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Matteo Cantiello edited MLT.tex
over 9 years ago
Commit id: b4087269bb4b74b7fd4dcbc56f21a64bfe29f27b
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F_{c} = \frac{1}{2} \rho \bar{v}\, \cp \, \lambda \bigg[ \frac{\D \T'}{\D r}-\frac{\D \T}{\D r}\bigg] ,
\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 $\cp$ are averages along the distance $\lambda$ of density, velocity and specific heat at constant pressure of upward and downward moving fluid elements.
Using
the equation~\ref{eq:deltat} we can write
\begin{equation}
F_{c} = \frac{1}{2} \rho \bar{v}\, \cp \,
\lambda \bigg[ \frac{\D \T'}{\D r}-\frac{\D \T}{\D r}\bigg] T \frac{\lambda}{\hp} ( \nabla - \nabla') ,
\end{equation}