Electrocaloric (EC) effect refers to the isothermal entropy change ΔS or adiabatic temperature change ΔT of a dielectric material when an electric field is applied or removed.^[1–5] After a giant EC effect was found in PbZr_0.95Ti_0.05O₃,^[6] it gets a renaissance. Various strategies have been studied to enhance EC effect, e.g., preparing ferroelectric thin film bilayers and novel layered ferroelectric, utilizing phase transitions and phase-boundary, and etc.^[7–10] Antiferroelectric ceramic shows an interesting negative EC effect.^[11,12] Some practical devices using EC effect for cooling.^[13–17] and electrical energy generation^[18] have been developed.

For ferroelectric ceramics, a high electric field has to be applied to induce a large EC effect.^[5] Thus, ceramics have to be fabricated very thin to increase the electrical breakdown field.^[19] The compromise is that the overall quantity of cooling is small due to reduced size. In the field of electronic ceramics, it is known that industrially manufactured multi-layer ceramic capacitors (MLCC) are an innovative result of increasing the value of capacitance while reducing the size. These mature products find also novel properties like magnetoelectric effects^[20–22] and EC effect^[23]. The EC effect of MLCC has also studied extensively.^[24–31] The dielectric materials used in MLCC commonly are BaTiO₃-based ceramics, which have poor thermal conduction. It is then interesting to ask if the thermal conduction of these ceramics can be enhanced through the EC effect. Thus, in this work, a simple MLCC is designed and the proper sequential electric field is applied. The result indicates that the EC effect can enhance the thermal conduction of the structure significantly.

The one-dimensional (1D) heat flow equation can be expressed as

$$ \begin{eqnarray}{\dot{Q}}_{{\rm{cond}}}=-kA{\rm{d}}T/{\rm{d}}X=-{\rm{d}}T/R,\end{eqnarray}$$ (1)

A simple MLCC structure is designed as shown in Fig. 1, which consists of two layers dielectric ceramics in between three layers electrodes. Thus, there are two EC cooling units EC1 and EC2. During the calculation, EC1 connects with a cooling load while EC2 connects with a heat sink.

The thermal behavior of the electrode layer can be modeled as the series of one thermal resistance R_e = L_e/k_eA_e and one thermal capacitance C_e = ρ_ec_eV_e.^[24] Here L_e is the length of an electrode measured on a path parallel to the heat flow; k_e is the thermal conductivity of the electrode; A_e is the cross-sectional area perpendicular to the path of heat flow; ρ_e is the density; c_e is the specific thermal capacity; V_e is the volume. The thermal capacitance of the EC layer is C_EC = ρ_ECc_ECV_EC. Here ρ_EC, c_EC, and V_EC are the density, the specific thermal capacity, and the volume of the EC layer.

By assuming that the cooling load temperature is T_load and the temperature of EC1 is T_EC1, the 1D heat transfer Eq. (1) can be further expressed as

$$ \begin{eqnarray}\dot{Q}(t)=({T}_{{\rm{load}}}-{T}_{{\rm{EC}}1}/R){{\rm{e}}}^{-t/Rc},\end{eqnarray}$$ (3)

For commercialized MLCC, the terminal electrodes connect with the electrical circuit. Thus, each ceramic layer has the same applied electric field. The additional components have been included to transport heat. For the proposed MLCC as shown in Fig. 1, the different sequential electric field is applied for each EC unit as shown in Fig. 2. An EC cooling cycle is achieved by two adiabatic and two heat transfer processes. In one period, there are four steps for each EC unit. For instance, in step 1, there is a positive ΔT for EC2 unit because of the increase of the electric field; in step 2 it experiences heat transfer with constant electric field; in step 3 there is a negative ΔT for EC2 unit because the decreasing of the electric field; in step 4 it conducts heat transfer. The EC1 unit has the converse process in one cycle. In a period, EC1 unit absorbs heat from the cooling load while EC2 unit release heat to heat sink. In a stable state, the balance arrives when the absorbed, transferred, and released heats are equal. By solving this heat transfer problem, the EC effect on heat transfer of the proposed structure is revealed.

The geometrical and physical parameters of a commercial BaTiO₃-based Y5V MLCC were applied during the calculation. Since ρ_EC = 5840 kg⋅m⁻³, c_EC = 434 J ⋅ K⁻¹ ⋅ kg⁻¹, L = 3.3 mm, the effective width W = 2.56 mm, the thickness d = 6.5 μm, the thermal capacitance C_EC is 1.391 × 10⁻⁴ J ⋅ K⁻¹. Since ρ_e = 8907 kg⋅m⁻³, c_e = 429 J ⋅ K⁻¹ ⋅ kg⁻¹, k_e = 94 W⋅K⁻¹ ⋅ m⁻¹, the thickness d = 2.0μm, the thermal capacitance C_e is 6.46×10⁻⁵ J ⋅ K⁻¹, and the thermal resistance R_e is 2.52 × 10⁻³ K ⋅W⁻¹.

By assuming that the EC temperature change of the EC unit is 0.5 K.^[23] The transferred heat during one cycle is calculated, which is the case 1 in Fig. 3. After calculating the overall thermal resistance of the proposed structure and the time constant, the heat transfer of the structure without the EC effect is gotten and plotted in Fig. 3 also, which is case 2. Finally, if the EC units are replaced by Ni metals, the heat transfer is plotted as the case III in Fig. 3. Obviously, although the heat transfer is less effective in comparison with the metal Ni, the EC effect prompts heat transfer significantly.

From the simulated result, the effective thermal conductivity of the proposed structure is 53.35 W⋅ m⁻¹ ⋅ K⁻¹, which is 20 times larger than that of the BaTiO₃-based ceramics.^[32]

In conclusion, after designing a simple MLCC structure and applying the proper sequential electric field, the result shows that the EC effect can fast heat transfer significantly. The effective thermal conductivity is 20 times larger than that of BaTiO₃-based Y5V ceramic. Our result demonstrates a novel strategy of applying the EC effect, prompting heat transfer.