The effects of recycle at the ends on the heat transfer through a concentric circular tube with uniform wall fluxes are studied analytically by an orthogonal expansion technique with eigenfunction power series expansion. The heat transfer problem is solved for fully developed laminar velocity profiles in a double-pass circular heat exchanger with ignoring axial conduction and fluid properties of temperature independence. Analytical results show the external recycle can enhance the heat transfer efficiency compared with that in an open tube (without an impermeable circular tube inserted and without recycle). The compensation between the forced-convection increment and heat-transfer driving force decrement are used to study the heat transfer behavior. The effects of the impermeable-tube location on heat transfer efficiency enhancement as well as the power consumption increment have been also discussed. (c) 2006 Elsevier Ltd. All rights reserved.