Tsuyoshi KawanamiShigeki Hirano Department of Mechanical Engineering,Kobe University,1-1,Rokkodai-cho,Nada-ku,Kobe657-8501,JapanMasahiro Ikegawa Division of Human Mechanical Systems andDesign,Graduate School of Engineering,Hokkaido University,N13-W8,Kita-ku,Sapporo060-8628,JapanKoji Fumoto Department of Mechanical Engineering, Kushiro National College of Technology,Otanoshike-Nishi2-32-1,Kushiro084-0916,Japan Cooling Characteristics of Regenerative Magnetic Refrigeration With Particle-Packed BedThe aim of our study was to elucidate the fundamental cooling characteristics and to improve the cooling characteristics of a room-temperature magnetic refrigerator oper-ated under an active magnetic regenerator(AMR)cycle.The AMR refrigeration cycle, which includes a thermal storage process and a regeneration process,is used to realize a practical magnetic refrigerator operating near room-temperature.The basic compo-nents of the target AMR system are a magnetic circuit,test section,fluid-displacing device,and associated instrumentation.Spherical gadolinium particles are packed in the test section as the magnetic working substance,and air and water are used as heat transferfluids.The cooling characteristics of the target AMR system under various op-erating conditions are investigated.The results show that the AMR cycle is very effective in improving the cooling performance of the room-temperature magnetic refrigerator.͓DOI:10.1115/1.4003450͔Keywords:magnetic refrigeration,magnetocaloric effect,heat pump,regenerative cycle1IntroductionIn recent years,global warming has become an international concern,and it has become essential to reduce the emission of greenhouse gases.Instead of chlorofluorocarbons͑CFCs͒,whose use is restricted because they cause a depletion of the ozone layer, hydrofluorocarbons͑HFCs͒are used as refrigerants.Recent re-searches,however,have shown that HFCs also have a large green-house effect.Therefore,it is desirable to develop a new alternative refrigerant and an environmentally friendly refrigeration system. Magnetic refrigeration is a cooling method that is based on the magnetocaloric effect͓1–3͔.This effect is an entropy change in-duced by a change in the magneticfield in a particular kind ofmaterial.The magnetic material generates and absorbs heat due tothe magneticfield change,and it can be used as a working mate-rial.The magnetic refrigerator does not require F-gases and thushas the potential of being an alternative refrigeration method.When the operation temperature of a magnetic refrigerator isshifted to near room-temperature,the heat capacity of the mag-netic working substance͑magnetocaloric material͑MCM͒͒in-creases,and the temperature change occurring due to the magneticfield change decreases.Therefore,an active magnetic regenerator ͑AMR͒cycle that includes a thermal storage process and a regen-eration process is a highly effective approach for increasing thetemperature difference between the hot and cold ends of a mag-netic refrigerator.The general concept of the AMR cycle wasproposed by Barclay and Steyert͓4͔,and they showed the possi-bilities of using an AMR in a room-temperature magnetic refrig-erator.Moreover,some experimental and analytical studies wereconducted for investigating the detailed cooling characteristics ofan AMR͓5–8͔.In addition,valuable operation data of prototyperoom-temperature magnetic refrigerators have been reported ͓9–12͔.Usually,water is used as the heat transferfluid in an AMRrefrigeration cycle.However,in an air conditioning system,room air can be used as the heat transferfluid.Therefore,experimental and analytical studies have been conducted to understand the fun-damental cooling characteristics and improve the performance of a magnetic refrigerator operated with an AMR refrigeration cycle using water and air as the heat transferfluids.The primary aim of the present study was to gain fundamental knowledge about how the efficiency of room-temperature mag-netic refrigerators can be improved.In this study,the cooling characteristics of the AMR refrigerator were estimated by per-forming a numerical simulation.2Magnetic Refrigeration2.1Magnetic Working Substance.It is well known that the magnetocaloric effect of a magnetic working substance becomes maximal at the Curie point.Spherical gadolinium particles are used as the magnetic working substance in this study.The physi-cal properties of gadolinium are listed in Table1.The adiabatic temperature change⌬T ad,which occurred when the magneticfield was removed from the magnetic working substance,was mea-sured experimentally,as shown in Fig.1.The horizontal axis shows the initial temperature of the material T i.Figure1shows that⌬T ad during the demagnetization process tends to be maxi-mum at around20°C because that is the Curie point of gado-linium;further,it is confirmed that the maximum values of⌬T ad are approximately4.2°C for2.0T and2.6°C for1.0T.2.2AMR Cycle.Figure2shows the basic cycle͑right side͒and T-s diagrams͑left side͒of the AMR refrigerator.In thisfig-ure,the dashed lines show thefluid temperature distribution of the packed bed in the AMR just after each process begins and the solid lines show the temperature at the end of each process.The AMR cycle includes the following four processes,which are based on the regenerative Brayton cycle:͑a͒magnetization pro-cess,͑b͒fluidflow process͑from cold end to hot end͒,͑c͒demag-netization process,and͑d͒fluidflow process͑from hot end to cold end͒.Because the temperature gradient in the packed bed becomes steeper with each passing cycle,the temperature difference be-tween the hot and cold ends increases gradually.However,after aContributed by the Heat Transfer Division of ASME for publication in the J OUR-NAL OF H EAT T RANSFER.Manuscript received November28,2009;final manuscriptreceived November11,2010;published online March4,2011.Assoc.Editor:Yo-gendra Joshi.sufficient number of cycles,the temperatures at both the hot and cold ends remain almost constant.The operation sequence of the present AMR cycle is shown in Fig.3.3Experiment3.1Experimental Apparatus.The schematic diagram of the experimental setup based on the AMR cycle is depicted in Fig.4.The experimental apparatus consists of a test section as the AMR particle-packing bed,a linear drive fluid displacer that drives the heat transfer fluid reciprocately with the electrical linear-motion slider ͑see Fig.4,“electric slider No.2”͒,a permanent magnetic circuit,and a data acquisition system.Both sides of the test sec-tion have retention spaces for the heat transfer fluid,which serve as a hot end and a cold end,and each end of the test section is connected to the fluid displacer.The magnetic circuit is a closed circuit composed of two opposite Halbach magnets with a 20mm gap distance.The maximum magnetic flux density is about 2.0T at the center of the gap between the two magnets,as shown in Fig.5.The test section and displacer are installed on the moving stage of the electrical linear-motion slider ͑see Fig.4,“electric slider No.1”͒controlled by a personal computer.Figure 6shows the test section.Spherical gadolinium particles ͑mean diameter:0.6mm ͒are packed in an acrylic tube.The length of the particle-packed bed is 60mm and the inner diameter is 12mm.The weight of the packed gadolinium is 33.4g.The gadolinium particles for testing are filled in the packed bed at an average packing rate of 0.63by volume ͑i.e.,porosity =0.37͒.The void volume of the particle-packed bed is filled with the heat transfer fluid.To measure the temperature distribution in the test section,three platinum resis-tance temperature detectors ͑RTDs ͒are installed at the hot end ͑T h ͒,center ͑T center ͒,and cold end ͑T c ͒of the test section.The operating frequency of the present AMR cycle was set from 4s to 10s,and all of temperature data were recorded every 0.1s intothe data acquisition system.From the result of the error analysis,the uncertainty of the present temperature measurement system is estimated as Ϯ0.38°C for 20°C.3.2Setting Parameters.The volume V of the fluid flow is obtained from the displaced volume of the displacer,and the flow rate F is calculated from the moving time of the displacer.The relative fluid flow volume V ءand relative volumetric flow rate F ءare defined as follows:V ء=V V void,F ء=F V void͑1͒where V void is the void volume in the particle-packed bed.4Experimental Results4.1Fundamental Temperature Change in AMR Refrigera-tion Cycle.Figure 7shows the transition of temperature at the hot end and the cold end of the water-based AMR apparatus for an applied magnetic field of 2.0T for V ء=0.43and F ء=0.87s −1.This result shows that the temperature difference ⌬T between the hot end and the cold end increases with time t .The temperature difference ⌬T after 800s is larger than the adiabatic temperature change of 4.2°C,as shown in Fig.1.Therefore,it is confirmed that the AMR refrigeration cycle is effective in increasing the temperature difference between the hot end and the cold end of the magnetic refrigerator near room-temperature.4.2Effect of Magnetic Field on Cooling Characteristics.The relationship between the temperature differences ⌬T and V ءis shown in Fig.8for various magnetic fluxes.The relationship be-tween the temperature differences ⌬T and F ءis shown in Fig.9.At 1.0T and 2.0T,the temperature difference shows the same tendency for both various V ءand various F ء.Moreover,it can be observed that under all operating conditions,the temperature dif-ference ⌬T at 2.0T is larger than that at 1.0T.This indicates that increasing the magnetic field is effective for improving the perfor-mance of the magnetic refrigerator.However,even when the magnetic field doubles,the amount by which ⌬T increases is small at low F ءregion.The reason for this behavior is probably the increase in heat loss.In the water-based AMR cycle,it is believed that the temperatures of the magnetic material at the ends of the particle-packed bed affect the attained hot and cold temperatures.Since the time period of the fluid flow process increases with a decrease in F ء,it will be considered that the effect of heat loss increases with a decrease in F ء.The tem-perature gradient is generated in the particle-packed bed,and heat loss by conduction always exists significantly at low F ءcondition.4.3Cooling Characteristics of Water-Based AMR Cycle.Figure 10shows the temperature difference ⌬T in the case of the water-based AMR cycle for various V ءand F ءusing 2.0T magnet.These data indicate that the largest ⌬T can be obtained if the parameters are set to optimum values.This is because the tem-perature distribution in the packed bed is significantly affected by the energy balance between the heat transferred from/to the mag-netic working substance to/from the fluid and that transported by the fluid flow.It is important to ensure the exchange of sufficient thermal energy between the magnetic working substance and the heat transfer fluid during the fluid flow process.However,the amount of exchanged thermal energy in a fluid flow process de-creases when the fluid flow volume is small.As a result,both the stored heat and the amount of heat regenerated in the AMR cycle decrease.On the other hand,when V ءand F ءincrease to a certain extent,it becomes difficult to bring about a larger temperature change because of the larger heat capacity of the fluid.Thus,the effectiveness of the thermal storage and the regeneration de-creases,and as a result,⌬T becomes small.Hence,in order toTable 1Physical properties of gadolinium †13,14‡QuantityValue Atomic No.64Atomic mass 157.26g Curie temperature 20°C Density7860kg /m 3Lattice heat capacity 298J /kg K Thermal conductivity8.8W /m KFig.1Adiabatic temperature change of gadolinium,the data were measured for 2.0T …closed diamonds …and 1.0T …open circles …obtain the largest ⌬T ,it is necessary to set an appropriate operat-ing condition as the temperature profile in the packed bed be-comes steep.4.4Cooling Characteristics of Air-Based AMR Cycle.The temperature transition at the hot and cold ends of the test section in the case of the air-based AMR is shown in Fig.11.From the figure,it is found that the temperature difference between the hot end and the cold end increases with time t .The temperature dif-ference ⌬T after 500cycles is larger than the adiabatic tempera-ture change shown in Fig.1.The effectiveness of the AMR cycle is confirmed even in the case when air is used as the heat transfer fluid.Figure 12shows the temperature difference ⌬T for various V ءand F ء.Although no optimum operating condition is found in the present parameter range,the air-based AMR shows the same ten-dency as the water-based AMR,i.e.,the temperature difference ⌬T increases as V ءand F ءincrease.However,the values of V ءand F ءof the air-based AMR under the optimized condition are much larger than those of the water-based AMR.The heat capacity of air is smaller than that of water;thus,a large-volume fluid is neces-sary for the air-based AMR.5Numerical AnalysisIt is extremely important to elucidate the heat transfer phenom-ena inside the particle-packed bed of the AMR in order to under-stand the fundamental cooling mechanism.The transitional tem-perature change in an AMR particle-packed bed was considering in detail ͓6͔.Moreover,the heat transfer characteristics in a packed bed were showed with a computer simulation in various parameters ͓7,8͔.Hence,in the present study,an appropriatesimu-Fig.2Transition of temperature distribution in a test section with AMR:…a …magnetization process,…b …fluid flow process,…c …demagnetization process,and …d …fluid flow processlation model of the heat transfer mechanism inside the packed bedis devised;further,numerical analyses of the temperature profile inside the particle-packed bed of the AMR cycle are performed.5.1Analytical Model.The schematic of the analytical model is shown in Fig.13.In this study,the particle-packed bed is as-sumed to be a structure having a bundle of many small circularchannels ͑channel diameter is D 2and number of channels is n t ͓͒15͔.The values of D 2and n t are defined on the basis of the void volume and the heat transfer surface area in the actual testing particle-packed bed,and they are given byD 2=d p ͑s D 12L −4M s ͒6M s ͑2͒n t =36M s2s d p 2L ͑s D 12L −4M s ͒͑3͒where d p M s ,L ,and s are the diameter of spherical magnetic material,the mass of magnetic material,the length of testsection,Fig.3Operation sequence for the present AMRcycleFig.4Schematic diagram of the experimental setup:…1…test section as the AMR particle-packing bed,…2…2.0T Halbach magnetic circuit with a 20mm gap distance,…3…fluid displacer that drives the heat transfer fluid reciprocately,…4…electric linear-motion slider No.1,…5…electric linear-motion slider No.2,…6…platinum resistance temperature detector,…7…data acquisi-tion unit,and …8…personalcomputerFig.5Distribution of magnetic field induction in-betweenmagnetsFig.6Dimension of the test section and installation of the temperaturedetectorsFig.7Experimental temperature distributions at 2.0T with wa-ter as the heat transfer fluid for V ء=0.43and F ء=0.87s−1Fig.8Distribution of temperature difference of water-based AMR as a function of relative flow volume and magnetic flux for F ء=0.21and the density of magnetic material,respectively.The heat transfer fluid,main flow velocity is u 1in the test section,passes through the small channels with a velocity u 2and it is defined asu 2=u 1͑4͒5.2Governing Equations.As shown in Fig.13,the test sec-tion is classified into three regions:͑i ͒fluid region outside the material-packed bed,͑ii ͒fluid region inside a small straight chan-nel,and ͑iii ͒solid region.In addition to the diameter of the flow channel assumed as D 2is quite small,the fluid flow varies from 0to u 0or −u 0almost stepwise and keeps constant through the fluid flow,as shown in Fig.3.Therefore,we assumed the flow through test section as laminar flow.The temperature profile in the material-packed bed is calculated by solving the energy balance equation for each region.The energy equations for each region are expressed as follows,where x is the coordinate in the flow direction.͑i ͒Fluid region outside the material-packed bedf c f ͩץT f ץt +u 1ץT f ץx ͪ=eff ץ2T f ץx 2+4D 1K out ͑T room −T f ͒͑5͒͑ii ͒Fluid region inside the small straight channelf c f ͩץT f ץt +u 2ץT f ץx ͪ=ͩD 1D 2ͪ2eff ץ2T f ץx 2+4D 2h fs ͑T s −T f ͒͑6͒Fig.9Distribution of temperature difference of water-based AMR as a function of relative volumetric flow rate and magnetic flux for V ء=0.87Fig.10Relationship between the temperature difference andthe operating conditions for 2.0T magnetic flux:water-basedAMRFig.11Experimental temperature distributions at 2.0T with air as the heat transfer fluid for V ء=350and F ء=88s−1Fig.12Relationship between the temperature difference and the operating conditions for 2.0T magnetic flux:air-basedAMRFig.13Details of the simulation model͑iii ͒Solid regionf c f ץT s ץt =s ץ2T s ץx 2+4n t D 2͑1−͒D 12h fs ͑T f −T s ͒−4D 1͑1−͒D 12K out ͑T room −T f ͒+Q s͑7͒where K out ,h fs ,eff ,and Q s are the overall heat transfer coefficientbetween the heat transfer fluid and the surrounding air,the heat transfer coefficient between the heat transfer fluid and the mag-netic material,the effective thermal conductivity of the fluid in the void of the particle-packed bed,and the unit volumetric heat gen-eration and absorption value obtained by the magnetocaloric ef-fect,respectively.h fs is calculated based on the Nusselt number Nu=3.66,which can be applied to developed laminar flow in a tube.eff is obtained from the effective thermal diffusivity with oscillating flow ͓16͔.Q s is calculated using the experimental re-sult of the adiabatic demagnetization shown in Fig.1.The tem-perature of the heat transfer fluid and the magnetic material are set to 20°C as an initial condition,and the surrounding temperature is maintained at 20°C as a boundary condition.The time step was calculated and set to satisfy Courant–Friedricks–Lewey ͑CFL ͒condition automatically.This time step is short enough ͑ordinary,less than 0.1s ͒compared with the operation frequency span that is from 4s to 10s.In addition,the grid size ⌬x is fixed at 0.5mm.6Analytical Results6.1AMR Refrigeration Cycle.Figure 14shows the com-puted temperature transition at the hot and cold ends of the test section in the case of repeated operation of the AMR refrigeration cycle using water.From this figure,it is found that the tempera-ture difference between the hot end and the cold end gradually increases with time and asymptotically approaches a constant value.As is the case with the experimental result,the computed temperature difference in the steady state of the AMR cycle ex-ceeds the temperature difference obtained by the magnetocaloric effect.6.2Cooling Characteristics of Water-Based AMR.Figure 15shows the effect of the relative flow volume V ءon the tem-perature difference ⌬T .The relationship between the temperature difference ⌬T and the relative volumetric flow rate F ءis shown in Fig.16.In these figures,the computed results are compared with experimental data,and both sets of data show that the maximum temperature difference can be attained at optimum values of V ءand F ء,although the optimum values obtained from the computed and experimental results are somewhat different.The reason for this difference may be that in our analysis,the flow field in the test section is assumed to be uniform and the mixing effect of flow is ignored.6.3Cooling Characteristics of Air-Based AMR.Figure 17shows the numerical results of the temperature transition at both ends of the test section in the case that air is used as the heat transfer fluid.The figure indicates that,as is the case with the water-based AMR,the temperature difference increases gradually with time and asymptotically approaches a constant value.However,the result of the numerical simulation differs from the experimental result ͑shown in Fig.11͒in that the time required to reach the steady state in the numerical simulation is shorter than that required experimentally.The reason for this behavior is that the mixing effect of flow,which is neglected in the analysis,dis-turbs the rapid growth of the temperature gradient in an actual gadolinium-particle-packed bed.The temperature difference ⌬T for various V ءand F ءis shown in Figs.18and 19,respectively,in comparison with experimental data.As observed from these figures,the experimental dataandFig.14Analytical temperature distributions at 2.0T with water as the heat transfer fluid for V ء=0.43and F ء=0.87s−1Fig.15Distribution of maximum temperature difference at 2.0T of the water-based AMR form the present simulation as a function of relative volumetric flow rate for V ء=0.43,the data were obtained from analysis …closed circles …and experiment …open diamonds…Fig.16Distribution of maximum temperature difference at 2.0T of the water-based AMR form the present simulation as a function of relative flow volume for F ء=1.3,the data were ob-tained from analysis …closed circles …and experiment …open diamonds …numerical analysis data show a similar tendency.However,all parameter values in the latter are up to roughly 4.1°C larger than those in the former,probably for the abovementioned reason.Figures 18and 19show the existence of an optimum flow vol-ume V ءthat is not observed in the experiment due to the limitation of the experimental pared with the water-based AMR,the maximum temperature difference attained in the air-based AMR cycle is about 1/3.This seems to be due to the effect of the thermophysical properties of the heat transfer fluid,particu-larly the effect of the thermal capacity.Through these investiga-tions,it is found that the physical properties of a heat transfer fluid have a significant effect on the cooling characteristics of an AMR refrigerator.7ConclusionsThe cooling characteristics of a room-temperature magnetic re-frigerator operated with an AMR refrigeration cycle have been studied experimentally and analytically.As for experimental study,we newly introduced F ء͑relative volumetric flow rate ͒and V ء͑relative flow volume ͒to appreciate the optimum operating condition of magnetic refrigeration with AMR cycle,and we also introduced a new approach for numerical analysis,which has bundles of small channels to exchange heat with the heat transfer fluid.The accuracy need to be improved but these associated data between experimental and numerical results of heat transfer through particle-packed bed will greatly contribute the reciprocat-ing magnet refrigerator with AMR cycle operation.The following conclusions may be drawn from the present study.͑1͒The cooling characteristics of the magnetic refrigeratorvary with the applied magnetic field.͑2͒Either water or air is capable as the heat transfer fluid,andmoreover,the water-based AMR has a high capacity of heat transport and a possibility to raise the temperature differ-ence with a low fluid volume displacement.͑3͒As compared with the water-based AMR cycle,in the air-based AMR cycle,the optimized operating condition in-cludes a larger flow volume and higher flow rate.However,the heat capacity of air is smaller than that of water;thus,a large-volume fluid is necessary for the air-based AMR.It would induce the increase of pressure loss during air blow processes.AcknowledgmentThis research was financially supported by the national project of “Development of Nonfluorinated Energy-Saving Refrigeration and Air Conditioning Systems”of the New Energy and Industrial Technology Development Organization ͑Grant No.P05029͒.Nomenclaturec ϭspecific heat,J kg −1K −1D ϭinner diameter,md p ϭdiameter of spherical magnetic material,m F ϭvolumetric flow rate,m 3s −1F ءϭrelative volumetric flow rate,s −1h fs ϭheat transfer coefficient,W m −2K −1K out ϭoverall heat transfer coefficient,W m −2K −1L ϭlength of test section,m n t ϭnumber of ideal channel M ϭmass,kgQ ϭunit volumetric heat by magnetocaloric effect,W m −3t ϭelapsed time,s T ϭtemperature,°C u ϭvelocity,m s −1V ϭflow volume,m 3V ءϭrelative flow volumeV voidϭvoid volume in material-packed bed,m3Fig.17Temperature change at 2.0T for AMR refrigeration cycle with air as the heat transfer fluid for V ء=350and F ء=88s−1Fig.18Distribution of maximum difference at 2.0T of air-based AMR as a function of the relative flow volume for F ء=88s −1,the data were obtained from analysis …closed circles …and experiment …open diamonds…Fig.19Distribution of maximum temperature difference at 2.0T of air-based AMR as a function of the relative volumetric flow rate for V ء=438,the data were obtained from analysis …closed circles …and experiment …open diamonds …⌬Tϭtemperature difference between hot and coldends,°C⌬T adϭadiabatic temperature change of gadolinium,°CGreek Symbolsϭporosityϭdensity,kg m−3ϭthermal conductivity,W m−1K−1Subscriptsadϭadiabaticcϭcold end 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