page_title: Heat flux
section_title: Multi-dimensional extension
hierarchical_section_title: Heat flux / Fourier's law / Multi-dimensional extension
caption_attribution_description: English: Diagram depicting heat flux through a thermal insulation material with thermal conductivity, k, and thickness, x. Heat flux can be directly measured using a single heat flux sensor placed on either surface or embedded within the material. Using this method, k and x of the material are not required.
context_page_description: Heat flux or thermal flux, sometimes also referred to as heat flux density, heat-flow 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. 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, the subscript q specifying heat flux, as opposed to mass or momentum flux. Fourier's law is an important application of these concepts.
context_section_description: The multi-dimensional case is similar, the heat flux goes "down" and hence the temperature gradient has the negative sign:
  where  is the gradient operator.
caption: Diagram depicting heat flux through a thermal insulation material with thermal conductivity, k, and thickness, x. Heat flux can be directly measured using a single heat flux sensor located on either surface or embedded within the material. Using this method, knowing the values of k and x of the material are not required.
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