per minute. Assuming

Euat the solution is stirred constaritly, how much alcohol will be in the tank after $10$ minutes?

$[12$ Marka$]$

Quchilen $2$ i

$A{E}_4,r_4=-4c_4$

Page $|3|$

fiffusion along the $z-$axis is controlled by a Fickian$-$like expression, so that in parallel with transport by convection due to the superficial velocity of the feed $v_0,($that is $A_n{v}_a{C}_A)$ there is also a diffusion$-$like flux given by the Fickian relation:

$J_A=-d_E\frac{d{C}_A}{dz},(\frac{\text{m}\text{o}\text{l}\text{e}\text{s}}{\text{A}\text{r}\text{e}\text{a}\text{t}\text{i}\text{m}\text{e}})$

acting along the longitudinal axis $($z$-$coordinate$).$

i$.$ Perform a Mass Balance for the reactant A under steady state conditions on an element $($AZ$)$ on the tube with constant cross$-$sectional area, $A_n,$ and obtain a second order ODE for $C_a(z).$

$[15$ Marks$].$

it$.$ Solve this problem $($Find $C_A(z)$ with all constants of integration$)$ with the boundary conditions.

$atZ=L,\frac{d{C}_A}{dZ}=0$ and $atZ=0,C_A=C_{A0}$