The second order irreversible $AB$ is carried out in a packed bed reactor. Pure A enters at a

volumetric flowrate of $0\mathrm{.}15\frac{m^3}{m}in$ and the reaction takes place at $460K$ and $380$kPa, with the rate

constant per unit area, $k^{\text{'}\text{'}}$ is given as $3\mathrm{.}82{10}^{-3}\frac{m^4}{m}ol.$s$.$ The pure $A$ is to be passed over a packed

bed of cylindrical particles $0f0\mathrm{.}25cm$ in diameter and $0\mathrm{.}5cm$ length, whereas the bulk density of the

catalyst is $2\mathrm{.}398k\frac{g}{m^3}$ with the void fraction $0.0\mathrm{.}6.$ The dynamic viscosity is given as $1\mathrm{.}246\frac{{10}^{-4}(kg)}{(m)*min}.$

Gas diffusivity $(D_{AB})=8\mathrm{.}08\frac{{10}^{-5}{m}^2}{\text{m}\text{i}\text{n}}.$ Effective diffusivity $(D_e)=4\mathrm{.}177\frac{{10}^{-12}{m}^2}{\text{m}\text{i}\text{n}}.$

Calculate the mass transfer coefficient, $k_c$ by using Thoenes$-$Kramers correlation if the free$-$stream

velocity, $U$ is $9000\frac{m}{m}in.$ Given the equation:

Volume $-$ average particle diameter, $d_p=6(\frac{D^{2}L}{4}{)}^{\frac{1}{3}}$

$Sc=\frac{v}{D_{AB}}$;$v=\frac{}{{}_b}$