The influences of recycle at the ends on multi-pass coolers or heaters through a parallel-plate channel with constant wall temperature are studied and an exact solution of this problem is presented using an orthogonal expansion technique. Analytical results show that the external refluxes can enhance the heat transfer efficiency due to the desirable convective effect having more influence than the undesirable preheating effect for all Graetz numbers, leading to considerably improved device performance in heat transfer. The results are represented graphically and compared with the heat transfer efficiency by the adjustment of channel thickness ratio in a single-pass operation (without inserting impermeable sheets). The suitable selections of the design and operating parameters on considering of both the heat transfer improvement and power consumption increment are also discussed. (C) 2003 Elsevier Ltd. All rights reserved.