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Matteo Cantiello edited MLT.tex
over 9 years ago
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In the ``Mixing Length Theory'' of convection it is assumed that an element of fluid rises in pressure equilibrium and retains its identity while it moves through a distance $\Delta r$, after which it mixes with its surroundings, releasing its excess heat energy. The distance $\Delta r$ is called mixing length and is usually denoted as $\lambda$.
The heat transferred by upward moving elements can then be quantified as:
\begin{equation}
F_{c} = \frac{1}{2} \rho
v \bar{v} c_{cp} \lambda \Delta \nabla T ,
\end{equation}
where the factor 1/2 comes from the fact that at each level approximately one-half of the matter is rising and one-half is descending. Here $\rho$, $\bar{v}$ and $c_p$ are averages along the distance $\lambda$ of density, velocity and specific heat at constant pressure of upward and downward moving fluid elements.