4.3. Cooling power of an ideal EC element

The cooling power of an ideal EC element is given by q\_ ¼ CECΔT=τc, where CEC is its heat capacity and ΔT� ¼ ΔTEC � ðTl � TsÞ is the temperature difference of the heat transfer steps. When the cycle time τ<sup>c</sup> is associated by a constant factor m with the thermal time constant τRC ¼ RthCEC of the EC element, the heat capacity cancels out. Consequently, q\_ is determined


Table 2. Material characteristics, the materials efficiency Φmat and the figure of merit selected EC refrigerants.

by the ratio of ΔT\* to the total thermal resistance Rth of the device. Taking into account that there are two heat transfer steps (heat absorption and heat rejection) with equal time constants and equal heat fluxes within both steps, the average cooling power per cycle yields [44]

$$\langle \dot{\boldsymbol{q}} \rangle \approx \frac{\Delta T^\* [1 - \exp\left(-m\right)]}{2m\mathcal{R}\_{\text{th}}},\tag{26}$$

where R<sup>00</sup> th <sup>¼</sup> <sup>A</sup> � Rth is the area-specific thermal resistance given in m<sup>2</sup> /KW. For thermal time constants with m > 2 (two isothermal steps at least with a duration τRC), the EC material's temperature decays to almost the steady-state value. Here, the cooling power increases linearly with frequency f. At smaller values of m, a temperature offset appears decreasing the effective ΔT\*. The maximum specific cooling power is obtained at a value of m ¼ ln2 ≈ 0:7 yielding

$$
\langle \dot{q} \rangle\_{\text{max}} = \frac{0.36 \Delta T^\*}{\sum\_i R\_{th,i}^{\prime}}.\tag{27}
$$

Table 3 compiles estimated specific cooling powers of hypothetical EC devices in dependence on the dominating thermal resistance of possible heat-releasing parts.
