In the present study, a comprehensive mathematical method is developed to realize the flame expansion in the melting furnace zones. For this purpose, the furnace is composed of two zones: flame and post flame zones. Two different scenarios are covered in this research: Using lycopodium as a substitute fuel which is then converted to methane after the vaporization process, supplying the system with methane directly as a conventional fuel. The equations governing the problem with the required boundary conditions are developed and solved in each zone. The obtained results show great compatibility with the experimental findings in this research. Since lycopodium as the replacement fuel mostly contains volatile materials, one of the challenges in this study lies on understanding the effect of particle vaporization on the temperature distribution in a furnace. It is concluded that the average temperature in zones α1, α2, β1, and β2, is reduced by about 5 K, while it is increased by approximately the same amount in zones χ1, χ2, δ1, and δ2 after considering lycopodium as a fuel. Moreover, the role of vaporization and radiation on the combustion characteristics is studied in details. The achieved results from this analysis can be implemented in several industrial applications aiming for improving the energy efficiency outcome from their systems.

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