Rotating reference frame: Difference between revisions

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m →‎References: Split into two columns using more universal alternative code
→‎Relation between positions in the two frames: Corrected argument of sin's and cos's to be general theta(t), because in the previous notation, Omega has to be a constant in order for the derivatives (du/dt) to be correct. Then the euler force is wrong
 
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{{Unreferenced|date=December 2009}}
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A '''heat current''' is a kinetic exchange rate between [[molecule]]s, relative to the material in which the [[Kinematics|kinesis]] occurs. It is defined as <math>\frac{dQ}{dt}</math>, where <math>Q</math> is [[heat]] and <math>t</math> is [[time]].  
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For [[Conduction (heat)|conduction]], heat current is defined by [[Fourier's law]] as
: <math> \frac{\partial Q}{\partial t} = -k \oint_S{\overrightarrow{\nabla} T \cdot \,\overrightarrow{dS}} </math>
where
:<math>\big. \frac{\partial Q}{\partial t}\big.</math> is the amount of heat transferred per unit time [W] and
:
:<math>\overrightarrow{dS}</math> is an oriented surface area element [m<sup>2</sup>]
The above [[differential equation]], when [[Integral|integrated]] for a homogeneous material of 1-D geometry between two endpoints at constant temperature, gives the heat flow rate as:
: <math> \big. \frac{\Delta Q}{\Delta t} = -k A \frac{\Delta T}{\Delta x} </math>
where
: ''A'' is the cross-sectional surface area,
: <math>\Delta T</math> is the temperature difference between the ends,
: <math>\Delta x</math> is the distance between the ends.
 
For [[thermal radiation]], heat current is defined as
:<math>W = \sigma \cdot A \cdot T^4</math>
where the [[constant of proportionality]] <math>\sigma</math> is the [[Stefan–Boltzmann constant]], <math>A</math> is the radiating surface area, and <math>T</math> is temperature.  
 
Heat current can also be thought of as the total [[phonon]] distribution multiplied by the energy of one phonon, times the [[group velocity]] of the [[phonon]]s. The phonon distribution of a particular phonon mode is given by the [[Bose–Einstein statistics|Bose-Einstein]] factor, which is dependent on temperature and [[phonon]] energy.
 
==See also==
* [[Thermal conduction]]
* [[Thermal conductivity]]
 
{{DEFAULTSORT:Heat Current}}
[[Category:Heat transfer]]
 
 
{{Physics-stub}}
 
[[de:Wärmestrom]]
[[eo:Varmokurento]]

Latest revision as of 22:40, 26 June 2014

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