A process plant has two streams of hot fluid and two streams of cold fluid, as defined in Table P19.1. It is required to minimise the energy which must be transferred to hot and cold utilities by transferring energy between the streams. If the minimum temperature difference for effective heat transfer is \(20^{\circ} \mathrm{C}\), design a network which achieves the requirement, and minimises the transfers to the utilities. Is there a pinch point in this problem, and at what temperature does it occur? Calculate the minimum heat transfers to and from the cold and hot utilities.

\(\left[105^{\circ} \mathrm{C}\right.\) (cold stream); \(\left.Q_{\mathrm{H}_{\text {min }}}=90 \mathrm{MJ} / \mathrm{h} ; Q_{\mathrm{C}_{\text {min }}}=140 \mathrm{MJ} / \mathrm{h}\right]\)

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Table P19.1 Data Related to P19.1 Stream No Stream Type Supply Temperature Ts/(C) Target Temperature TT/(C) Heat Flow Capacity 1 Hot 205 65 mC/(MJ/hK) 2.0 234 Hot 175 75 4.0 Cold 45 180 3.0 Cold 105 155 4.5