Highly efficient regenerators for magnetic cooling
In the present project the core of a magnetic refrigeration device, the active magnetic regenerator (AMR), is in focus. It is key to have a regenerator that simultaneously has relatively low flow friction and large (enough) heat transfer coefficient / area. Those are the two parameters that are of the most interest in this project. However, a range of other circumstances are also very important for successful application of AMRs. These include material properties (both magnetocaloric and thermal), demagnetizing effects etc.
Regenerator geometries and their properties
The geometry of a thermal regenerator is crucial for its performance. The specification of the geometry includes the outer dimensions of the regenerator bed (length and cross sectional area) as well as the specific properties of the bed. These are the porosity (or voidage) of the bed, the hydraulic diameter of the bed, the specific heat transfer surface area and other related properties. The hydraulic diameter is an equivalent diameter that essentially describes the flow resistance (i.e. how much pressure drop there will be across the bed for a given Reynolds number). The specific heat transfer surface area describes the contact between the heat transfer fluid and the active regenerator solid.
How does an active magnetic regenerator work?
An active magnetic regenerator (AMR) has several tasks to do. It acts as a thermal storage medium (i.e. a classical thermal regenerator), while also supplying the required work input to achieve a cooling effect. The latter happens through the magnetocaloric effect (MCE), which is an intricate property arising in ferromagnetic material when an applied field is varied over them. The former is a device, or actually a specific type of heat exchanger, that undergoes four phases. Firstly, a cold fluid enters at the cold end. Secondly, the fluid is at rest. Thirdly, a hot fluid enters at the hot end and fourthly the fluid is at rest again. If this cycle is timed with the application / removal of an external magnetic field it is possible to build up and maintain a temperature gradient between the two ends. The one where the hot fluid enters would, in the case of domestic refrigeration, be the backside of the refrigerator and the one where the cold fluid enters would be the inside of the refrigerator.
The efficiency of this process is a function of many process variables and geometric parameters. Further down on this website these are described in some detail. The research conducted in this two-year project includes many aspects of the AMR as well as external stays at the University of Wisconsin, Madison (autumn 2012) and the University of Victoria, BC, Canada (Spring 2013).
Solid thermal conductivity
One of the many properties investigated in this project is the solid thermal conductivity of the regenerator material. The questions that needed answering were: is there an optimal value or should it “just” be as high as possible? And: what is tolerable range of values that is acceptable?
This was enlightened in a recent publication  where the performance of an AMR was investigated as a function of the solid thermal conductivity. It was found that at values above 8-10 W/(m*K) the AMR is on safe grounds. Below this value the performance may decrease drastically depending on the operating conditions. The whole point is that a certain balance between longitudinal (or axial) conduction and transverse conduction should be in place. Ideally, the transverse conduction should be infinite while the longitudinal should be zero. That is of course not possible, and an optimum region thus exists and was found and described in the reference .
In general when a magnetic field is applied to a ferromagnetic material it will respond with a so-called demagnetizing field. This means that the actual magnetic field inside the solid is smaller than the applied field. Since the MCE is a function of the internal magnetic field (higher is better), it is crucial to minimize demagnetizing effects or at least to know how to handle them.
The demagnetizing field is very much a function of geometry (shape and aspect ratio of the magnetic material) as well as the orientation of the applied field and the properties of the magnetic material (its magnetization as a function of temperature) and thus also the temperature itself. To correctly account for demagnetization it is thus necessary to couple the applied field (which will vary in space and time periodically), the regenerator geometry and the transient temperature profile across the bed as well as having high quality data for the magnetic properties of the material. This has been described in detail in a range of publication where K.K. Nielsen has contributed significantly and the impact on the AMR performance is described in detail in Ref. .
Heterogeneous parallel plate stacks
Certain regenerator geometries are regular in the sense that they experience laminar flow profiles where the flow path is not broken downstream. Such geometries have very little flow resistance compared to geometries where the flow path is broken several times downstream (which happens for, e.g., packed particles). As an example, parallel plates were considered. These promise a relatively high heat transfer to flow resistance ratio and are thus interesting. However, it has been found through vast experiments that as the flow channels decrease in size (and are well below 1 mm in height), the performance decreases. In the current project it has been found both experimentally () and theoretically ([I,III]) that this is at least partially caused by heterogeneity in the stack, i.e. the individual channels have different heights (caused by manufacturing tolerances). The impact on bulk (overall) heat transfer performance was quantified in Ref. [I] and the impact on the performance of AMRs in Ref. [III].
The influence of the regenerator wall / housing
This is ongoing… more info will follow soon!
List of publications
(Published in international peer-reviewed journals)
 K.K. Nielsen
, A. Smith, C.R.H. Bahl, U.L. Olsen, “The influence of demagnetizing effects on the performance of active magnetic regenerators”, 2012, Journal of Applied Physics, 112, 094905 
A. Smith, C.R.H. Bahl, R. Bjørk, K. Engelbrecht, K.K. Nielsen
, N. Pryds, “Review: Materials challenges for high performance magnetocaloric refrigeration devices”, 2012, Advanced Energy Materials, 2 (11), 1288-1318 
K. Engelbrecht, D. Eriksen, C.R.H. Bahl, R. Bjørk, J. Geyti, J.A. Lozano, K.K. Nielsen, F. Saxild, A. Smith, N. Pryds, “Experimental results for a novel rotary active magnetic regenerator”, 2012, International Journal of Refrigeration, 35 (6), 1498-1505 
C.R.H Bahl, D. Velazquez, K.K. Nielsen, K. Engelbrecht, K.B. Andersen, R. Bulatova, N. Pryds, “High performance magnetocaloric perovskites for magnetic refrigeration”, 2012, Applied Physics Letters 100, 121905 
K.K. Nielsen, K. Engelbrecht, D.V. Christensen, J.B. Jensen, A. Smith, C.R.H. Bahl, ”Degradation of the performance of microchannel heat exchangers due to flow maldistribution”, 2012, Applied Thermal Engineering 40, 236-247 
K.K. Nielsen and K. Engelbrecht, “The influence of thermal conductivity of the solid in active magnetic regenerators”, Journal of Physics D: Applied Physics, 2012, 45, 145001 
C.R.H. Bahl, R. Bjørk, K.K. Nielsen, A. Smith, ”Properties of magnetocaloric materials with a distribution of Curie temperatures”, 2012, Journal of Magnetism and Magnetic Materials 324 (4), 564-568. 
A. Tura, K.K. Nielsen, A. Rowe, “Experimental and Modeling results of a parallel-plate based active magnetic regenerator”,
International Journal of Refrigeration, 2012 35 (6), 1518-1527
 C.R.H. Bahl, K. Engelbrecht, R. Bjørk, D. Eriksen, A. Smith, K.K. Nielsen, N. Pryds, ”Design concepts for a continuously rotating active magnetic regenerator”, 2011, International Journal of Refrigeration 34, 1792-1796
(Submitted to international peer-reviewed journals)
K.K. Nielsen, K. Engelbrecht, C.R.H. Bahl, “The influence of thermal cross talk and flow maldistribution on the performance of inhomogeneous parallel plate heat exchangers”, 2012, submitted to International Journal of Heat and Mass Transfer [II]
J.A. Lozano, K. Engelbrecht, C.R.H. Bahl, K.K. Nielsen, U.L. Olsen, J.R. Barbosa Jr., A.T. Prata, N. Pryds, “Performance analysis of a rotary active magnetic refrigerator”, 2012, submitted to Applied Energy
[III] K.K. Nielsen, C.R.H. Bahl and K. Engelbrecht, ”Flow maldistribution in heterogeneous parallel-plate active magnetic regenerators”, 2012, submitted to Journal of Physics D: Applied Physics
(Published in conference proceedings)
[i] K.K. Nielsen
, C.R.H. Bahl, A. Smith, K. Engelbrecht, U.L. Olsen, N. Pryds, “The influence of non-magnetic properties on the AMR performance”, 2012, in proc. Fifth International Conference on Magnetic Refrigeration at Room Temperature, ed. P.W. Egolf [ii]
J.A. Lozano, K. Engelbrecht, C.R.H. Bahl, K.K. Nielsen
, J.R. Barbosa Jr., A.T. Prata, N. Pryds, “Experimental and numerical results of a high frequency rotating active magnetic refrigerator”,
2012, in proc. Fifth International Conference on Magnetic Refrigeration at Room Temperature, ed. P.W. Egolf [iii]
C.R.H. Bahl, K. Engelbrecht, D. Eriksen, J.A. Lozano, R. Bjørk, J. Geyti, K.K. Nielsen
, A. Smith, N. Pryds, “Development and experimental results from a 1 kW prototype AMR”, 2012, in proc. Fifth International Conference on Magnetic Refrigeration at Room Temperatur, ed. P.W. Egolf [iv]
L. von Moos, K.K. Nielsen
, K. Engelbrecht, C.R.H. Bahl, “Experimental investigation of the effect of thermal hysteresis in MnFeP1-xAsx materials applied in AMR devices”, 2012, in proc. Fifth International Conference on Magnetic Refrigeration at Room Temperature, ed. P.W. Egolf
[v] U.L. Olsen, C.R.H. Bahl, K. Engelbrecht, K.K. Nielsen, Y. Tasaki, H. Takahashi, Y. Yasuda, “Modeling of in-vehicle magnetic refrigeration”, 2012, in proc. Fifth International Conference on Magnetic Refrigeration at Room Temperature, ed. P.W. Egolf
Kaspar K. Nielsen greatly acknowledge the support of the Danish Research Council for Independent Research | Technology and Production Sciences under the Danish Ministry of Science, Technology and Innovation (project nr. 10-092791).