Effect of heat transfer on the performance of a thermoelectric heat pump driven by a thermoelectric generator Lingen Chen*, Fankai Meng, and Fengrui Sun Postgraduate School, Naval University of Engineering, Wuhan 430033, P.R. China. Recibido el 13 de enero de 2009; aceptado el 9 de junio de 2009 A model of a thermoelectric heat pump driven by a thermoelectric generator with external heat transfer irreversibility is proposed. The performance of the combined thermoelectric heat pump device obeying Newton’s heat transfer law is analyzed using the combination of ﬁnite time thermodynamics and non-equilibrium thermodynamics. Two analytical formulae for heating load versus working electrical current, and the coefﬁcient of performance (COP) versus working electrical current, are derived. For a ﬁxed total heat transfer surface area of four heat exchangers, the allocations of the heat transfer surface area among the four heat exchangers are optimized for maximizing the heating load and the COP of the combined thermoelectric heat pump device. For a ﬁxed total number of thermoelectric elements, the ratio of the number of thermoelectric elements of the generator to the total number of thermoelectric elements is also optimized for maximizing both the heating load and the COP of the combined thermoelectric heat pump device. The inﬂuences of thermoelectric element allocation and heat transfer area allocation are analyzed by detailed numerical examples. The optimum working electrical currents for maximum heating load and maximum COP at different total numbers of thermoelectric elements and different total heat transfer areas are provided, respectively. Keywords: Combined thermoelectric device; thermoelectric generator; thermoelectric heat pump; heat transfer; ﬁnite-time thermodynamics; non-equilibrium thermodynamics. En el presente trabajo se propone un modelo de una bomba de calor termoel´ ctrica controlada por un generador termoel´ ctrico con transe e ferencia de calor externa irreversible. Se analiza el desempe˜ o de la bomba de calor combinada, la cual obedece a la ley de Newton de n transferencia de calor, usando la combinaci´ n de termodin´ mica de tiempo ﬁnito y termodin´ mica fuera de equilibrio. Se obtienen dos o a a f´ rmulas anal´ticas: para la carga de calor y para el coeﬁciente de desempe˜ o, ambas en funci´ n del trabajo de corriente el´ ctrica. Se realiza o ı n o e una optimizaci´ n de la posici´ n de la superﬁcie de transferencia de calor entre cuatro intercambiadores para maximizar la carga de calor y el o o coeﬁciente de desempe˜ o de la bomba de calor termoel´ ctrica combinada. Para este mismo ﬁn, se optimiza tambi´ n la raz´ n entre el n´ mero n e e o u de elementos termoel´ ctricos del generador y el total. Se analiza, mediante ejemplos num´ ricos detallados, la inﬂuencia entre las posiciones e e ´ del elemento termoel´ ctrico y del area de transferencia de calor. e Descriptores: Dispositivo termoel´ ctrico combinado; generador termoel´ ctrico; bomba de calor termoel´ ctrica; transferencia de calor; tere e e modin´ mica de tiempo ﬁnito; termodin´ mica fuera de equilibrio. a a PACS: 05.30-d; 05.70.-a; 05.60.Gg

1. Introduction

Semiconductor thermoelectric power generation, based on the Seebeck effect, and semiconductor thermoelectric cooling, based on the Peltier effect, have very interesting capabilities with respect to conventional power generation, cooling systems and heating systems [1-3]. The absence of moving components results in an increase in reliability, a reduction in maintenance, and an increase in system life; the modularity allows for application in a wide-scale range without significant losses in performance; the absence of a working ﬂuid prevents dangerous environmental leakage; and the noise reduction appears also to be an important feature. Thermoelectric generators, refrigerators, and heat pumps have been used in military, aerospace, instruments, and industrial or commercial products, as power...

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