Diffusion with a homogeneous chemical reaction

Input(s)

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

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

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

c: Total Molar Concentration (mol/ft3)\left(\mathrm{mol} / \mathrm{ft}^{3}\right)

Output(s)

\emptyset: Thiele Modulus (dimensionless)

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

Formula(s)

=(k( L2)DAB)0.5 N=(cDABL)tanh(π)\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.


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