It is proposed to improve the energy utilisation of a steel works by transferring the heat from the gases leaving the blast furnace at \(600{ }^{\circ} \mathrm{C}\) to those entering the furnace at \(50{ }^{\circ} \mathrm{C}\) (before the heat exchanger is fitted). The minimum temperature of the flue gases is limited to \(150{ }^{\circ} \mathrm{C}\) to avoid condensation of sulfurous acid in the pipework at exit pressure of \(1 \mathrm{bar}\).

Draw a simple schematic diagram of the heat exchanger you would design, showing the hot and cold gas streams. Explain with the aid of \(T-s\) diagrams, why a counterflow heat exchanger is the most efficient. If the minimum temperature difference between the hot and cold streams is \(10^{\circ} \mathrm{C}\), calculate the minimum loss of exergy for both types of heat exchanger, based on deadstate conditions of 1 bar and \(20^{\circ} \mathrm{C}\).

\([-72.33 \mathrm{~kJ} / \mathrm{kg} ;-45.09 \mathrm{~kJ} / \mathrm{kg}]\)