Problem $3.$ Assessment of Non$-$isothermal Particle Performance $(20$ points$)$

We plan to run a first order reaction $AR$ in a reactor filled with $6mm$ porous catalyst

pellets $(L={10}^{-3}(m)).$ At a point in the reactor where $C_A=100mo\frac{l}{m^3}$ find

$.$ whether pore and$/$or film diffusion effects are likely to intrude to affect the rate

$.$ whether nonisothermal effects are likely to intrude; in effect, estimate the

temperature at the surface and at the center of catalyst pellets

$.$ the rate of reaction, $-r_A^{\text{'}\text{'}\text{'}}$

the effectiveness factor $$ based on an isothermal particle at $T_g$ free of mass transfer

effects

Thermodynamic tables, physical property and rate measurements reported by the

catalyst manufacturer, and estimated transfer coefficients for the expected operating

conditions are as follows.

$T_g=1000K$

$H_r=10k\frac{J}{m}ol$

$E=167k\frac{J}{m}ol$

$D_{\text{e}\text{f}\text{f}}=1{10}^{-8}\frac{m^2}{s}$

$k_{\text{e}\text{f}\text{f}}=1{10}^{-1}\frac{W}{m}$ catalyst$-K$

$k^{\text{'},}=1{10}^4{m}^3$ fluid $\frac{?}{m^3}$ catalyst$-s$

$h=1{10}^1\frac{W}{m^2}$ catalyst$-K$

$k_g=1{10}^{-1}\frac{m^3}{m^2}$ catalyst$-s$