Two continuously stirred tanks are connected in series as shown in the figure. Each tank

has constant volume $V=3m^3,$ and constant volumetric flow rate $Q=2\frac{m^3}{h}r.$ Initially

the concentration of the tracer in each tank as well as the tracer concentration in the feed

stream to the first tank is $C_0=1$kmo$\frac{l}{m^3}.$

Feed stream

At $t=0h,$ the tracer concentration in the feed stream is dropped to zero. Then, find the tracer

concentration in each tank $C_1$ and $C_2$ as a function of time using $(1)$ Euler, and $(2)4$th order

Runge$-$Kutta by writing a MATLAB code.

Use different values for the time step $h$ as$,$

a$)3hr,2hr$ and $0\mathrm{.}5hr,$

b$)$ For all time steps, plot $C$ versus $t$ for both tanks on the same graph, then discuss

your results for different values of time step.

c$)$ For all findings, do error analysis by comparing your calculations with the

analytical results given as

$C_1(t)=C_0{e}^{-\frac{Q}{V}t},$ and $C_2(t)=e^{-\frac{Q}{V}t}[\frac{Q}{V}{C}_{0}t+C_0]$

Please include your MATLAB code, and plots in your submitted assignment.