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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.
For heat flow, the heat equation follows from the physical laws of conduction of heat and conservation of energy (Cannon 1984). By Fourier's law for an isotropic medium, the rate of flow of heat energy per unit area through a surface is proportional to the negative temperature gradient across it: =
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 . However, the tensorial description only becomes necessary in materials which are anisotropic .
In the study of heat conduction, the Fourier number, is the ratio of time, , to a characteristic time scale for heat diffusion, . This dimensionless group is named in honor of J.B.J. Fourier , who formulated the modern understanding of heat conduction. [ 1 ]
The equation of heat flow is given by Fourier's law of heat conduction. Rate of heat flow = - (heat transfer coefficient) * (area of the body) * (variation of the temperature) / (length of the material) The formula for the rate of heat flow is: = where is the net heat (energy) transfer,
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 ...
Thermal conductivity is the property of a material to conduct heat and is evaluated primarily in terms of Fourier's law for heat conduction. Convection The transfer of energy between an object and its environment, due to fluid motion. The average temperature is a reference for evaluating properties related to convective heat transfer. Radiation
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.