A first$-$order chemical reaction occurs in a tubular $($cylindrical$)$ plug$-$flow reactor. You are

interested in modeling the steady$-$state concentration of reactant $A$ as a function of $r$ and $z$ in

this reactor. You may assume that flow is laminar and as a result the velocity profile is:

$v_z=v_{\text{m}\text{a}\text{x}}(1-(\frac{r}{R}{)}^2)$

where $v_{\text{m}\text{a}\text{x}}$ is the velocity at the center line and $R$ is the internal radius of the tube.

a$)[$ChE$312$ Assignment$]$ Write the simplified continuity equation describing this system in

terms of the flux of $A$ in the $r-$ and $z-$ direction. Clearly state all assumptions.

b$)[$ChE$312$ Assignment$]$ Simplify Fick's rate equation to determine an equation for the flux of

$A$ in the $r-$ and $z-$ direction. Clearly state all assumptions.

c$)[$ChE$312$ Assignment$]$ Write the continuity equation in terms of the concentration of $A,c_A.$