V. N. Snytnikov^{1, 2}, E. E. Peskova¹

¹National Research Mordovia State University (Saransk, Russian Federation)

²Boreskov Institute of Catalysis SB RAS (Novosibirsk, Russian Federation)

Abstract. Mathematical models of laser catalytic thermochemistry for subsonic dynamics of a viscous multicomponent gas are considered. Solved problems with azimuthal symmetry relate to producing valuable hydrocarbons from methane. In particular, the problems of methane conversion in a round tube without and with laser radiation are numerically solved. The chemical processes were simulated using a kinetic scheme of radical-chain reactions with the leading role of the hydrogen atom. Furthermore, the results of modeling the catalytic conversion of methane in a nanoparticle flow are presented, including the conversion under additional heating by radiation. On the surface of catalytic nanoparticles a hydrogen atom detaches from a methane molecule, with radicals escaping into the gas phase. A 75% calculated conversion of methane under radiation exposure is achieved. Heat fluxes between the pipe wall and the reaction medium are determined, too. Current mathematical problems in thermochemistry are related to the transition to spatially three-dimensional formulations, which often involve bifurcations or may be unstable when parameters are changed. Computational experiments require a flexible code as a research tool with fully known properties. The creation of such programs requires the involvement of mathematicians with various specializations.

Key Words: Navier-Stokes equations, mathematical modeling, subsonic flow, thermochemistry, radiation, natural gas, non-oxidative methane conversion

For citation: V. N. Snytnikov, E. E. Peskova. Contemporary mathematical problems in thermochemistry with radiation. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 28:3(2026), 280–307. DOI: https://doi.org/10.15507/2079-6900.28.202603.280-307

Information about the authors:

Valeriy N. Snytnikov, Ph.D. (Phys.-Math.), Leading Researcher, Department of Applied Mathematics, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), Leading Researcher, Boreskov Institute of Catalysis SB RAS (5 Lavrentiev Ave., Novosibirsk 630090, Russia), ORCID: https://orcid.org/0000-0002-6769-9456, snyt@catalysis.ru

Elizaveta E. Peskova, D.Sc. (Phys.-Math.), Chief Researcher, Department of Applied Mathematics, National Research Mordovia State University (68/1 Bolshevistskaya St., Saransk 430005, Russia), ORCID: http://orcid.org/0000-0003-2618-1674, e.e.peskova@math.mrsu.ru