Abstract
A magnetocaloric cascade contains a sequence of magnetocaloric material layers having different Curie temperatures T.sub.C, wherein the magnetocaloric material layers include a cold-side outer layer, a hot-side outer layer and at least three inner layers between the cold-side outer layer and the hot-side outer layer.
Claims
1. A magnetocaloric cascade, comprising: a sequence of magnetocaloric material layers having different Curie temperatures T.sub.C, wherein the magnetocaloric material layers comprise a cold-side outer layer, a hot-side outer layer and at least three inner layers between the cold-side outer layer and the hot-side outer layer, for each pair of next neighboring magnetocaloric material layers of the magnetocaloric cascade there exists a respective crossing temperature, at which an entropy parameter mS of both respective neighboring magnetocaloric material layers assumes the same crossing-point value, the entropy parameter mS being defined as a product of the mass m of the respective magnetocaloric material layer and an amount of its isothermal magnetic entropy change S in a magnetic phase transition of the respective magnetocaloric material layer, at least two of the inner layers have masses m differing from each other, and all crossing-point values of the entropy parameter mS of all pairs of next neighboring inner layers are equal, either exactly or within a margin of 15%, to a mean value of all crossing-point values of all pairs of next neighboring inner layers of the magnetocaloric cascade.
2. The magnetocaloric cascade of claim 1, wherein all crossing-point values of the entropy parameter mS of all pairs of next neighboring inner layers are equal, either exactly or within a margin of 10%, to the mean value of all crossing-point values of all pairs of next neighboring inner layers of the magnetocaloric cascade.
3. The magnetocaloric cascade of claim 1, wherein a cold-side outer layer pair formed by the cold-side outer layer and its next neighboring cold-side inner layer or a hot-side outer layer pair formed by the hot-side outer layer and its next neighboring hot-side inner layer or the hot-side and the cold-side outer layer pair exhibit a crossing-point value of the entropy parameter mS that is equal, either exactly or within the margin of 15%, to the mean value of all crossing-point values of all pairs of next neighboring inner layers of the magnetocaloric cascade.
4. The magnetocaloric cascade of claim 1, wherein each pair of next neighboring magnetocaloric layers of the magnetocaloric cascade has a respective Curie-temperature difference amount T.sub.C between their respective Curie temperatures, and wherein the hot-side outer layer or the cold-side outer layer or both the hot-side and cold-side outer layer exhibits a larger ratio mS.sub.max/T.sub.C of the maximum of the entropy parameter mS and the Curie-temperature difference amount T.sub.C in comparison with any of the inner layers.
5. The magnetocaloric cascade of claim 4, wherein the hot-side outer layer or the cold-side outer layer exhibits an amount of the ratio mS.sub.max/T.sub.C that is at least 1% larger in comparison with any of the inner layers.
6. The magnetocaloric cascade of claim 4, wherein one of the hot-side and cold-side outer layers has a higher amount of the ratio mS.sub.max/T.sub.C than the other, and wherein the other of the hot-side and cold-side outer layers has a higher amount of the ratio mS.sub.max/T.sub.C than any of inner layers.
7. The magnetocaloric cascade of claim 4, wherein the hot-side layer or the cold-side layer exhibits a smaller amount of T.sub.C in comparison with any of the inner layers.
8. The magnetocaloric cascade of claim 7, wherein the hot-side layer or the cold-side layer exhibits an amount of T.sub.C that is no less than 0.5K.
9. The magnetocaloric cascade of claim 1, wherein the hot-side outer layer or the cold-side outer layer or both the hot-side and cold-side outer layer comprises a sublayer sequence of at least two hot-side sublayers or cold-side sublayers, respectively.
10. A magnetocaloric regenerator, comprising: the magnetocaloric cascade according claim 1.
11. A heat pump, comprising: the magnetocaloric regenerator according to claim 10.
12. The heat pump of claim 11, further comprising a hot-side interface in thermal communication with the hot-side outer layer, a cold-side interface in thermal communication with the cold-side outer layer, and a heat transfer system, which is configured to provide a flow of a heat-transfer fluid between the hot-side interface and the cold side interface through the magnetocaloric cascade, wherein the Curie temperature of the hot-side outer layer is selected to be higher than a temperature of the hot-side interface in operation of the heat pump, or the Curie temperature of the cold-side outer layer is selected to be lower than a temperature of the cold-side interface in operation of the heat pump.
13. A method for fabricating a magnetocaloric cascade, comprising: fabricating a sequence of different magnetocaloric material layers having different Curie temperatures T.sub.C, wherein the magnetocaloric material layers include a cold-side outer layer, a hot-side outer layer and at least three inner layers between the cold-side outer layer and the hot-side outer layer; fabricating at least two of the inner layers with masses m differing from each other, wherein for each pair of next neighboring magnetocaloric material layers of the magnetocaloric cascade there exists a respective crossing temperature, at which an pumping power entropy parameter mS of both respective neighboring magnetocaloric material layers assumes the same crossing-point value, the entropy parameter mS being defined as a product of the mass m of the respective magnetocaloric material layer and an amount of its isothermal magnetic entropy change S in a magnetic phase transition of the respective magnetocaloric material layer; and wherein all crossing-point values of the entropy parameter mS of all pairs of next neighboring inner layers are equal, either exactly or within a margin of 15%, to a mean value of all crossing-point values of all pairs of next neighboring inner layers across the magnetocaloric cascade.
14. A heat-pumping method, comprising performing a heat-pumping sequence using a magnetocaloric regenerator comprising a magnetocaloric cascade according to claim 1.
15. The heat-pumping method of claim 14, wherein the heat-pumping sequence includes a temperature increase of the magnetocaloric regenerator andthe heat-pumping sequence is performed in thermal communication with a heat sink, which is operated at a temperature that is between 0.5 K and 5 K higher than a Curie temperature of the hot-side outer layer.
Description
[0063] In the following, further embodiments will be described with reference to the enclosed drawings. In the drawings:
[0064] FIG. 1 shows a schematic diagram illustrating a difference in a dependence of magnetic entropy on temperature for the cases of exposure and non-exposure of a magnetocaloric material to a magnetic field near its Curie temperature;
[0065] FIG. 2 shows an embodiment of a magnetocaloric cascade;
[0066] FIG. 3 shows an illustration of a temperature dependence of an isothermal magnetic entropy change S in a magnetic phase transition of respective magnetocaloric material layers of a cascade in accordance with the prior art;
[0067] FIG. 4 shows an illustration of a temperature dependence of the mass-weighted isothermal magnetic entropy change in a magnetic phase transition (i.e., the entropy parameter) of the respective magnetocaloric material layers of the cascade of FIG. 2;
[0068] FIGS. 5 and 6 are illustrations of the temperature dependence of the mass-weighted isothermal magnetic entropy change in a magnetic phase transition (i.e., the entropy parameter) of two next neighboring magnetocaloric material layers in two different embodiments of a magnetocaloric cascade;
[0069] FIG. 7 shows an illustration of a temperature dependence of the mass-weighted isothermal magnetic entropy change in a magnetic phase transition (i.e., the entropy parameter) of the respective magnetocaloric material layers of a reference cascade, which is used as an illustrative example of a cascade that is not in accordance with the present invention.
[0070] FIG. 8 shows, for comparison, an illustration of a temperature dependence of the mass-weighted isothermal magnetic entropy change in a magnetic phase transition (i.e., the entropy parameter) of the respective magnetocaloric material layers of an embodiment according to the present invention.
[0071] FIG. 9 is a diagram showing the cooling power (CP, in units of Watt) of the cascades of FIG. 7 and FIG. 8 as a function of the temperature span (TS) between the hot-side outer layer and the cold-side outer layer (in units of Kelvin).
[0072] FIG. 10 shows a diagram illustrating an improvement in cooling power (abbreviated as ICP) of the embodiment of the magnetocaloric cascade of FIG. 8 in comparison with the reference cascade of FIG. 7 for different temperature spans between a hot-side temperature and a cold-side temperature.
[0073] FIG. 11 shows an illustration of a temperature dependence of the mass-weighted isothermal magnetic entropy change in a magnetic phase transition (i.e., the entropy parameter) of the respective magnetocaloric material layers of a reference cascade, which is used as an illustrative example of a cascade that is not in accordance with the present invention.
[0074] FIG. 12 shows, for comparison with FIG. 11, an illustration of a temperature dependence of the mass-weighted isothermal magnetic entropy change in a magnetic phase transition (i.e., the entropy parameter) of the respective magnetocaloric material layers of an embodiment according to the present invention.
[0075] FIG. 13 is a diagram showing the cooling power (CP, in units of Watt) of the cascades of FIG. 11 and FIG. 12 as a function of the temperature span (TS) between the hot-side outer layer and the cold-side outer layer (in units of Kelvin).
[0076] FIG. 14 shows a diagram illustrating an improvement in cooling power (abbreviated as ICP) of the embodiment of the magnetocaloric cascade of FIG. 12 in comparison with the reference cascade of FIG. 11 for different temperature spans between a hot-side temperature and a cold-side temperature.
[0077] FIG. 1 shows a diagram in which an entropy S is plotted in linear units (Joule/Kelvin) as a function of temperature T, also in linear units of Kelvin for a magnetocaloric material layer. The curves shown in the diagram are also referred to as ST curves. The diagram is purely schematic and only serves to illustrate the following. The magnetocaloric material layer exhibits different ST curves under application of magnetic fields of different amounts. Two exemplary curves A and B illustrate the cases H=0 (no magnetic field applied) and H0 (application of a magnetic field of a certain amount). The ST curve of the case H=0 is found at higher entropy levels, which is due to the higher contribution of the magnetic entropy to the shown overall entropy of the magnetocaloric material layer. Further contributions to the entropy S are provided by the crystal lattice and by the electrons of the magnetocaloric material of the layer. Under application of the magnetic field that is strong enough to cause a phase transition of the magnetocaloric material layer leading to an orientation of all magnetic moments along the direction of the magnetic field vector the magnetic entropy at the given temperature drops by an amount S.sub.max. This gives rise to a temperature increase. A maximum of the temperature increase in an adiabatic process amounts to T.sub.ad, max and occurs at a temperature that is different from that, at which S.sub.max is observable, as shown in FIG. 1.
[0078] In the following, reference is made in parallel to FIGS. 2 to 4. FIG. 2 shows an embodiment of a magnetocaloric cascade 10 for use as a magnetocaloric regenerator, and thus as a working body of a cooling device for pumping heat in a direction indicated by arrows 11. FIG. 3 shows an illustration of a temperature dependence of an isothermal magnetic entropy change S in a magnetic phase transition of respective magnetocaloric material layers of the cascade of FIG. 2. FIG. 4 shows an illustration of a temperature dependence of the mass-weighted isothermal magnetic entropy change in a magnetic phase transition (i.e., the entropy parameter) of the respective magnetocaloric material layers of the cascade of FIG. 2.
[0079] The cascade 10 is formed of a layer sequence of magnetocaloric material layers 12 to 20. In particular, the cascade has a cold-side outer layer 12 followed by a plurality of magnetocaloric inner layers, of which the inner layers 14, 16 and 18 are provided in the present example. Furthermore, the cascade has a hot-side outer layer 20. The layer pair (12,14) formed by the cold-side outer layer 12 and the next neighboring inner layer 14 is herein also referred to as the cold-side outer layer pair. The layer pair (18, 20) formed by the hot-side outer layer 20 and the next neighboring inner layer 18 is herein also referred to as the hot-side outer layer pair.
[0080] The layer sequence of the magnetocaloric cascade 10 has the following particular feature illustrated by way of FIGS. 3 and 4: first, FIG. 3 shows FIG. 3 shows a schematic illustration of a temperature dependence of an mass-weighted isothermal magnetic entropy change S in a magnetic phase transition of respective magnetocaloric material layers of a cascade in accordance with the prior art. The magnetocaloric cascade underlying the illustration of FIG. 3 has five magnetocaloric material layers similar to the structure of FIG. 2. The magnetocaloric layers are referred to as 12 to 20. However, the magnetocaloric cascade referred to in FIG. 3 is a structure in accordance with the prior art, as will become clear from the following explanation.
[0081] The different magnetocaloric material layers 12 to 20 have identical masses and different Curie temperatures T.sub.C, which in FIG. 3 are labelled with a view to the respective reference labels of the corresponding layers as T.sub.C.sup.(12), T.sub.C.sup.(14), T.sub.C.sup.(16), T.sub.C.sup.(18) and T.sub.C.sup.(20) in a sequence of gradually increasing values between the cold-side outer layer 12 and the hot-side outer layer 20. For each pair of next neighboring magnetocaloric material layers of the magnetocaloric cascade, i.e., for the layer pairs (12, 14), (14, 16), (16, 18) and (18, 20) there exists a respective crossing temperature T1, T2, T3, and T4, at which the product mS of layer mass and isothermal magnetic entropy change S in a magnetic phase transition of the respective magnetocaloric material layer is identical for both respective neighboring magnetocaloric material layers. The corresponding crossing points are labelled as C1, C2, C3 and C4. A mean crossing point value mS.sub.mean of all pairs of next neighboring inner layers, i.e., layer pairs (14, 16) and (16, 18) can be calculated and is indicated in the diagram of FIG. 3. As FIG. 3 shows, the values of mS at the crossing points C1, C2, C3 and C4 are different. In particular, the crossing point values of mS at C2 and C3 for the pairs (14, 16) and (16, 18) of inner layers are outside a margin of 15% around the mean .sup.value mS.sub.mean of all crossing-point values of all pairs of next neighboring inner layers of the magnetocaloric cascade. The upper and lower limits of the margin around the mean crossing point value mS.sub.mean are labelled mS.sub.mean+15% and ms.sub.mean15% in FIG. 3, meaning ms.sub.mean+0.15*ms.sub.mean and ms.sub.mean0.15*ms.sub.mean. It is noted that the diagram is schematic and may therefore not show values to scale.
[0082] In contrast, FIG. 4 shows an illustration of a temperature dependence of the mass-weighted isothermal magnetic entropy change in a magnetic phase transition (i.e., the entropy parameter) of the respective magnetocaloric material layers of the cascade of FIG. 2. It is assumed that the Curie temperatures of the respective layers, T.sub.C.sup.(12), T.sub.C.sup.(14), T.sub.C.sup.(16), T.sub.C.sup.(18) and T.sub.C.sup.(20) are identical to those of the prior-art cascade referred to in FIG. 3. However, this is only for the purpose of simplicity of explanation. As shown in FIG. 4 for the embodiment of FIG. 2, the materials and masses of the different layers 12 to 20 of the cascade 10 are adapted individually to form an embodiment of the present invention. In other words, in the cascade 10, at least two of the magnetocaloric material layers have masses m differing from each other. By suitable material selection and design of the layer masses, identical crossing-point values C1, C2, C3 and C4 of the mass-weighted entropy change, i.e., the entropy parameter mS defined hereinabove are achieved. More specifically, the entropy parameter mS being defined as a product of the mass m of the respective magnetocaloric material layer and an amount of its isothermal magnetic entropy change S in a magnetic phase transition of the respective magnetocaloric material layer is identical at the crossing temperatures T1, T2, and T3 and T4 and differ from the crossing temperatures T1, T2, T3 and T4. All crossing-point values C1, C2, C3 and C4 of the entropy parameter mS across the magnetocaloric cascade are thus exactly equal in the present embodiment. In other embodiments, they are equal within a margin of 15%, to the mean value mS.sub.mean of all crossing-point values of all pairs of next neighboring inner layers of the magnetocaloric cascade.
[0083] It is a particular feature of the present embodiment that in fact all crossing-point values C1, C2, C3 and C4 of the entropy parameter mS with respect to next neighboring magnetocaloric layers are identical. This is not a necessary requirement in accordance with the present invention, which only requires all inner layers to have equal crossing-point values of the entropy parameter mS with next neighboring inner layers, either exactly or within a margin of 15%, to the mean value mS.sub.mean of all crossing-point values of all pairs of next neighboring inner layers of the magnetocaloric cascade. As will be shown further below, further embodiments in accordance with the present invention have hot-side and cold-side outer layers, which are designed to exhibit crossing point values outside the mentioned margin around mS.sub.mean.
[0084] As a further particular feature of the present embodiment, the maximum amount of mS is equal for all layers. However, this is not a necessary requirement.
[0085] Based on the design explained, the cascade 10 achieves a particularly high performance in heat-pumping applications.
[0086] FIGS. 5 and 6 are illustrations of the temperature dependence of the mass-weighted isothermal magnetic entropy change in a magnetic phase transition (i.e., the entropy parameter) of two next neighboring magnetocaloric material layers 52, 54 and 62, 64 in two different embodiments of a magnetocaloric cascade according to the present invention. The magnetocaloric cascades referred to in FIGS. 5 and 6 comprise a plurality of magnetocaloric layers. In particular at least three inner layers are provided, which are in accordance with the described requirements regarding equality or margin of the crossing points with respect to the mean value mS.sub.mean of all crossing-point values of inner-layer pairs. However, any such information about the further layers of the cascade is omitted in FIGS. 5 and 6 for reasons of simplicity. The two next neighboring magnetocaloric material layers 52, 54 and 62, 64, which are shown, form a respective outer layer pair. In other words, the layers 52 and 62 are hot-side or cold-side outer layers, and will be referred to in short as outer layers in the following. The respective next neighboring layers 54 and 64 form inner layers in the wording of the claims.
[0087] The outer layers 52 and 62 of both embodiments are strengthened in these two embodiments of the present invention, as will be explained in the following. In the embodiment of FIG. 5, the outer layer 52 has a higher maximum amount mS.sub.max of the entropy parameter mS in comparison with the next neighboring inner layer 54. This property of the outer layer 52 can be achieved by proper material selection or by suitable setting of the mass of the outer layer 52. Selecting a material and/or a mass for the outer layer 52 that in comparison with the next neighboring inner layer 54 leads to a higher maximum amount mS.sub.max of the entropy parameter mS tends to increase the crossing point value C5 of mS of the two curves shown in FIG. 5, given a suitable actual amount of mS.sub.max and the full width at half maximum of the temperature dependence of the entropy parameter mS. In some embodiments implementing the situation of FIG. 5 the crossing point value C5 is outside the margin of 15% with respect to the mean value mS.sub.mean of all crossing-point values of all pairs of next neighboring inner layers of the magnetocaloric cascade. In other embodiments, it falls within this margin, however fulfilling exact equality.
[0088] In the embodiment of FIG. 6, the outer layer 62 has the same maximum amount mS.sub.max of the entropy parameter mS in comparison with the next neighboring inner layer 64. However, the materials of the layers are selected so that their Curie temperature spacing T.sub.C is smaller in comparison with the embodiment of FIG. 5. This also leads to an increased crossing-point value C6 of the entropy parameter mS with reference to its respective highest maximum value across the cascade. Selecting a the Curie-temperature difference between the outer layer 62 and the next neighboring inner layer tends to increase the crossing point value C6 of mS of the two curves shown in FIG. 5, given a suitable full width at half maximum of the temperature dependence of the entropy parameter mS. In some embodiments implementing the situation of FIG. 6 the crossing point value C6 is outside the margin of 15% with respect to the mean value mS.sub.mean of all crossing-point values of all pairs of next neighboring inner layers of the magnetocaloric cascade. In other embodiments, it falls within this margin, without, however fulfilling exact equality.
[0089] Both measures described achieve an improvement of heat-pumping performance.
[0090] In the following, further embodiments of cascades will be discussed with reference to FIGS. 7 to 14.
[0091] FIGS. 7 to 14 show the results of virtual experiments, which were carried out using a physical model similar to that described by Engelbrecht: A Numerical Model of an Active Magnetic Regenerator Refrigeration System, http://digital.library.wisc.edu/1793/7596). A one-dimensional model was employed. The total mass of magnetocaloric material of the cascades was 0.025 kg. The pumped volume per blow was 410.sup.6 m.sup.3.
[0092] Reference cascades were used in the virtual experiments to demonstrate the advantageous effects on pumping power achieved with the embodiments. In particular, in the reference cascades shown in FIGS. 7 and 11, all magnetocaloric material layers have the same mass. Example 1:
[0093] A cooling power was determined for a reference cascade according to FIG. 7 that is not in accordance with present invention and used for comparison only. The reference cascade has the following properties. It comprises a sequence of six magnetocaloric layers 1 to 6, exhibiting Curie temperatures corresponding to the maxima of the curves shown in FIG. 7. The layers have the same reference mass, and the total mass of all magnetocaloric layers is 0.025 kg. A pumped volume per blow amounts to 410.sup.6 m.sup.3. Only for the purpose of simplified graphical representation, the mass was assumed to be 1 kg per layer for determining the curves in FIGS. 7 and 8. For the actual power calculations shown in FIGS. 9 and 10, the actual mass was used.
[0094] The crossing points of the curves of the entropy parameter as a function of temperature are as specified in Table 1:
TABLE-US-00001 TABLE 1 Crossing points for reference cascade of FIG. 7 C1 C2 C3 C4 C5 m * S [J/K] 10.44 10.68 9.27 8.17 7.1 Deviation 14.3% 17.0% 1.5% 10.5% 22.3% from mean
[0095] The deviations from the mean value given in Table 1 are calculated with respect to a mean value of the crossing points C1 to C5, which is 9.17 J/K.
[0096] In comparison, the cascade represented by FIG. 8 is based on the same magnetocaloric materials in the different layers 1 to 6. However, some of the layers of the cascade of FIG. 8 have different masses than the corresponding layers of the reference cascade of FIG. 7. The relative masses are given in Table 2, wherein a mass of 1 corresponds to 0.0025 kg divided by the number of layers, i.e., six. The layers are numbered as Layer 1 to Layer 6, which means layer 1 (cold-side outer layer) to layer 6 (hot-side outer layer) for the reference cascade of FIG. 7, and layer 1 (cold-side outer layer) to layer 6 (hot-side outer layer) of the embodiment of FIG. 8.
TABLE-US-00002 TABLE 2 Relative masses of the layers of the reference cascade and embodiment Layer Layer Layer 1 Layer 2 3 Layer 4 5 Layer 6 Sum Reference, 1 1 1 1 1 1 6 FIG. 7 Embodiment, 0.9 0.8 1 0.9 1.1 1.3 6 FIG. 8
[0097] With the mass changes of layers 1, 2, 4, 5 and 6 in the embodiment of FIG. 8 in comparison with the reference cascade of FIG. 7, as shown in Table 2, the following crossing point values are achieved for the embodiment of FIG. 8:
TABLE-US-00003 TABLE 3 Crossing points for the cascade embodiment of FIG. 8 C1 C2 C3 C4 C5 m * S [J/K] 8.55 9.04 8.79 8.24 8.48 Deviation 0.8% 4.9% 2.0% 4.4% 1.6% from mean
[0098] The deviations from the mean value given in Table 1 are calculated with respect to a mean value of the crossing points C1 to C5, which is 8.62 J/K.
[0099] The cooling power was determined for the reference cascade of FIG. 7 and for the embodiment of the cascades of the present invention of FIG. 8. FIG. 9 is a diagram showing the cooling power (CP, in units of Watt) of the cascades of FIG. 7 and FIG. 8 as a function of the temperature span (TS) between the hot-side outer layer and the cold-side outer layer (in units of Kelvin). Different symbols used represent different cascades: the CP values obtained for the embodiment of FIG. 8 are represented by full squares, and the CP values obtained for the reference cascade (FIG. 7) are represented by full diamonds. The cooling power of the embodiment of FIG. 8 is clearly higher than that of the reference cascade of FIG. 7 for all temperature spans. FIG. 10 shows an improvement of the cooling power (ICP) of the embodiment of FIG. 8 in units of percent in relation to the cooling power of the reference cascade described above (FIG. 7) for an operating temperature at the hot-side interface of the cascade of 23.9 C. for different temperature spans TS in units of K, i.e., different operating temperatures at the cold-side interface of the cascade, in the range of temperatures spans TS between 0 and 20 K. The temperature values used for determining the respective temperature spans are to be taken at the hot-side and cold-side entry points into the cascade.
[0100] The diagrams of FIG. 9 and FIG. 10 clearly show a significant improvement in cooling power of the magnetocaloric cascade of the embodiment of FIG. 8 in comparison with the reference cascade of FIG. 7 in the full range of temperature spans TS between 0 and 20 K. The improvement is almost the same for all temperature spans.
Example 2
[0101] A cooling power was determined for a reference cascade according to FIG. 11 that is not in accordance with present invention and used for comparison only. The reference cascade has the following properties. It comprises a sequence of five magnetocaloric layers 1 to 5, exhibiting Curie temperatures corresponding to the maxima of the curves shown in FIG. 11. The layers have the same reference mass, and the total mass of all five magnetocaloric layer is 0.025 kg. A pumped volume per blow amounts to 410.sup.6 m.sup.3. As before, only for the purpose of simplified graphical representation, the mass was assumed to be 1 kg per layer for determining the curves in FIGS. 11 and 12. For the cooling power calculations shown in FIGS. 13 and 14, the actual mass of 0.025 kg divided by the number of layers, i.e., five, was used.
[0102] The crossing points of the curves of the entropy parameter for the reference cascade as a function of temperature are as specified in Table 4:
TABLE-US-00004 TABLE 4 Crossing points for the reference cascade of FIG. 11 C1 C2 C3 C4 m * S [J/K] 13.4 9.89 9.82 11.71 Deviation 19.6% 11.7% 12.4% 4.5% from mean
[0103] The deviations from the mean value given in Table 1 are calculated with respect to a mean value of the crossing points C1 to C4, which is 11.21 J/K.
[0104] In comparison, the cascade represented by FIG. 12 is based on the same materials in the different layers 1 to 5. However, some of the layers of the cascade of FIG. 12 have different masses than the corresponding layers of the reference cascade of FIG. 11. The relative masses are given in Table 2, wherein a mass of 1 corresponds to 0.0025 kg. The layers are numbered as Layer 1 to Layer 5, which means layer 1 (cold-side outer layer) to layer 5 (hot-side outer layer) for the reference cascade of FIG. 11, and layer 1 (cold-side outer layer) to layer 5 (hot-side outer layer) of the embodiment of FIG. 12.
TABLE-US-00005 TABLE 5 Relative masses of the layers of the reference cascade and embodiment Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 Sum Reference, 1 1 1 1 1 5 FIG. 11 Embodiment, 0.85 0.9 1.25 1 1 5 FIG. 12
[0105] With the mass changes of layers 1, 2, and 3 shown in Table 2, the following crossing point values are achieved for the embodiment of FIG. 12:
TABLE-US-00006 TABLE 6 Crossing points for the cascade embodiment of FIG. 12 C1 C2 C3 C4 C5 m * S [J/K] 11.73 11.48 11.75 11.72 11.73 Deviation 0.5% 1.7% 0.7% 0.4% 0.5% from mean
[0106] The deviations from the mean value given in Table 1 are calculated with respect to a mean value of the crossing points C1 to C4, which is 11.67 J/K.
[0107] The cooling power was determined for the reference cascade of FIG. 11 and for the embodiment of the cascades of the present invention of FIG. 12. FIG. 13 is a diagram showing the cooling power (CP, in units of Watt) of the cascades of FIG. 11 and FIG. 12 as a function of the temperature span (TS) between the hot-side outer layer and the cold-side outer layer (in units of Kelvin). Different symbols used represent different cascades: the CP values obtained for the embodiment of FIG. 12 are represented by full squares, and the CP values obtained for the reference cascade (FIG. 11) are represented by full diamonds. The cooling power of the embodiment of FIG. 12 is clearly higher than that of the reference cascade of FIG. 11 for all temperature spans up to 6 K. FIG. 14 shows an improvement of the cooling power (ICP) of the embodiment of FIG. 12 in units of percent in relation to the cooling power of the reference cascade described above (FIG. 11) for an operating temperature at the hot-side interface of the cascade of 9.8 C. for different temperature spans TS in units of K, i.e., different operating temperatures at the cold-side interface of the cascade, in the range of temperatures spans TS between 0 and 8 K. The temperature values used for determining the respective temperature spans are to be taken at the hot-side and cold-side entry points into the cascade.
[0108] The diagrams of FIG. 13 and FIG. 14 clearly show a significant improvement in cooling power of the magnetocaloric cascade of the embodiment of FIG. 8 in comparison with the reference cascade of FIG. 11 in the range of temperature spans TS between 0 and 6 K.
[0109] The improvement is the same for all temperature spans in this range.
[0110] The results are similar for cascades where the two outer layers (or even more) at one or both sides are modified using a higher mass per layer or a smaller Curie temperature spacing).
