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Matteo Cantiello edited Convective Efficiency.tex
over 9 years ago
Commit id: b0f422f568bfa040a731fd396120c237eb288f9a
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\end{equation}
with $\Delta T $ the temperature difference between the center of the turbulent element and the surrounding matter averaged over its lifetime. Given the area $A$ of the element and its lifetime $\lambda/\bar{v}$ the total radiated energy is
\begin{equation}
E_{rad} = -\frac{4ac}{3}\frac{T^3}{\kappa \rho}\frac{\Delta T}{\lambda/2} \frac{\lambda
A}{\bar{v}} A}{\bar{v}}.
\end{equation}
The energy excess content carried by the convective element before dissolving is $\cp \rho \Delta T^{*} V$ with $\Delta T^{*}$ here being the temperature excess of the element over its surroundings at the end of its path. Obviously $\Delta T^{*} \simeq \Delta T$, and in the classic B\{"}ohm-Vitense work the choice $\Delta T^{*} = 2 \Delta T$ is made.