Heat conduction or
thermal conduction is the spontaneous
transfer of thermal energy through matter, from a region of higher
temperature to a region of lower temperature, and acts to equalize temperature differences.
Thermal energy, in the form of continuous random motion of the particles of the matter, is transferred by the same coulomb forces that act to support the structure of matter, so can be said to move by physical contact between the particles.
Heat can also be transferred by radiation and/or convection, and often more than one of these processes occur in a given situation.
The law of heat conduction, also known as Fourier's law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area at right angles, to that gradient, through which the heat is flowing. We can state this law in two equivalent forms the integral form, in which we look at the amount of energy flowing into or out of a body as a whole, and the differential form, in which we look at the flows or fluxes of energy locally.