Second-law performance of heat exchangers for waste heat recovery

Exergy change rate in an ideal gas flow or an incompressible flow can be divided into a thermal exergy change rate and a mechanical exergy loss rate. The mechanical exergy loss rates in the two flows were generalized using a pressure-drop factor. For heat exchangers using in waste heat recovery, the consumed mechanical exergy is usually more valuable than the recovered thermal exergy. A weighing factor was proposed to modify the pressure-drop factor. An exergy recovery index (η_II) was defined and it was expressed as a function of effectiveness (?), ratio of modified heat capacity rates (C^∗), hot stream-to-dead-state temperature ratio, cold stream-to-dead-state temperature ratio and modified overall pressure-drop factor. This η_II–? relation can be used to find the η_II value of a heat exchanger with any flow arrangement. The η_II−Ntu and η_II−Ntu_h relations of cross-flow heat exchanger with both fluids unmixed were established respectively. The former provides a minimum Ntu design principle and the latter provides a minimum Ntu_h design principle. A numerical example showed that, at a fixed heat capacity rate of the hot stream, the heat exchanger size yielded by the minimum Ntu_h principle is smaller than that yielded by the minimum Ntu principle.