DIFFERENTIAL DIFFUSION EQUATIONS AND HEAT CONDUCTION: THEIR IMPORTANCE FOR MODERN TECHNOLOGICAL PROCESSES

Аннотация

Abstract: This article explores the significance of diffusion equations and heat conduction in modern technological processes. Diffusion, the process where particles move from a region of higher concentration to a lower one, and heat conduction, the transfer of thermal energy within materials, are described using differential equations. These processes are critical in fields such as nanotechnology, 3D printing, and energy storage systems. Mathematical models like Fick's Law for diffusion and Fourier's Law for heat conduction are used to optimize performance and efficiency in these areas. Additionally, numerical methods, such as Runge-Kutta and finite element methods, are employed to solve these equations and enhance technological innovations. The article demonstrates the growing importance of understanding and applying these equations for sustainable and efficient advancements in technology.