text: 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 heat flux density is the amount of energy that flows through a unit area per unit time.
  where (including the SI units)
  *  is the local heat flux density, W/m,
  *  is the material's conductivity, W/(m·K),
  *  is the temperature gradient, K/m.
  The thermal conductivity  is often treated as a constant, though this is not always true. While the thermal conductivity of a material generally varies with temperature, the variation can be small over a significant range of temperatures for some common materials. In anisotropic materials, the thermal conductivity typically varies with orientation; in this case  is represented by a second-order tensor. In non-uniform materials,  varies with spatial location.
  For many simple applications, Fourier's law is used in its one-dimensional form, for example, in the  direction:
  In an isotropic medium, Fourier's law leads to heat equation
  with a fundamental solution famously known as heat kernel.