Authors : Anand Kumar Mishra; Pranav Kumar Pandey

Volume/Issue : Volume 10 - 2025, Issue 11 - November

Google Scholar : https://tinyurl.com/mr3dccye

Scribd : https://tinyurl.com/3emztv92

DOI : https://doi.org/10.38124/ijisrt/25nov1045

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Abstract : This study presents a comprehensive mathematical analysis of hydrogen com- bustion and its energy conversion efficiency. A dimensionless nonlinear model is developed, integrating chemical kinetics, temperature evolution, and efficiency dy- namics. Five theorems are rigorously proved, ensuring the boundedness, stability, and convergence of temperature and efficiency, thereby validating the physical fea- sibility of the model. Numerical simulations, performed using the Runge-Kutta 4th-order method, illustrate the nonlinear decay of hydrogen and oxygen concen- trations, the initial rapid temperature rise followed by stabilization, and the conver- gence of energy conversion efficiency to a steady-state value. The impact of initial hydrogen concentration on efficiency is also examined, providing actionable insights for system optimization. The combination of theoretical analysis and numerical val- idation bridges the fields of physics and mathematics, offering a robust framework for designing high-efficiency hydrogen-based energy systems. The results are rele- vant for both fundamental research and practical applications in sustainable energy technologies.

Keywords : Hydrogen Combustion, Mathematical Modeling, Energy Conversion, Differential Equations, Thermodynamic Efficiency.

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