Heat equation
The
heat equation or
diffusion equation is an important
partial differential equation which describes the temperature in a given region over time. It is:
where:
- is the rate of change of temperature at a point over time
- , , and are the second spatial derivatives (thermal conductions) of temperature in the x, y, and z directions, respectively
- k is a material-specific constant (thermal diffusivity)
Solutions of the heat equation are characterized by a gradual smoothing of the initial temperature distribution by the flow of
heat from warmer to colder areas of an object.
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