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The defining equation for thermal conductivity is =, where is the heat flux, is the thermal conductivity, and is the temperature gradient. This is known as Fourier's law for heat conduction. Although commonly expressed as a scalar , the most general form of thermal conductivity is a second-rank tensor .
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.
is the thermal diffusivity, a material-specific quantity depending on the thermal conductivity, the specific heat capacity, and the mass density. The heat equation is a consequence of Fourier's law of conduction (see heat conduction ).
The equation of heat flow is given by Fourier's law of heat conduction. ... the proportionality constant, is the thermal conductivity of the material. [2] ...
A 2008 review paper written by Philips researcher Clemens J. M. Lasance notes that: "Although there is an analogy between heat flow by conduction (Fourier's law) and the flow of an electric current (Ohm’s law), the corresponding physical properties of thermal conductivity and electrical conductivity conspire to make the behavior of heat flow ...
Heat conduction in a Newtonian context is modelled by the Fourier equation, [4] namely a parabolic partial differential equation of the kind: = , where θ is temperature, [5] t is time, α = k/(ρ c) is thermal diffusivity, k is thermal conductivity, ρ is density, and c is specific heat capacity.
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.
When stated in terms of temperature differences, Newton's law (with several further simplifying assumptions, such as a low Biot number and a temperature-independent heat capacity) results in a simple differential equation expressing temperature-difference as a function of time. The solution to that equation describes an exponential decrease of ...