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Continuity equation
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== Energy and heat == [[Conservation of energy]] says that energy cannot be created or destroyed. (See [[#General relativity|below]] for the nuances associated with general relativity.) Therefore, there is a continuity equation for energy flow: <math display="block">\frac{ \partial u}{\partial t} + \nabla \cdot \mathbf{q} = 0</math> where * {{math|''u''}}, local [[energy density]] (energy per unit volume), * {{math|'''q'''}}, [[energy flux]] (transfer of energy per unit cross-sectional area per unit time) as a vector, An important practical example is [[Heat transfer|the flow of heat]]. When heat flows inside a solid, the continuity equation can be combined with [[Thermal conduction#Fourier's law|Fourier's law]] (heat flux is proportional to temperature gradient) to arrive at the [[heat equation]]. The equation of heat flow may also have source terms: Although ''energy'' cannot be created or destroyed, ''heat'' can be created from other types of energy, for example via [[friction]] or [[joule heating]].
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