Device-Level Thermodynamic and Heat Transfer Model for a Barocaloric Solid State Refrigerator

Solid state refrigeration based on caloric materials has demonstrated the ability to replace existing vapor compression cooling systems that are inefficient, difficult to scale and have a high global warming potential. Unlike solid state cooling based on electrocaloric, magnetocaloric and elastocaloric effects, barocaloric refrigeration – based on the entropy change due to applied hydrostatic pressure – have received comparatively less attention but have recently demonstrated significant potential in material-level studies. However, device-level numerical and experimental studies are still missing in the literature. This work presents a thermodynamic and heat transfer model for a barocaloric refrigerator comprising commercially-available nitrile butadiene rubber (NBR) and operating between a hot and a cold thermal reservoir. We combine experimentally-validated barocaloric properties of NBR with transient heat conduction modeling to evaluate the performance of a reverse Brayton refrigeration cycle. Specifically, we evaluate the coefficient of performance (COP), energy density and power density of the device, and quantify the contributions of device geometry, operating frequency, heat transfer coefficient, and applied pressure. We show that a barocaloric refrigerator operating with a 2.3 K temperature span, 10 mHz cycle frequency and 0.1 GPa applied pressure change can achieve a COP as high as 8 – exceeding that of traditional vapor compression-based refrigerators. Additionally, we show that increasing the thermal conductivity of the elastomeric solid-state refrigerant can substantially improve performance – increasing the COP by 67% when the refrigerant's thermal conductivity was raised from 0.2 W m^-1 K^-1 to 1 W m^-1 K^-1. This work demonstrates the promise of solid state cooling devices based on soft barocaloric materials and provides a framework to quantify its performance at the device-level.