Q$.1.$ The source and target temperatures of cold and hot streams involved in a heat exchanger network $($HEN$)$ are,

$\backslash$table$[[$Stream$,\backslash$table$[[$Source temperature$],[($T $\{$:$^($s$)$in$\backslash$deg C$)]],\backslash$table$[[$Target temperature$],[\{$:$($T$^($t$)$in$\backslash$deg C$)]],\backslash$table$[[$Flowrate of heat capacity$],[($m$\_($p$)$C$\_($P$)$ in kW$/$K$)]]],[$H$1,250,40,],[$H$2,210,70,-],[$C$1,20,180,-],[$C$2,30,170,-],[$C$3,25,170,-]]$

Design engineers have developed a HEN for an industrial process as shown in Figure $($A$).$ From PDP course, it is clear that the given network is not an optimized design and heat loops must be reduced to minimize the number of heat exchangers.

$($a$)$ Fill the heat capacity values for all streams shown in the table.

$($b$)$ Find heat duties of hot and cold utilities in Fig $($A$).$

$($c$)$ Find the possible minimum number of heat exchangers $($HXs$).$

$($d$)$ Optimize the given HEN that contains minimum number of HXs by using heat loop concept.

Figure $($A$)$ Heat exchange network consisting two hot and three cold streams