Derive a mechanistic model for the system stated. Atkimsoe Chemicals Company has a process tank system shown in Figure $1.$ The requirement for this

syatem is to ensuse that the tempersture of the exit liquid is cooled down to the required tempor ature

before transferring to downstream processes. Curreurly, a controller is used to maintain the lisquid level in

the tank and this sllowr the plent operntors to focus ces maintsining the tempernture of the exit liguid by

changing the inlet flow rate of cooling water to the jacket. Occasionally, the operators will check on the

changra. Borh the foed flow rate and cooling whter temperature, on the other hand, enn be asmmed to

be constant.

The sollowing were scers infornstice with regands to the procose sposter$-$

respectively sad $T_{\text{;}}$abd $T_{**}^{**}$ as as the letrgerarese $($in $"$C$)$ of codirg wener in and out af the jadiet,

remectively

$E_0$ and $b_7$ an coriling water domx $($in $y)$ in and out of the jaclat, rexpoctively.

c$.$ At asy point of operation, the entive jacket is filled with ocoling uster.

volurae $$ appocaimutaly $3\mathrm{.}1m^3.$

e$.$ The bout coperitios $($in $\frac{k}{kg})$ of liquid and comlar, wher wen npproxiansely $401$ and $1\mathrm{.}21,$ reapec$-$

tivaly.

solowing relationship:

$Q=k,A_2{F}_z^Q(x_{**}^{+}-T_{**}^{**})$

lewt trasker arcs letween the tani ned the coolar. joslet.

etimaved deley of $25$ nirs in $T_p,$ end $20$ mirs in $T_e.$

A sirulater of the process tank system in Motlas Siaslink will be given as an atruchoerk to help

$T=sin.$