A two-dimensional steady-state numerical model is developed to study the heat transfer in a run-around heat recovery system with two exchangers each with a combination of counter and cross (counter/cross) flow between parallel plates or membranes. A finite difference method is used to solve the steady-state equations of continuity, momentum and heat transfer. The simulated values for the effectiveness of each counter/cross flow heat exchanger and the overall run-around system are used to develop effectiveness correlations which agree within +/-2% of the simulated effectiveness of individual heat exchangers and overall system. It is shown that the effectiveness of this new run-around heat exchanger (RAHE) falls between the effectiveness of similar run-around systems with either two cross-flow exchangers or two counter-flow exchangers. For a given total surface area of the exchangers, the highest overall sensible effectiveness is achieved with exchangers which have a small exchanger aspect ratio and relatively small solution flow inlet and outlet lengths. (C) 2009 Elsevier Ltd. All rights reserved.