Heat density

Heat flux or thermal flux, sometimes also referred to as heat flux density or heat flow rate intensity is a flow of energy per unit of area per unit of time. In SI its units are watts per square metre (W⋅m⁻²). It has both a direction and a magnitude, and so it is a vector quantity. To define the heat flux at a certain point in space, one takes the limiting case where the size of the surface becomes infinitesimally small.

Heat flux is often denoted ${\displaystyle {\overrightarrow {\phi _{\text{q}}}}}$, the subscript q specifying heat flux, as opposed to mass or momentum flux. Fourier's law is an important application of these concepts.

For most solids in usual conditions, heat is transported mainly by conduction and the heat flux is adequately described by Fourier's law.

The heat flux associated with a temperature profile ${\displaystyle T(x)}$ in a material of thermal conductivity ${\displaystyle k}$ is given by

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