Performance Optimization for a Multielement Thermoelectric Refrigerator with Linear Phenomenological Heat Transfer Law
Lingen Chen, Fankai Meng, Yanlin Ge, Huijun Feng
Abstract
Abstract A model of a multielement thermoelectric refrigerator with another linear heat transfer law, the linear phenomenological heat transfer law <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="italic">Q</m:mi> <m:mo stretchy="false">∝</m:mo> <m:mi mathvariant="normal">Δ</m:mi> <m:mo mathvariant="normal" fence="true" stretchy="false">(</m:mo> <m:mn>1</m:mn> <m:mo mathvariant="normal" stretchy="false">/</m:mo> <m:mi mathvariant="italic">T</m:mi> <m:mo mathvariant="normal" fence="true" stretchy="false">)</m:mo> </m:math> Q\propto \Delta (1/T) , is established. The refrigerating capacity and coefficient of performance (COP) are analyzed and optimized. The junction temperature solution equations are derived. The optimum electrical currents and thermal conductance allocation are discussed. The influences of thermoelectric element quantity and refrigerating temperature difference on the optimum performances and optimum electrical currents are analyzed. The results show that different optimization objectives have different requirements for the distribution of electrical current and thermal conductance. The refrigeration capacity is not proportional to the number of thermoelectric elements. It is found that the refrigerating capacity can be achieved only when the number of thermoelectric elements is matched for fixed external heat exchangers. The input electrical current and the allocation of the thermal conductance between the two heat exchangers can be optimized synchronously to achieve maximum refrigerating capacity or maximum COP. Performance is compared with that with a Newtonian heat transfer law. The influences of the Thomson effect are also examined. Performance of the refrigerator with Newtonian heat transfer law is higher than that of the refrigerator with linear phenomenological heat transfer law. The Thomson effect can improve the performance of the refrigerator.