Mathematical Analysis of Hydrogen Combustion and Energy Conversion Efficiency

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.