless systems placed into an electroconducting medium, Combust. Explos. Shock Waves 49 (2013) 668–675, https://doi.org/10.1134/S0010508213060051.
[8] V. A. Knyazik and A. S. Shteinberg, Regularities of thermal explosion in a system with additional (non-chemical) heat source, Dokl. Ross. Akad. Nauk. 328 (1993) 580–584.
[9] I. Kuzin and S. Pohozaev, Entire Solutions of Semilinear Elliptic Equations, Birkhäuser Basel, 1997.
[10] V. Berdichevsky, Variational Principles of Continuum Mechanics. I. Fundamentals, Berlin, Springer, 2009.
[11] V. S. Zarubin and A. V. Rodikov, Mathematical simulation of the temperature state of an inhomogeneous body, High Temp. 45 (2007) 243–254, https://doi.org/10.1134/S0018151X07020150.
[12] V. S. Zarubin, V. N. Zimin and G. N. Kuvyrkin, Temperature state of a hollow cylinder made of a polymer dielectric with temperature-dependent characteristics, J. Appl. Mech. Tech. Phys. 60 (2019) 59–67, https://doi.org/10.1134/S0021894419010097.
[13] G. C. Wake and M. E. Rayner, Variational methods for nonlinear eigenvalue problems associated with thermal ignition, J. Differential Equations 13 (1973) 247–256, https://doi.org/10.1016/0022-0396(73)90017-X.
[14] T. I. Zelenyak, V. S. Beskov and M. G. Slin’ko, Qualitative analysis of equations describing exothermal processes. Catalytic process on a porous plate. Kinet. Katal. 7 (1966) 865–873. (in Russ.)
[15] S. P. Fedotov, Stochastic analysis of the thermal ignition of a distributed explosive system, Phys. Lett. A. 176 (1993) 220–224, https://doi.org/10.1016/0375-9601(93)91038-7.
[16] A. M. Grishin, Some problems of ignition theory, Prikladnaya Mekhanika i Tekhnicheskaya Fizika 5 (1962) 75–79. (in Russ.)
[17] S. I. Anisimov and E. I. Vitkin, Some variational problems in thermal explosion theory, J. Appl. Mech. Tech. Phys. 7 (1966) 109–110, https://doi.org/10.1007/BF00917676.
[18] J. G. Graham-Eagle and G. C. Wake, Theory of thermal explosions with simultaneous parallel reactions. II. The two- and three-dimensional cases and the variational method, Proc. R. Soc. Lond. A 401 (1985) 195–202. https://doi.org/10.1098/rspa.1985.0094.
[19] D. D. Joseph, Non-linear heat generation and stability of the temperature distribution in conducting solids, Int. J. Heat Mass Transf. 8 (1965) 281–288,
https://doi.org/10.1016/0017-9310(65)90115-8.
[20] D. Lynden-Bell and R. Wood, The gravo-thermal catastrophe in isothermal spheres and the onset of red-giant structure for stellar systems, Mon. Not. R. astr. Soc. 138 (1968) 495–525, https://doi.org/10.1093/mnras/138.4.495.
[21] S. O. Ajadi, The influence of viscous heating and wall thermal conditions on the thermal ignition of a poiseuille/couette reactive flow, Russ. J. Phys. Chem. B 4 (2010) 652–659, https://doi.org/10.1134/S1990793110040172.
[22] V. S. Zarubin, G. N. Kuvyrkin and I. Y. Savel’eva, The variational form of the mathematical model of a thermal explosion in a solid body with temperature-dependent thermal conductivity, High Temp. 56 (2018) 223–228, https://doi.org/10.1134/S0018151X18010212.
[23] I. Yu. Savelyeva, Variational formulation of the mathematical model of stationary heat conduction with account for spatial nonlocality, Herald of the Bauman Moscow State Technical University, Series Natural Sciences 2 (2022) 68–86 (in Russ.), https://doi.org/10.18698/1812-3368-2022-2-68-86.
[24] H. Biyadi, M. Er-Riani and M. El Jarroudi, Numerical study of an exothermic reaction with convective boundary conditions, Annals of the University of Craiova. Math. Comp. Sci. Ser. 47 (2020) 67–75.
[25] V. S. Zarubin, G. N. Kuvyrkin, I. Yu. Savelyeva and A. V. Zhuravsky, Conditions for a thermal explosion in the plate under convective-radiation heat transfer, Herald of the Bauman Moscow State Technical University, Series Natural Sciences. 6 (2020) 48–59, htps://doi.org/10.18698/1812-3368-2020-6-48-59.
[26] R. Blouquin and G. Joulin, On a variational principle for reaction/radiation/conduction equilibria, Combust. Sci. Technol. 112 (1996) 375–385, https://doi.org/10.1080/00102209608951968.
[27] A. I. Karpov, A. V. Kudrin and M. Y. Alies, Calculation of the stationary flame propagation velocity by the variational principle of irreversible thermodynamics, Case Stud. Therm. Eng. 30 (2022) #101767, https://doi.org/10.1016/j.csite.2022.101767.
[28] I. G. Donskoi, Variational problems for combustion theory equations, J. Appl. Mech. Tech. Phys. 63 (2022) 773–781, https://doi.org/10.1134/S0021894422050054.
[29] A. Kapahi, A. Alvarez-Rodriguez, S. Kraft, J. Conzen and S. Lakshmipathy, A CFD based methodology to design an explosion prevention system for Li-ion based battery energy storage system, J. Loss Prev. Process Ind. 83 (2023) #105038,
https://doi.org/10.1016/j.jlp.2023.105038.
[30] H. Fu, J. Wang, L. Li, J. Gong and X. Wang, Numerical study of mini-channel liquid cooling for suppressing thermal runaway propagation in a lithium-ion battery pack, Appl. Therm. Eng. 234 (2023) #121349, https://doi.org/10.1016/j.applthermaleng.2023.121349.
[31] A. V. Luikov, Analytical Heat Diffusion Theory, Academic Press, 1968.
[32] E. A. Eremin, Stability of steady plane-parallel convective motion of a chemically active medium, Fluid Dyn. 18 (1983) 438–441, https://doi.org/10.1007/BF01090565.
[33] A. Gritsans, A. Kolyshkin, F. Sadyrbaev and I. Yermachenko, On the stability of a convective flow with nonlinear heat sources, Mathematics 11 (2023) #3895,
https://doi.org/10.3390/math11183895.
[34] H. Akbi, A. Mekki and S. Rafai, New linear integral kinetic parameters assessment method based on an accurate approximate formula of temperature integral, Int. J. Chem. Kinet 54 (2022) 28–41, https://doi.org/10.1002/kin.21538.
[35] A. Aghili, N. Sukhorukova and J. Ugon, Bivariate rational approximations of the general temperature integral, J. Math. Chem. 59 (2021) 2049–2062, https://doi.org/10.1007/s10910-021-01273-z.
[36] I. G. Donskoy, Determining critical conditions in the thermal explosion problem using approximate variational formulations, Inf. Math. Technol. Sci. Manag 1 (2022) 7–20.
[37] I. G. Donskoy, Steady-state equation of thermal explosion in a distributed activation energy medium: numerical solution and approximations, iPolytech Journal 26 (2022) 626–639, https://doi.org/10.21285/1814-3520-2022-4-626-639.
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