\documentclass{article}
\title{Formulario Segundo Parcial \\ Fenomenos de transporte 3}
\author{OR}
\date{\today}
\begin{document}
\maketitle
Para pared plana semiinfinita en terminos masicos
\begin{equation}
\frac{\rho _A - \rho _{A,O}}{\rho _{A,S}-\rho _{A,0}} = 1-erf\left( \frac{x}{2\sqrt[]{D_{AB}t}} \right)
\end{equation}
Derivada de la funcion error
\begin{equation}
\frac{d}{dx}(erf(n)) = \frac{2}{\sqrt[]{\pi}}\exp{(-n^2)}\frac{dn}{dx} \cdots \cdots \cdots n=\frac{x}{2\sqrt[]{D_{AB}t}}
\end{equation}
Para pared plana y $Fo\geq 0.2$
\begin{equation}
C^* = C_1 \exp(-\zeta ^2 Fo)\cos (\zeta x^*)
\end{equation}
Para pared cilindrica
\begin{equation}
C^* = C_1 \exp(-\zeta ^2 Fo)J_o (\zeta r^*)
\end{equation}
Para pared esferica
\begin{equation}
C^* = C_1 \exp(-\zeta ^2 Fo)\frac{1}{\zeta r^*} sen(\zeta r^*)
\end{equation}
Adimencionalizacion
\begin{equation}
C^* = \frac{C-C_\infty}{C_i-C_\infty} \cdots r^* = \frac{r}{r_0} \cdots x^*=\frac{x}{x_o}
\end{equation}
Numeros adimencionales
\begin{equation}
Fo = \frac{D_{AB}t}{L_0^2}
\end{equation}
\begin{equation}
Bi = \frac{K_{C}L}{D_{AB}}
\end{equation}
Para placa plana
\begin{equation}
C^*=\frac{C_A-C_{A_o}}{C_{A,S}-C_{A_o}}=erfc(\frac{x}{2\sqrt[]{D_{AB}t}})
\end{equation}
Densidad de flujo local en $x=0$
\begin{equation}
\left[ N_A\right] _{x=0} = \sqrt[]{\frac{D_{AB}}{t}}
\end{equation}
\end{document}
