The differential form of Fourier 's Law of thermal conduction shows that the local heat flux density , , is equal to the product of thermal conductivity , , and the negative local temperature gradient , .
The law of heat conduction , also known as Fourier 's law , means that the rate , in time , 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 : where Q is the amount of heat transferred , t is the time taken , k is the material 's conductivity .