This paper shows that the main architectural features of a counterflow heat exchanger can be determined based on thermodynamic optimization subject to volume constraint. It is assumed that the channels are formed by parallel plates, the two fluids are ideal gases, and the flow is fully developed, laminar or turbulent. In the first part of the paper, it is shown that the irreversibility of the heat exchanger core is minimized with respect to (1) the ratio of the two-channel spacings, and (2) the total heat transfer area between the two streams. In the second part, the entropy generation rate also accounts for the irreversibility due to discharging the spent hot stream into the ambient. It is shown that the design can be optimized with respect to (1), (2) and (3) the ratio of the capacity rates of the two streams. The optimized features of the geometry are robust with respect to whether the external discharge irreversibility is included in the entropy generation rate calculation. Copyright (C) 2000 John Wiley & Sons, Ltd.