Heat equation

 Heat is the process through which thermal energy is transferred between bodies.

Hot :

The particles of the bodies are not at rest but are in constant agitation. As a consequence of this agitation, bodies have a certain thermal energy. Temperature is an indicator of the thermal energy that bodies have. In general, we can say that the higher the temperature, the higher the energy of this type. Well, bodies and systems can exchange thermal energy. This exchanged thermal energy is called heat. Sometimes the process of energy transfer itself is also called heat.

Heat equation:

It is an important differential equation in partial derivatives of the parabolic type that describes the distribution of heat (or variations in temperature) in a region over the course of time.

The heat equation is obtained from Fourier's law and the principle of conservation of energy. According to Fourier's law, the rate of change of heat energy flux per unit area through a surface is proportional to the gradient negative surface temperature

Where k is the thermal conductivity and u is the temperature. In one dimension, the

gradient is an ordinary spatial derivative, and so Fourier's law is:

 The heat equation governs the diffusion of heat, that is, it is another diffusion process, such as the diffusion of particles or the propagation of the action potential in neuronal cells. However they are not diffusive in nature, some quantum mechanical problems are also governed by an equation analogous to the equation of heat.

"The deep study of nature is the most fertile source of mathematical discoveries."