Nanotechnology in new magnetic heating, refrigeration

and energy conversion devices

 P.W. EGOLF^(a), L. GRAVIER^(b), M. CROCI^(b)

University of Applied Sciences of Western Switzerland

^(a)Institute of Thermal Sciences and Engineering,

^(b)Institute of Micro and Nanotechniques

Research on magnetic heating and energy conversion is still very rare, but starts to develop more and more. Substantial efforts are occurring in the domain of domestic magnetic refrigeration, with devices having power consumptions from 50 up to 100 Watt. Up-to-present there have been built approximately forty such prototypes and first specialized industrial companies start to discuss production lines for their magnetic refrigerators, which are predicted to show higher performance than their conventional counterparts. 

Nonetheless of such first important progress, magnetic heat pumps, refrigerators and energy conversion prototypes, with an operation based on the magnetocaloric effect, usually show a restriction in their frequency of operation to a few Hertz. Related to this permanent magnets with high masses are demanded, which show a high cost and lead to an economic drawback.

Therefore, in 2010 Kitanovski and Egolf proposed to apply a new technology – based on (nanotechnology) thermal switches – to overcome this barrier. In this article the new thermal switch refrigerator is presented in detail.

MAGNETIC HEATING, REFRIGERATION AND ENERGY CONVERSION

The magnetocaloric technology has been presented in numerous articles, review articles and books and shall only briefly be described in the next section of this article. A very brief overview of only eight pages is given in an Informatory Note of the International Institute of Refrigeration (IIF/IIR) (see Egolf and Rosensweig (2007)). One can find a longer and more comprehensive description of this technology, for example, in a journal of the Italian Industria & Formazione, which was produced in collaboration with the International Institute of Refrigeration and the United Environmental Programme, UNEP, (see Egolf and Rosensweig, 2008). Extensive and good explanations of the magnetocaloric effect and its applications are given in a standard text book published by Tishin and Spichkin (2003).This and other sources, as e.g. the review articles of Gschneidner et al. (2005) and Brück (2005), allow a deeper understanding of the magnetocaloric phenomenon and specialities of the magnetocaloric effect in different kinds of materials in which maybe some rare earths are present. On the other hand, Yu et al. (2010a) have reviewed on all the built magnetic heat pump and refrigerator prototypes built before 2010. This publication and the one of Kitanovski and Egolf (2006) contain much knowledge on thermodynamic cycles and machine building. The operation principle of a magnetic heat pump or/and refrigerator is shown in Fig. 1 on the left-hand side to the top and the one of a conventional heat pump/refrigerator just beneath it.

Figure 1: The four magneto-thermodynamic process stages each of a magnetic heat pump or/and refrigerator shown at the top and of a conventional gas heat pump or/and refrigerator in the lower part. Heating by magnetization and cooling by demagnetization is explained by spin orientation shown in two times three small pictures on the right-hand side.

In a conventional device a compressor heats up a gas (process No. I), which then is cooled (process No. II) and expanded (process No. III) where it becomes cold and takes up heat from a heat source (process No. IV), which needs to be refrigerated. If these four processes are repeated in a cyclic manner, one obtains a thermodynamic process of a heat pump/refrigerator.

In a magnetic heat pump or/and refrigerator exactly the same four-stage process occurs, but instead of compressing a gas, a solid is magnetized.

The magnetization of a magnetocaloric material (process No. I) leads to a heating effect. Then also heat is released (process No. II) and just after that the material is cooled by demagnetization (process No. III). You have probably realized that demagnetization is the analogue process to the expansion in a conventional thermodynamic machine! The cold solid now also acts as absorber for heat of a heat source (process No. III), which usually is the interior part of e.g. a refrigerator. The operation of a heat pump and refrigerator are practically identical, in the first case the ejected heat at high temperature and in the second case the absorbed heat at cold temperature are of main interest.

The operation of a magnetic energy conversion machine works inversely. In this case, from injected heat, mechanical energy and furthermore electric energy can be produced.

The cooling effect in magnetocaloric materials can be explained with some pictures on spin alignement shown on the right-hand side of figure 1.

Because a high frequency of the four just explained processes is required, the magnetization and demagnetization processes are fast and there is no time for a heat exchange. Scientists name such a process an adiabatic or isentropic process. Isentropic means that the total entropy does not change.

In many magnetocaloric materials the total entropy is the sum of thermal and magnetic entropy.

The thermal entropy describes mainly the movement (vibrations, phonons) of the crystalís lattice. The higher the amplitude of the vibration is, the higher the thermal entropy is.

The magnetic entropy is related to the order of the electronic spins. If the spins are aligned, the order is high and the magnetic entropy low. Now if a magnetocaloric material is exposed to a magnetic field, the spins align, and the magnetic entropy reduces (see upper three small pictures on the righthand side). Because the thermal entropy is the total entropy minus the magnetic entropy, now a smaller quantity is subtracted from the constant total entropy value.

Therefore, the thermal entropy, and with it the temperature, increases. By moving magnetocaloric material out of a magnetic field demagnetization and the inverse disordering process of the spins occurs (see lower three small pictures on the right-hand side).

Finally this results in a cooling of the material. The periodically occurring four stages of such a process can ideally be realized in a linear reciprocating or a rotational machine (see e.g. Fig. 2).

Figure 2: A cut through a magnetic device with a porous rotor (design: Andrej Kitanovski).

The advantage of a rotational machine is that no acceleration and deceleration work has to be performed, so that it is expected that this version is slightly more efficient. Here a machine is shown that has four sectors of 90° each, in which alternatively the magnetocaloric wheel is magnetized by magnetic fields created by permanent magnets and in which, because of a lack of nearby magnets, there is no magnetic field. By a rotation of the magnetocaloric wheel through these different sectors, a periodic magnetization and demagnetization of double frequency compared to the frequency of the basic rotation of the cylindrical wheel is obtained. Because the wheel is performed by a porous matrix of magnetocaloric material, it can be transversed by heat exchanging fluids.

There are separated heat transfer fluids in the hot magnetized and the cold demagnetized part, which extract heat from and export heat into the magnetocaloric material of the wheel. By this, in the most economic manner, the four stages of the overall thermodynamic process are realized.

In a numerical study for the Swiss Federal Office of Energy Kitanovski et al., 2008a have shown that magnetic refrigeration reaches higher coefficient of performance and exergy efficiency than conventional refrigeration.

Applying conservative methods, taking all the energy losses into consideration, depending on the frequency of the magnetic refrigerator up to a doubling of the values (improvement of 100%) have been obtained. Economic realistic values will correspond to improvements of 30%-50%. The final conclusion is that with this technology instead of the conventional one, high amounts of electrical energy doesn’t need to be utilized and can be saved for future generations. Furthermore, the environmental benign and noiseless operation of magnetic refrigeration are convincing arguments to concentrate more means into final development steps of this technology.

The already promising prospect for magnetic refrigeration is even topped by a new development, named the thermal switch technology (see Chapt. 3). This technology shows the same level of efficiency of the machines, but allows higher frequencies of operation and by this a lower mass of the permanent magnets assembly, which is related to a smaller weight and cost of the machines under consideration.

This is a key issue for wider/deeper market penetrations.

THE STATE-OF-THE-ART MAGNETIC REFRIGERATOR AND ITS LIMITS

In magnetic heat pumps or/and refrigerators heat must be transported into and out of the solid refrigerant – which is the magnetocaloric material – by diffusion.

Diffusion is known to be a slow physical process. Egolf et al. (2007) presented in their article a well-known criterion for the frequency of diffusion, based on the Fourier number criteria: Fo=1. These results are adapted to plates of Gadolinium (Gd), which is taken as characteristic material for these considerations (see Fig. 3).

Figure 3:The frequency that can be obtained to transport heat out of a magnetocaloric structure of thickness s is presented in this figure. It is assumed that a symmetric situation occurs, where the heat flows away from the centre of a plate to its two sides. The characteristic physical properties are given by the following listing:

Density: ρ=7900 kg m-3,

Thermal conductivity: k = 10.5 W m-1 K-1,

Heat capacity: c_H= 886 J kg-1K-1,

FThermal diffusivity: α = 1.5 10-6 m2 s-1.

In symmetric plates it is the half thickness which defines the maximal characteristic diffusion length. One can see, for example, that with a plate thickness of 0.25 mm, one can build a machine operating up to 100 Hz. If heat has to be transferred from the magnetocaloric material to a fluid, then also a contact resistance occurs leading to a tailback effect. But this doesn’t influence the frequency.

Another physical phenomenon leads to an even more restrictive condition for the frequency of operation of a machine. It is the carry-over leakage.

In numerous types of machine designs two different fluids flow through parts of the magnetocaloric porous matrix. If this matrix moves or rotates to fast, captured fluid in the matrix is transported from the cold part without a magnetic field to the hot part with a magnetic field and vice versa. This leads to undesired mixing of the different fluids and a related loss of energy. This phenomenon is also described in Egolf et al. (2007), but is nothing else than a summary of long known knowledge of rotary heat exchangers applied in the field of air conditioning. This effect restricts the practical operation frequency to a few Hertz. The criterion here is also defined by a non-dimensional number, which in this case is the Strouhal number.

It relates the time of flight of a fluid lump through the heat exchanger to its rotation frequency. To limit the carryover leakage, it is necessary to demand an order of magnitude higher time period for the rotation compared to the time of flight of a fluid lump through the rotor. Results of this criterion are presented in Fig. 4.

Figure 4:
The limit to avoid a substantial carry-over leakage in a rotary machine. Different than in Egolf et al. (2007) here the factor of safety is taken ten instead of five. The figure shows, for example, that in a wheel of 25 mm length and a fluid velocity of 0.25 m/s the frequency should not be higher than 1 Hz, if a remarkable carry-over leakage shall be avoided. One notes that usually the carry-over leakage criterion is the stricter criterion than the one of heat diffusion in the magnetocaloric matrix.

The second of the two discussed criteria is usually the more restrictive and in the end demands low frequencies of magnetocaloric machines. Because the power of a machine is approximately direct proportional to the frequency of a machine, high frequencies are essential for the competitiveness of the magnetocaloric technology in comparison with the conventional gas compression heating and cooling technology. It now has also become clear that higher frequencies lead to smaller magnetís assemblies and, therefore, also to smaller overall machines.

Smaller machines are more economic in their production and of lower cost.

Furthermore, to get the magnetocaloric machines to be an alternative for automobile refrigeration, small magnet’s masses are essential and, therefore, new solutions to allow them are required.

HIGH-FREQUENCY MODULES

Kitanovski and Egolf (2010) made a proposal how higher frequencies than in up-to-present realized prototypes can be obtained. In their solution a thin magnetocaloric material layer is built in a sandwich structure between two thermomagnetic layers (see Fig.’s. 5-7).

Furthermore, these three components are layered between two microchannels occurring on each side of the now complete module. A stack of such modules yields the core of an alternative magnetic heat pump, refrigerator or energy conversion machine.

In such a new machine the operation principle is completely different than in prototypes described, for example, in Yu et al. (2010a). The magnetocaloric material is layered and does not need to be porous. Porosity would even be a disadvantage, because the thermal conductivity is usually reduced by the  occurring voids containing fluid.

Furthermore, the material is not rotating from one fluid domain to the other.

In the new device the material is located statically between two fluid channels, one with cold and the other with hot fluid. A schematic drawing of such a device is shown in Fig. 5 and a cylindrical practical realization in Fig. 6.

Figure 5: The proposed sandwich structure contains a magnetocaloric material layer between two thermoelectric switches and two microchannels. The small arrows represent heat flows from hot to cold areas.

Figure 6: A full single cylindrical layer of a new magnetic heating device, refrigerator or energy conversion apparatus is shown in this perspective view on the left and a zoomed part of it on the right-hand side (from Kitanovski and Egolf, 2010).

Figure 7: Nanowires performed with Ni with a characteristic diameter of d=200 nm. Thermoelectric materials integrated in the composites can be of several kind: conventional thermoelectric materials like Bismuth, Tellurium are advantageous, but we  also explore the potential of metallic alloys, like NiCu and NiCr, which exhibit interesting figures of merit Z at nanoscale. Picture: Anne-Gabrielle Pawlowski.

In the magnetized state the magnetocaloric material heats up and the thermal switch to the left is closed and avoids any heat to flow away into the channel containing the cold fluid (see Fig. 5 on the left-hand side). The thermal switch on the right is open and on this side lets heat flow into the channel with hot fluid.The occurring processes are just contrary in the demagnetized state shown in Fig. 5 on the right-hand side. Here the thermal switch on the left-hand side is open and heat can flow from the cold fluid to the even colder magnetocaloric material layer that has just left the magnetic field.

The demagnetization process is the actual cooling process. Now in this time period, the thermal switch on the right-hand side does not permit any heat to flow from the hot fluid into the magnetocaloric material domain. If a machine contains such sandwich structures, the switching gates allow the cold and hot fluid to constantly flow in the same direction through their channels. The flows in the two channels are preferably designed to be counter current flows. With such elements there are no limits to the frequency of the system given by the fluids.

Restrictions only occur by the diffusion of the heat into and out of the magnetocaloric material, the switching frequency of the thermal gates or the magnetocaloric effect itself.

Magnetocaloric materials with a second-order phase transition perform much better than those with a first-order transition. The transition time of a second-order phase transition can reach the order of a millisecond corresponding to a frequency of 1000 Hz (Brück, 2009).Therefore, this should not be the limiting factor in the proposed newmagnetocaloric device! Eventually the magnets themselves could be the limiting factor (see Chapt. 8).

CLASSICAL AND NANO-SCALE PELTIER ELEMENTS

Thermoelectric devices are applied in the Péltier mode to heat or/and to cool and in the Seebeck mode for energy conversion (see e.g. in CRC Handbook of Thermoelectrics (Rowe, 1995). The devices must be designed and optimized for each of these applications

and usually cannot be used for both processes, because also the temperature levels are very different and that demands elements designed with different materials.

Nanotechnology now opens the door for new developments of efficient small Péltier element layers or films. Such developments were performed by Kumar et al. (2010) in ultrathin films, quantum wires and carbon nanotubes. Dillner (2008) studied the effect of thermotunneling on the performance (figure of merit) of such ndevices. Three dimensional nano pattern films were produced and studied recently by Yu et. al. (2010b). Furthermore, Gravier et al. (2006) performed physical modelling and numerical simulations of nano pillars and compared numerical results withnexperimental data, showing that in certain applications the thermal inertianshows an influence on the performancenand must be taken into consideration.

Nanowires performed from Ni are shown in Fig. 7. The thermal switch used and presented in the present article is a flexible ultra-thin Péltier module made up of 20 micrometer thick nanostructured composite films. The thin films make them particularly suitable to coat practically any surface.

AN EXPLANATION OF THE THERMOELECTRIC SWITCH

Thermoelectricity denotes the effect of interrelations between electricity and thermodynamics. One distinguishes three such main effects, namely then Péltier effect, the thermoelectric effect (Seebeck effect), and the Thomson effect. They are all physically related. For the present work actually only the first one is relevant. The Péltier effect is the effect where an electric current leads to a cold and hot part in a device, which is usually located at the two different boarder sides of a plate-like structure. It is the inverse effect, of the Seebeck effect, which produces from a source and a sink at different temperatures a current. It now becomes clear that with a Péltier device one can heat and cool and with a device applying the Seebeck effect one can produce electricity from a thermal source and sink. The Thomson effect, discovered in 1856 by William Thomson, who was later named Lord Kelvin, describes the change in heat transport in a circuit showing a temperature gradient and a current. This effect is overlapped by the resistance heating, and because it is a very small effect, it is not so easy observable.

The full and detailed theory, briefly described in this chapter, is presented in Egolf et al. (2012). For a more popular-scientific explanation of the phenomena, we observe Fig. 8, where a metal is heated at its left-hand side and cooled at the right-hand side.

Figure 8: A horizontal temperature directional derivative gives rise to an electric potential (after Kasap, 1997). The situation describes a metal or a n-type semiconductor. The white little spherical objects represent electrons. Their mean velocity is higher at the hot end.

The electrons in the heated region contain more energy and have greater velocities than the ones at the cold end. This leads to electron diffusion to the cold end and the electron density increases at the right-hand side. Because of this, on the left-hand side more positive ions are found. After some time, an equilibrium situation is reached, where the created electric field prevents a further increase of this electron diffusion.

This explains the potential difference as shown in the drawing of the positive and negative sides of the metal or ntype semiconductor slab. In the case of a p-type semiconductor, it is the holes that are more energetic on the left-hand side. In this case they diffuse horizontally to the right. Therefore, now the negative overall charge is located on the left-hand side and the positive on the right-hand side, just opposite to the situation in a n-type semiconductor. The nanowire n and p elements are connected to create a thin film Péltier thermal switch. By adapting the temperature on the outer part of these switches contacted by the fluid to the fluid’s temperature, a heat flux can be avoided.

On the other hand, in the other mode by increasing the temperature between the switches and the fluid even more an even higher heat flux is obtained. This leads to a kind of electronic pumping of heat.

THE COEFFICIENT OF PERFORMANCE

The quality of thermodynamic devices is described by their coefficient of performance, COP. The highest obtainable value in nature or technics is the COP of a Carnot machine. If one divides the COP of a real device by the COP of the ideal Carnot device, COPCarnot, one obtains a value between zero and one, because the second value (denominator) is equal or larger than the first number (nominator).

This measure is named exergy efficiency and is very often given in percentage.

The coefficient of performance COP of the thermal switches must be distinguished from the COP of the overall magnetic heat pump or/and refrigerator.

The COP of the thermal switches takes into account how much electrical energy is demanded to produce a cold and hot side each. The utilization of hot and cold leads to an improvement of the COP compared to applications where only one part is of importance.

The full theory of the determination of the COP of the thermal switches is outlined in a scientific-technical article, which was frequently published (see Egolf et al., 2012). Its results are graphically presented in Fig. 9.

Figure 9: The coefficient of performance of a Péltier element that is simultaneously cooling and heating on the two opposite sides is shown in this figure. Such an element yields a thermal switch. As a basis for this figure the COP of the Carnot thermal switch is assumed to show the arbitrarily chosen value COPCarnot=100. A very strong decrease of the COP with an increase of θ₂can be noticed in this figure.

To have a good interpretation of this figure, one needs to have knowledge on the two dimensionless numbers given as abscissa and as a free parameter. There are three powers, respecttively energy fluxes of importance.

The first is the electrical power to drive the thermal switch. The second is the electrical heating by the electric resistance of the device and the third the internal heat flux from the hot to the cold side. The two last energy fluxes are energy losses and must be as

good as possible minimized. The first dimensionless number θ₁is the ratio of the internal heat flux to the driving electric power of the device. Therefore, it is clear that a low value of

θ₁is favorable.The second dimensionless number θ₂is the ratio of the electric energy loss divided by the electric energy consumption. Also here a high loss in the nominator leads correctly to a smaller coefficient of performance as can be seen in the figure.

Generally one can see that high values of the COP are actually possible to be obtained. But it is expected that the power to drive the thermal switches is of minor importance compared to the energy per unit of time which the magnetic refrigerator demands, so

that its influence on the overall COP of the machines will show practically no impact.

An interesting idea is that the electric power to operate the thermal switches is directly taken from the sweeping magnetic field, which leads to an electric induction in well-positioned coils. Such can only be performed with accurate electronics to obtain a good synchronization of the involved processes. On the other hand, this new idea simplifies the system substantially.

FIRST EXPERIMENTAL RESULTS

The experimental data listed in Table 1 are first results obtained with specimens of thermal switches performed with Ni nanowires. The Seebeck coefficient and the electrical resistance were measured in an experimental set-up configuration transverse to the film.

At the present stage of development, we demonstrate a temperature difference of up to 5 K across a film of a Nibased composite film in a free-standing configuration, i.e. without any load.

The obtained elevated temperature gradient of 2.5 105 K/m corresponds to a fictious temperature difference of 750 K across a 3 mm-thick commercial Peltier module!

AN ESTIMATE OF NEW REFRIGERATOR PROPERTIES

In the following a small and very approximate pocket calculator estimate of the performance of a magnetic refrigerator of the types built up to present is compared to that of a future magnetic refrigerator applying the new thermal nanowire switch technology.

To keep the discussion of these results reasonably brief, we propose you to concentrate mainly on the blue lines with the numbers 1, 4, 10, 14, 19 and finally 30. In line No. 1 the nominal cooling power of a refrigerator is presented.

Naturally for a comparison these values have to be identical for the conventional magnetic refrigerator, e.g. an active magnetic regenerator (AMR) machine (column on the lefthand side), and the new (in this article proposed) magnetic refrigerator with thermal switches (column on the righthand side). One sees that we have assumed a faster rotation of the new machine by a factor of only five (line No. 4). We are optimistic that higher values can be obtained.

On the other hand, Tishin and Spichkin (2012) made the remark that, beside the frequency limits given by the thermal switch, the magnetocaloric effect and the heat diffusion time, also the permanent magnet itself could show a limit as a result of its remanence property.

In future research the study of this effect must also be taken into consideration.

As already mentioned the operation of the thermal switches utilizes a minor amount of energy per time unit and therefore can be neglected.

This insight leads to identical coefficient of performance of the two types of machines as seen in line No. 10. Because of the higher frequency the magnetocaloric material makes correspondingly more heating and cooling cycles and by this the necessary mass of this solid refrigerant can be chosen smaller by a factor of six (line No. 14)! The smaller rotator demands a smaller magnets assembly and the mass of the permanent magnets is estimated to drop down at least a factor of three (line No. 19).

This is essential for the size, weight and cost of a magnetic refrigerator.

For the thermal switches a combination of three layers was assumed to be applied and the calculated coefficient of performance, COP, for this combined system is estimated to be approximately twenty (line No. 30). One has to note that the thermal resistance has not yet been taken into consideration, because of a lack of successfully determining it experimentally. Therefore, a lower value must be expected to finally occur.

CONCLUSIONS AND OUTLOOK

At present the most important limit to high-performance magnetic refrigerators is their low frequency. This results in large magnets assemblies which cause rather high costs of the envisaged magnetic refrigeration machines.

The proposal is an alternative solution which applies thermal switches that allows higher frequencies than in up-to-present realized prototypes of magnetic refrigerators and these

switches and their experimental and theoretical investigation yield the basis for this work.

The predictions made by simple estimates and calculations are based on first experimentally determined characteristic quantities of the nanowire thermoelectric switches, which are the Seebeck coefficient, the electric resistance (which still is too high) and would be the thermal resistance (not yet measured).

Further improvement by optimization is expected to occur! Additional important experiments will be the examination of the behavior with load and the determination of the maximal switching frequency of the thermal switches.

A central further new idea is to drive the Péltier thermal switches by currents induced by the anyway occurring moving magnetic field in a magnetic refrigerator. Finally also many practical aspects must be investigated as e.g. the durability of the thermal switches and simple and cheap production methods! If this technology will work, it will be possible to beat conventional refrigeration in numerous important refrigeration markets.

This technology is so promising that even magnetic automobile refrigeration, where a high mass is very critical, could become feasible! Initiated by us automobile companies today already perform extensive research on this new technology (see e.g. Tasaki et al., 2012).

ACKNOWLEDGEMENTS

We are grateful to Andrej Kitanovski for inventive ideas and Gilles Courret and Anne-Gabrielle Pawlowski for helpful remarks. Furthermore, we thank Axel Hartenstein (Energie and Innovation AG, Winterthur) for his interest in this technology.

_

REFERENCES

Brück E., 2005. Developments in magnetocaloric refrigeration, Institute of Physics Publishing. J Phys. D: Appl. Phys. 38, R381-R391.

Brück E., 2009. Personal communication with the first author.

Dillner U., 2008. The effect of thermotunneling on the thermoelectric figure of merit. Energy Convers. Mgmt 49, 3409-3416.

Egolf, P.W., Rosensweig, R.E., 2007. Magnetic refrigeration at room temperature. 20th Informatory Note on Refrigeration Technologies of the International Institute of Refrigeration, Paris, October, 1-8.

Egolf P.W., Gendre F., Kitanovski A., 2007.Magnetic heat pumps – An approximate energy efficiency and cost study: Part II, Second International Conference on Magnetic Refrigeration at Room Tempertaure of the International Institute of Refrigeration IIF-IIR,

Portoroz, Slovenia, 11-13 April, 399-408.

Egolf P.W., Rosensweig R.E., 2008.Magnetic refrigeration at room temperature. Industria&Formazione, Special Issue Refrigeration and Air Conditioning, in collaboration with the International Institute of Refrigeration, IIF/IIR and the United Nations Environmental Programme, UNEP, 45-50.

Egolf P.W., Gravier L., Francfort T., Pawlowski A.-G., Courret G., Croci M., 2012, Nanowire thermal switches for magnetic heating, refrigeration and energy conversion, Final report Hesso project ThEleMac II, June. 

Gravier L., Fukushima A., Kubota H., Yamamoto A., Yuasa S., 2006.Peltier effect in multilayered nanopillars under high density charge current. J. Phys. D: Appl. Phys. 39, 5267- 5271.

Gschneidner Jr. K.A., Pecharsky V.K., Tsokol A.O., 2005. Recent developments in magnetocaloric materials. Inst. of Phys. Publishing, Reports on Progress in Physics, 68, 1479-1539.

Kasap S.O., 1997, Thermoelectric effects in metals: Thermocouples. e-booklet.

Kitanovski A., Egolf P.W., 2006. The thermodynamics of magnetic refrigeration. Review article of the International Journal of Refrigeration, 29, 3-21. 

Kitanovski A., Diebold M., Vuarnoz D. Gonin C., Egolf P.W., 2008a. Application of magnetic refrigeration and its assessment, Final report of the project 101’776/152’191 for the Swiss Federal Office of Energy, 1-42, April.

Kitanovski A., Egolf P.W., 2008b, Application of magnetic refrigeration and its assessment. Moscow International Symposium on Magnetism, MISM, Moscow, 20-25 June, 23RP-D-6.

Kitanovski, A., Egolf, P.W. 2010. Innovative ideas for future research on magnetocaloric technologies. Int. J. Refrigeration, 33 (3), 449-464.

Kumar A., Choudhury S., Saha S., Pahari S., De D., Bhattacharya S., Ghatak K.P., 2010. Thermoelectric power in ultrathin films, quantum wires and carbon nanotubes under classically large magnetic field: Simplified theory and relative comparison. Physics B 405, 472-498.

Rowe D.M. (Ed.), 1995. CRC Handbook on Thermoelectrics. CRC Press, Boca Raton, ISBN 0-8493-0146-7.

Tasaki Y., Takahashi H., Yasuda Y., Okamura T., Ito K., 2102. A study on the fundamental heat transport potential of an in-vehicle magnetic refrigerator. Fifth International Conference on Magnetic Refrigeration at RoomTemperature of the International Institute of Refrigeration IIF-IIR, Grenoble, France, 17-20 September, 445-452.

Tishin A.M., SpichkinY.I., 2003.The magnetocaloric effect and its applications. Series in condensed matter physics, Institute of Physics, Bristol, United Kingdom.

Tishin A.M., Spichkin Y.I., 2012. Personal communication at the Fifth International Conference on Magnetic Refrigeration at Room Temperature Thermag V in Grenoble, 17-20 September.

Yu B., Liu M., Egolf P.W., Kitanovski A., 2010a. A review of magnetic refrigerators and heat pump prototypes built before the year 2010. Int. J. Refrigeration 33 (6), 1029-2060.

Yu Y. Hu Z.-D., Zhi J.-F., Sun W.-T., Chen Q., Peng L.-M., 2010b. Three-dimensional Bi2Se3 nanopattern films self-assembled with ultrathin nanosheets on the surface of Se nanotubes. Journal of Crystal Growth 312, 3455-3460.