The performance of multi-element thermoelectric-generators, assuming heat-transfer irreversibilities which obey the linear phenomenological heat-transfer law Q proportional to (Delta T-1), is studied in this paper by combining finite-time thermodynamics with non-equilibrium thermodynamics. The performance characteristics of the output power, efficiency and working electrical-current are described by numerical examples. (c) 2004 Elsevier Ltd. All rights reserved.