Improving Refrigeration and Heat Pump Cycles with Time-Modulated Thermal Reservoirs

With climate change causing worsening heat waves globally [1], our reliance on air conditioning systems to provide thermal comfort in the engulfing heat has increased significantly, further worsening the climate crisis due to increased energy usage [2]. Thus, working toward improving the efficiency of these systems is critical. Solid-state refrigerants are emerging as highly efficient, environmentally friendly alternatives to conventional vapor-compression refrigeration. These include magnetocaloric materials, which increase or decrease in temperature (heat up or cool down) when adiabatically magnetized or demagnetized, respectively, particularly near a magnetic phase transition (e.g., paramagnetic to ferromagnetic). However, even refrigeration and heat pump cycles based on solid-state refrigerants cannot surpass the efficiency of the ideal reverse Carnot cycle, which itself is unachievable under real world constraints due to non-conservative losses such as friction. The coefficient of performance (COP) is used to measure how well refrigerators and heat pumps can cool or heat objects, respectively, with higher COP generally meaning better performance. COP is inversely proportional to the difference between the heat absorbed from the cold reservoir and rejected to the hot reservoir (ΔQ = Qc − Qh). Thus, to maximize COP, we can either reject a Qh commensurate with Qc or decrease the temperature difference between the reservoirs, neither of which is always practical or desirable. However, given the nonlinear relationship between COP and ΔQ, a decrement in ΔQ increases COP disproportionately more than an equivalent increment in ΔQ decreases COP. Therefore, if ΔQ is periodically modulated about some average value, the time-averaged COP may be higher compared to the static case. We have developed a theoretical model of a reverse Brayton cycle with a time-modulated Qh, which we use to probe the feasibility of such an improvement to refrigeration cycles. We further propose using magnetocaloric materials as a practical way to periodically modulate the temperature of the hot reservoir and thus Qh via a fast, non-contact, bulk heating and cooling process. Our work points toward exploring new methods to more effectively provide cooling and heating via time modulation, with potential for real-world implementation. This work is supported in part by ARO MURI (Grant No. W911NF-19-1-0279) via U. Michigan. X. C. gratefully acknowledges support from a direct funding award via the MIT UROP Office. S. P. gratefully acknowledges support from the NSF GRFP under Grant No. 2141064.<br/><br/>References<br/>[1] B. Abrahms, N. H. Carter, T. J. Clark-Wolf, K. M. Gaynor, E. Johansson, A. McInturff, A. C. Nisi, K. Rafiq, L. West, Nat. Clim. Chang. 13, 224 (2023).<br/>[2] F. P. Colelli, I. S. Wing, E.D. Cian, Sci. Rep. 13, 4413 (2023).