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 (eta(parallel to)) was defined and it was expressed as a function of effectiveness (epsilon), 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 eta(parallel to)-epsilon relation can be used to find the eta(parallel to) value of a heat exchanger with any flow arrangement. The eta(parallel to)-Ntu and eta(parallel to)-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. (C) 2010 Elsevier Ltd. All rights reserved.