Diffusion with a homogeneous chemical reaction

Input(s)

$\mathrm{k}$: Rate Constant $(\mathrm{mol} \mathrm{cm} / \mathrm{s})$

L: Length $(\mathrm{cm})$

$\boldsymbol{D}_{\boldsymbol{A} \boldsymbol{B}}$: Diffusivity $(\mathrm{cm} \mathrm{cm} / \mathrm{s})$

c: Total Molar Concentration $\left(\mathrm{mol} / \mathrm{ft}^{3}\right)$

Output(s)

$\emptyset$: Thiele Modulus (dimensionless)

$\mathrm{N}$: Molar Flux $\left(\mathrm{mol} \mathrm{L/ \textrm {cm } ^ { 2 } )}\right.$

Formula(s)

$$ \begin{gathered} \varnothing=\left(\frac{\mathrm{k} *\left(\mathrm{~L}^{2}\right)}{\mathrm{D}_{\mathrm{AB}}}\right)^{0.5} \\ \mathrm{~N}=\left(\frac{\mathrm{c} * \mathrm{D}_{\mathrm{AB}}}{\mathrm{L}}\right) * \varnothing * \tanh (\pi) \end{gathered} $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 18, Page: 555.