Modelling heat exchangers for thermoelectric generators J. Esarte a,* , G. Min b , D.M. Rowe b a Depto. Ingenieria Mecanica, Energetica y Materiales (edi®cio los Pinos), Universidad Publica de Navarra, Campus Arrosadia s/n, 31006 Pamplona, Spain b School of Engineering, University of Wales Cardiff, Wales, UK Received 13 April 2000; received in revised form 25 July 2000; accepted 29 July 2000 Abstract In order to further studies on thermoelectric generators, an analysis of the in¯uence of ¯uid ¯ow rate, heat exchanger geometry, ¯uid properties and inlet temperatures on the power supplied by the thermoelectric generator has been done. Different expressions and graphs showing this in¯uence are shown in this paper, in order to give some practical guidelines for the thermoelectric generators design. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Thermoelectric generators 1. Introduction The thermoelectric power generator, as shown in Fig. 1, consists of a Peltier module sandwiched between two heat exchangers, hot and cold that create a temperature distribu- tion through the module ``t 1 t 2 ''. By virtue of this temperature difference (Dt  t 1  t 2 ) the module supplies electrical power (W), this phenomenon is known as Peltier effect. Although, a lot of work has been done in this area, traditionally efforts have mainly been focused on the improvement of the thermoelectric properties of the materials and new techniques and guidelines for optimising the Peltier module geometry [1,2] in terms of a higher power output but always with Dt supposedly known. However, little attention has been paid on how the tempera- ture difference Dt is obtained and what parameters affect it. Thus, when a new thermoelectric generator design is planned, it is found that a tedious work to determine Dt has to be done. In order to facilitate this task, an easy and compact expression for Dt is given in this paper. This study would remain incomplete, if the power con- sumed by the pump driving the ¯uid through the circuit and the thermoelectric generator was not considered. The pump consumption is proportional to the pressure drop through the circuit in which the pressure drop in the generator DP is included. So, the higher the pressure drop, the bigger the pump consumption. Since the bare power is de®ned as the total power supplied by the thermoelectric generator minus the pump consumption, the design parameters will be those that provide the most appropriate pair of values for Dt and DP (maximum and minimum, if possible, respectively). This work is intended to give some guidelines for deter- mining the optimum operating parameters of thermoelectric generator. 2. Analytical expression Consider the basic thermoelectric generator, shown in the Fig. 1. The cold water (hot water) enters the cold exchanger (hot exchanger) at a temperature t ci (t hi ) and exits at a temperature t co (t ho ). As a result of this temperature difference between the cold and hot sinks put in contact each other through the Peltier module, a heat ¯ux appears. The heat transfer mechanism, here present is the so called conduction. Conduction is the heat transfer inside the bodies or from one body to another in physical contact with it. It takes place at the molecular level and involves the transfer of energy from the more energetic molecules (higher temperature regions) to those with a lower energy level (lower temperature regions). At macroscopic level the heat ¯ux (q) is proportional to the temperature gradient reached inside the body and it is given by q k dT dn (1) Journal of Power Sources 93 (2001) 72±76 * Corresponding author. Tel.: 34-948-169295; fax: 34-948-169099. E-mail address: jesus.esarte@unavarra.es (J. Esarte). 0378-7753/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII:S0378-7753(00)00566-8