A CSTR is a common piece of processing equipment. In this application, consider the

modelling of a CSTR for startup and control purposes. In this case, there is a cascade of three

jacketed CSTRs in series with cooling provided in either a co$-$current or counter$-$current

direction. The cascade is shown in Fig. $3$ and indicates a countercurrent flow situation.

Because of the physico$-$chemical nature of this system, multiple steady states can occur

due to the balance between cooling and heating in each reactor. This directly affects the

performance of the reactors. In one case, low temperature in both reactor and cooling

systems leads to low conversions of around $20\%.$ In contrast, the high temperature scenario

leads to conversions around $99\%.$ Other intermediate states are also possible in this system.

All the data are included: Figure $3$: Cascade of continuous

stirred reactors.

Data on the problem are as follows:

The reaction is first$-$order exothermic, $AB,$ with $r=k{C}_A,$ and $k=$

$k_0{e}^{-\frac{E}{RT}},k_0=2000s^{-1}.$

Heat transfer area per reactor, $A_H=0\mathrm{.}09m^2.$

Reactor volume, $V_i=0\mathrm{.}8m^3,$ cooling jacket volume, $V_{C_i}=0\mathrm{.}1m^3.$

Heat capacity of mixture, $C_P=0\mathrm{.}565k\frac{J}{k}gK,$ heat capacity of coolant, $C_{PC}=$

$4\mathrm{.}1868k\frac{J}{k}gK.$

Density of mixture, $=850k\frac{g}{m^3},$ density of coolant, ${}_C=1000k\frac{g}{m^3}$

Feed flowrate, $F=0\mathrm{.}0025\frac{m^3}{s},$ coolant flowrate, $F_C=0\mathrm{.}002\frac{m^3}{s}.$

Overall heat transfer coefficient, $U=167\mathrm{.}5\frac{W}{m^2}K.$

Initial feed concentration, $C_0=0\mathrm{.}6$kgmo$\frac{l}{m^3}.$

Heat of reaction, $H_R=146,538k\frac{J}{k}g$ mol.

Activation energy, $E=42,287k\frac{J}{k}$gmol.

Gas constant, $R=8\mathrm{.}314k\frac{J}{k}$gmol$*K.$

$1.$ State all modelling assumptions and indicate balance boundaries.

$2.$ Develop the mathematical model with mass and energy balance. explain the development states.

$3.$ Develop a steady state model in matlab.