We present a comprehensive analysis and optimization of the thermoelectric (TE) heat pump and refrigeration in contact with two constant-temperature reservoirs, followed by a discussion of their cost effectiveness. In many applications in electronics cooling, the heat source temperature is constrained as well as the gas or liquid cooling heat sink. We optimize the thermoelectric design by changing both the element (leg) thickness and drive current simultaneously in order to achieve maximum energy efficiency, i.e., to obtain the highest coefficient of performance (COP) for the heat pump. Each variable and performance is considered per unit area.

COP vs cooling capacity, which is the heat amount pumped, by changing the driving current, shows a unique characteristic and it looks like the Greek character ‘beta’ in a plot. This ‘beta plot’ gives a global view of the performance of various TE heat pump systems. We discuss the similarity with the graph obtained in power generation in contact with the constant temperature reservoirs when the trade-off between the efficiency and power output is considered. In this plot, the maximum COP is found at a much smaller current compared to the maximum heat cooling capacity Qmax. This Qmax is found when the internal resistance is sqrt (1 + ZT) times the sum of the external resistances, but only when these contacts are symmetric and the net temperature difference is zero. The ratio increases slightly as the net temperature difference increases (heat pumping to a higher temperature). This shows some differences compared to the power generation mode where an impedance match happens when the ratio of internal to external resistances is constant at sqrt (1 + ZT). If the contact thermal resistances with the hot and cold sides are asymmetric, Qmax and the optimum resistance ratio are both reduced when the heat sink resistance increases and they both increase as the heat sink resistance decreases.

TE materials are expensive relative to the other components; hence, it is important to minimize the material use. The COP per cost and cooling capacity per cost are investigated. Similar to power generators, the TE element can be thinner as the fractional area coverage of the TE elements is reduced, while maintaining a constant internal thermal resistance. The most cost effective design is found to be thinner than that of the maximum performance. Also, the ZT value impact for the cost performances is smaller, especially in COP.

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