Given the following process streams that should be heat integrated as much as possible.

Stream Stream Supply Target $m*Cp$

No$.$ Type Temp. $(C)$ Temp. $(C)(k\frac{W}{}C)$

It is assumed that $Tmin=10C$ gives a reasonable trade$-$off between capital cost $($heat exchangers$)$ and operating cost $($energy in the form of external heating and cooling$).$ It

is further assumed that steam is available at $200C$ while cooling water is available at $10C$

a$)$ Show for example by using the so$-$called Heat Cascade that the following is true for this heat recovery problem:

Minimum external heating: $QH,$min$=20kW$

Minimum external cooling: $QC,$min$=60kW$

Pinch temperature $($hot $/$ cold$)$: Tpinch $=90\frac{C}{80}C$

b$)$ What is the minimum number of heat exchangers $($Umin$)$ for this problem when we aim for some heat recovery, and what is the minimum number of units $($Umin$,$ MER$)$

which is compatible with minimum energy consumption $($i$.$e$.$ maximum heat recovery$)?$

Task $2$: Heat Exchanger Network using the Pinch Design Method

As a follow up of Task $1($above$)$ a so$-$called Maximum Energy Recovery $("$MER$")$ Heat Exchanger Network should be designed using the Pinch Design Method. Check whether

the network achieves the established Performance Targets from Task $1$ for energy and the number of units, and explain the reason for any cifferences.

Task $3$: If Umin is lower than Umin $($MER$)$ re$-$adjust your design using the energy relaxation method to allow the reduction of heat exchanger units.