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Merge pull request #15135 from rmcdermo/master
FDS Tech Guide: fix equation reference in appendix
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Manuals/FDS_Technical_Reference_Guide/Appendices.tex

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@@ -1015,7 +1015,7 @@ \subsection{Analytical Jacobian formulation}
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\subsection*{Calculation of $\frac{\partial \boldsymbol{\dot{\hat{C}}_A}}{\mathbf{\partial \hat{C}}}$}
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Here, $\dot{\hat{C}}_{k,A} = \dot{\omega}_{k}$.
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By taking derivative of Eq.~(\ref{eq:chemistry_ode_system_appendix}) with respect to concentration, we can write:
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By taking derivative of Eq.~(\ref{eq:chemistry_ode_system}) with respect to concentration, we can write:
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\begin{align}\label{eq:JacCAC}
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\frac{\partial \dot{\omega}_k}{\partial \hat{C}_{l}} &= \sum_{i=1}^{N_{reac}} \left[ \nu_{ki} \ r_i \ \frac{\partial b_i}{\partial \hat{C}_{l}} + b_i \nu_{ki} \ \left( k_{f,i} \nu_{li}^{'} \ \frac{\prod_{j=1}^{N_{\rm s}} (\hat{C}_j)^{{\nu}_{ji}^{'}} }{\hat{C}_{l}} - k_{r,i} \ \nu_{li}^{''} \ \frac{\prod_{j=1}^{N_{\rm s}} (\hat{C}_j)^{{\nu}_{ji}^{''}} }{\hat{C}_{l}} \right) \right],
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\end{align}

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