Reaction waves in solid fuels for adiabatic competitive exothermic reactions

Zhejun Huang, Harvinder Sidhu, Isaac Towers, Zlatko Jovanoski, Vladimir Gubernov


We investigate travelling premixed reaction waves in a diffusional-thermal model with a two-step competitive reaction mechanism where both reactions are exothermic. Travelling waves are assumed to propagate at constant speed. An approximation of the Arrhenius reaction rate is adopted to simplify the combustion model. Based on this assumption, an asymptotic theory is presented for solid fuels under adiabatic conditions. This approach provides a convenient way to analyse the system in the phase plane. The asymptotic speeds for the flame fronts are compared with numerical solutions by solving the governing partial differential equations. In addition, piecewise approximate solutions for the temperature and fuel mass fraction profiles are presented and compared with those obtained numerically. Our results can be applied to combustion synthesis in the production of advanced materials.

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competitive exothermic reactions, reactive waves, phase plane, piecewise linear approximation.

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.