The equivalent thermal resistance of a heat exchanger is defined based on the concept of the entransy dissipation rate, which measures the irreversibility of heat transfer for the purpose of object heating or cooling, rather than from the heat to work conversion. The relationships between the heat exchanger effectiveness and the thermal resistance (or conductance) are developed, which do not depend on its flow arrangement, and hence useful for the performance comparison among heat exchangers with different flow arrangements. In addition, such relationships bridge a gap between the heat exchanger irreversibility and its effectiveness. The monotonic decrease of the effectiveness with increasing the thermal resistance shows that the heat exchanger irreversibility can be described by its thermal resistance when evaluated from the transport process viewpoint, while the so-called entropy generation paradox occurs, if the irreversibility is measured by the entropy generation number for a heat exchanger. (C) 2010 Elsevier Ltd. All rights reserved.