Fourier’s law of heat conduction. The basic relation for conductive heat transport is Fourier’s law, which states that the heat flux q, or the flow of heat per unit area per unit time, at a point in a medium is directly proportional to the temperature gradient at the point. In one dimension, Fourier’s law takes the form
where K is the coefficient of thermal conductivity and z is the spatial coordinate. The minus sign appears because heat flows in the direction of decreasing temperature.
The temperature gradient in the continental crust is much higher than in the mantle because radioactive elements are more concentrated in the crust. The result is a gradient of ~25 K/km near the surface, steepening with depth.
The geotherm is not constant but depends on heat-producing elements, conductivity, and convection. A sketch for the entire Earth by P. Wyllie is shown below.
