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Scaling Laws of Elastocaloric Regenerators

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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 pumping 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 pumping power [W g−1]

t :

Time [s]

V * :

Displaced fluid volume ratio

\(\dot{V}\) :

Volumetric flow rate [m3 s−1]

W pump :

Pumping 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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Authors and Affiliations

  1. Department of Refrigeration and Cryogenic Engineering, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Suxin Qian

  2. Department of Materials Science and Engineering, University of Maryland, College Park, MD, 20742, USA

    Ichiro Takeuchi

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Correspondence to Suxin Qian or Ichiro Takeuchi.

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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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