Optimization of cooling power of a thermoelectric refrigerator: A unified approach

TL;DR

This paper presents a unified steady-state framework for optimizing the cooling power of thermoelectric refrigerators, incorporating both endoreversible and exoreversible models, and deriving practical expressions for their performance.

Contribution

It introduces a comprehensive model that unifies different irreversibility assumptions and provides explicit formulas for optimizing and evaluating thermoelectric refrigerator performance.

Findings

Cooling power optimization is feasible in the near-reversible regime with large but finite external conductances.

Derived a closed-form expression for COP depending on thermoelectric figure of merit and conductance ratios.

For small temperature differences, irreversibilities lower COP below 0.5, matching observed single-stage TER performance.

Abstract

We analyze the steady-state formalism for optimizing the cooling power of a thermoelectric refrigerator (TER), unifying the endoreversible and exoreversible approximations within one framework. Although the cooling power is non-optimizable within the endoreversible model based on Newtonian heat-transfer law, we show that the issue can be circumvented in the near-reversible regime where the external thermal conductances are large, but finite. We extend this analysis to optimize the cooling power in the presence of both internal and external irreversibilities and derive a closed-form expression for the coefficient of performance (COP) that depends on the thermoelectric figure of merit and the ratio of internal to external thermal conductances. The model reproduces the endoreversible and the exoreversible limits as special cases. We conclude that for small temperature differences, the combined irreversibilities reduce the COP to values below 1/2, which aligns with the observed performance of the single-stage TER, and can provide realistic estimates for the COP.