Читать книгу An Introduction to the Finite Element Method for Differential Equations - Mohammad Asadzadeh - Страница 25

The heat equation can be used to model the heat flow in solids and fluids, in the latter case, however, it does not take into account the convection phenomenon; and provides a reasonable model only if phenomena such as macroscopic currents in the fluid are not present (or negligible). Further, the heat equation is not a fundamental law of physics, and it does not give reliable answers at very low or very high temperatures.

Since temperature is related to heat, which is a form of energy, the basic idea in deriving the heat equation is to use the law of conservation of energy. Below we derive the general form of the heat equation in arbitrary dimension.