deletions | additions       diff --git a/Convective Efficiency.tex b/Convective Efficiency.tex  index 2f09846..51af55d 100644  --- a/Convective Efficiency.tex  +++ b/Convective Efficiency.tex 
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where we used the fact that $V/A=\lambda/6$ for a sphere of diameter $\lambda$. Note how $\Gamma$ is related to the Peclet number $\rm{Pe}$, which is defined as the ratio between the thermal and the dynamical timescales. The next step is substituting the calculated average velocity from \ref{eq:velocity} to obtain  \begin{equation}\label{eq:gamma}  \Gamma = \frac{\cp}{12\sqrt{2} a c}\frac{\kappa g Q^{1/2} \rho^{5/2} \lambda^2}{\P^{1/2} T^3}(\nabla - \nabla')^{1/2} = \mathscr{A} \, (\nabla - \nabla')^{1/2}  \end{equation} where $\mathsc{A} \equiv \frac{Q^{1/2} \cp ]kappa g \rho^{5/2} \lambda^2}{12\sqrt{2}ac\P{1/2}T^3}$ is essentially the ratio of the convective to the radiative conductivities.