Q$1.$ A tubular packed be reactor is used for the following reaction:

$A(g)+2B(g)C(g)+\frac{1}{2}D(g)r_A=-k{C}_A{C}_B^{1\mathrm{.}5}$

The reactor is fed at $190C$ at a pressure of $\frac{8}{b}ar.$ The volumetric flowrate into the reactor is

$300\frac{L}{s}$ and the mole fractions of A and $B$ are $0\mathrm{.}3$ and $0\mathrm{.}7,$ respectively. The reactor is cooled

by water on the shell side boiling at $200C.$ The tube radius is $5cm$ and the overall heat

transfer coefficient is $50\frac{W}{m^2}.K.$

Arrhenius parameters: $A=1200\frac{m^{4\mathrm{.}5}}{m}o{l}^{1\mathrm{.}5}.s,E=70k\frac{J}{m}ol$

Heat of reaction: ${}_{r}H(25C)=-35k\frac{J}{m}ol$

Ideal gas heat capacity data $(T$ is in $K)$:

a$)$ Derive two ODEs that can be used to determine conversion and temperature versus reactor

volume. Also derive the equations that need to be evaluated as part of the ODEs. These

equations should match your code$/$spreadsheet used in the next sections.

b$)$ Plot temperature and conversion of A vs volume up to $6m^3.$ What is the final conversion?

What is the maximum temperature, in $C,$ reached in the reactor? Solve your ODEs

numerically. Attach our code$/$spreadsheet used for the integration and plotting.

c$)$ Repeat b$)$ with a tube radius of $2\mathrm{.}5cm.$ Plot temperature and conversion of A vs volume up

to $6m^3.$ What is the final conversion? What is the maximum temperature reached in the

reactor? No need to re$-$attach your code$/$spreadsheet$.$ It will be assumed that it is the same

as part b$)$ with the tube radius changed.

d$)$ Does the difference between b$)$ and c$)$ make sense? Why might c$)$ be preferred over b$)?$

Explain in a few sentences.

e$)$ If the profile in part c$)$ is preferred, how many tubes are required so the maximum fluid

velocity is $0\mathrm{.}5\frac{m}{s}?$ How long are the tubes? What is the total heat transfer area?