Power Generation Efficiency with Extremely Large Z factor Thermoelectric Material
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Power Generation Efficiency with Extremely Large Z factor Thermoelectric Material Kazuaki Yazawa, Ali Shakouri 1 Baskin School of Engineering, University of California Santa Cruz, Santa Cruz, CA 95064 , U.S.A.
ABSTRACT A recently developed generic model of a thermoelectric power generation system suggests a promising future for cost effective and scalable power generation. The model is based on cooptimizing the thermoelectric module together with the heat sink. Using this model, efficiency at maximum output power is calculated. It is shown that this approaches the Curzon-Ahlborn limit at very large Z values which is consistent with thermodynamic systems with irreversible heat engines. However, this happens only when the thermal resistances of the thermoelectric device with hot and cold heat sinks exactly match. For asymmetrical thermal resistances, the efficiency at maximum output power is different. This is consistent with the very recent results for the thermodynamic engines. Finally, we study the impact of lowering the thermal conductivity of the thermoelectric material or increasing its power factor and how these affect the performance of the thermoelectric power generation system. INTRODUCTION Thermoelectric materials are getting more attention and interest due to the emergent need for green technology. The low efficiency of the energy conversion is a concern in many direct thermal to electrical energy conversion applications. Typically, Carnot efficiency is invoked as the maximum theoretical limit when the material figure-of-merit (ZT) goes to infinity. This is analogous to the thermodynamic reversible heat engines and it is true only when the system does not generate heat loss. This happens when the output power goes to zero. The efficiency at the maximum power output is quite important in many applications. Research in thermoelectrics has been mostly focused on improving the figure-of-merit (ZT) of the material [1][2][3]. This ZT factor is critical to extract useful power. However, developing the material is not enough to improve the power output of the whole system. Recent work shows that the system efficiency at the maximum power output is linearly dependant on the sum of the heat dissipation on both the hot side and the cold side thermal resistances with the reservoirs [4]. The optimum condition is found only when the thermoelectric device thermal impedance matches the impedance of the system both electrically and thermally by a factor of sqrt(1+ZT). This phenomenon was partially understood and reported in the literature on thermoelectric systems [5][6][7][8]. In the following, we have performed a comprehensive and full optimization based on the generic model with asymmetric thermal resistances with hot and cold reservoirs. MODEL DEVELOPMENT The model of the thermoelectric power generation system contains thermal resistance with a hot reservoir, ψh, and a cold reservoir, ψc as seen as Fig.1. A thermoelectric element (leg) is placed in the middle of two thermal resistances. Heat flux qh is supplied by the
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