Comparative Analysis of the Finite-Difference Method of Finite Elements in Heat Conduction Modeling

In this paper, heat transfer equations describing heat propagation processes in solids, liquids, and gases are considered. The physical nature of heat conduction, the fundamental laws governing heat transfer, and their mathematical description are investigated. Particular attention is paid to the derivation of the heat conduction equation, the formulation of initial and boundary conditions, and the methods for solving the corresponding problems. Practical applications of heat transfer equations in physics, engineering, and technical calculations are also discussed. The obtained results can be used for the modeling of thermal processes and the analysis of temperature distribution in various media.