Abstract
Specific cooling power (SCP), a.k.a. cooling power density, measures the cooling power of a unit mass of solid-state refrigerant. Comparing SCP is popular but is only reasonable if SCP is an intensive parameter that does not change with system size. However, to the best of our knowledge, there is no evidence that this fundamental assumption is valid. To address this question, we have derived the scaling laws of SCP and other performance metrics in terms of size and the hydraulic diameter for elastocaloric regenerators. The resulting scaling laws indicate that in many cases the specific cooling power does vary with the system size, subject to specific design constraints. Therefore, there is no engineering significance to compare the SCP among different systems with different sizes unless one maintains the same constraints including pum** power density, efficiency, etc. Although the present scaling laws were developed specifically for elastocaloric regenerators, the methodology can be easily adopted for other caloric cooling technologies.
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17 April 2024
Truncated Equations 2 and 17 and overlapped equation numbers fixed in XML.
Abbreviations
- A c :
-
Cross-sectional area [m2]
- A :
-
Heat transfer area [m2]
- COP :
-
Coefficient of performance
- c :
-
Specific heat [J g−1 K−1]
- d h :
-
Hydraulic diameter [m]
- eC:
-
Elastocaloric
- F :
-
Force [kN]
- f :
-
Friction factor
- G :
-
Mass flux [kg m−2 s−1]
- h :
-
Convective heat transfer coefficient [W m−2 K−1]
- k :
-
Thermal conductivity [W m−1 K−1]
- L :
-
Length [m]
- m :
-
Mass [kg]
- \(\dot{m}\) :
-
Mass flow rate [kg s−1]
- Nu :
-
Nusselt number
- Re :
-
Reynolds number
- SCP :
-
Specific cooling power [W g−1]
- SCP sys :
-
System-level cooling power density [W g−1]
- SF :
-
Specific force [kN m−3]
- SHL :
-
Specific heat loss [W g−1]
- SMA:
-
Shape-memory alloy
- SPP :
-
Specific pum** power [W g−1]
- t :
-
Time [s]
- V * :
-
Displaced fluid volume ratio
- \(\dot{V}\) :
-
Volumetric flow rate [m3 s−1]
- W pump :
-
Pum** power [W]
- \({\delta }_{{\text{SMA}}}\) :
-
Equivalent thickness, inverse of specific heat transfer area [m]
- \(\Delta p\) :
-
Pressure drop [Pa]
- \(\Delta {T}_{{\text{ad}}}\) :
-
Adiabatic temperature change [K]
- \({\eta }_{{\text{pump}}}\) :
-
Efficiency of pumps
- \(\rho\) :
-
Density [kg m−3]
- \(\sigma\) :
-
Stress [MPa]
- \(\mu\) :
-
Dynamic viscosity [Pa s]
- 0:
-
Baseline
- b:
-
Buckling
- ld:
-
Loading
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Acknowledgements
This work was financially supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 52376015 and 51976149. The work at the University of Maryland was supported by the U.S. Department of Energy under DE-EE0009159.
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This invited article is part of a special topical focus in Shape Memory and Superelasticity on Elastocaloric Effects in Shape Memory Alloys. The issue was organized by Stefan Seelecke and Paul Motzki, Saarland University.
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Qian, S., Takeuchi, I. Scaling Laws of Elastocaloric Regenerators. Shap. Mem. Superelasticity (2024). https://doi.org/10.1007/s40830-024-00482-0
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DOI: https://doi.org/10.1007/s40830-024-00482-0