NIST Technical Note 1931 

Novel Method and Apparatus Design 

for Testing Small Magnetocaloric 

Samples 

M. A. Kedzierski 

W. V. Payne 

H. M. Skye 

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.TN.1931 
 

 

 

NIST Technical Note 1931 

Novel Method and Apparatus Design for
 

Testing Small Magnetocaloric Samples
 

M. A. Kedzierski 

W. V. Payne 

H. M. Skye 

Energy and Environment Division 

Engineering Laboratory 

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.TN.1931 

September 2016 

U.S. Department of Commerce 

Penny Pritzker, Secretary 

National Institute of Standards and Technology 

Willie May, Under Secretary of Commerce for Standards and Technology and Director 
 

 

 

 

 

Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. 

Such identification is not intended to imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor is it intended to imply that the 

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Technical Note 1931 

Natl. Inst. Stand. Technol. Tech. Note 1931, 31 pages (September 2016) 

CODEN: NTNOEF 

This publication is available free of charge from: 

http://dx.doi.org/10.6028/NIST.TN.1931 
 

 

 

 

 

 

 

Novel Method and Apparatus Design for Testing Small Magnetocaloric
 

Samples
 

M. A. Kedzierski1
 

W. V. Payne
 

H. M. Skye
 

National Institute of Standards and Technology
 

Gaithersburg, MD 20899
 

ABSTRACT 

This report presents a design for a novel test apparatus to directly measure the magnetocaloric 

effect (MCE). The design of the apparatus was focused primarily on being able to measure the 

MCE with minimized uncertainties for test samples of 5 g. The effort is meant to aid U.S. 

industry in selecting new, limited-quantity magnetocaloric (MC) materials for commercial 

development. A different measurement approach is also required because of the small test 

sample size and because of the wide disagreement in the validity of some indirect measurement 

techniques. These concerns require an accurate and direct measure of MCE in order to develop 

superior room temperature magnetocaloric materials. For the test apparatus design presented 

here, the estimated uncertainties for the adiabatic temperature change and the increased internal 

energy are 0.3 K and 0.6 % of the measurement, respectively. The small uncertainties were 

achieved for the small sample by leveraging the incompressibility of liquid as an amplifier to 

increase the sensitivity of energy measurement. Drawings, parts list, and required test equipment 

were specified for the construction of the test apparatus. A calibration technique using a first law 

of thermodynamics approach was outlined. 

Keywords: magnetic refrigeration, magnetocaloric 

1 Corresponding author. Tel./fax: (301) 975-5282/(301) 975-8973. E-mail address: Mark.Kedzierski@NIST.gov 

1
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

TABLE OF CONTENTS
 

ABSTRACT............................................................................................................................. 1
 

TABLE OF CONTENTS ....................................................................................................... 2
 

LIST OF FIGURES ................................................................................................................ 2
 

LIST OF TABLES .................................................................................................................. 3
 

INTRODUCTION................................................................................................................... 4
 

NIST TEST APPARATUS DESIGN .................................................................................... 6
 

Design Considerations ............................................................................................................ 6
 

Test Apparatus Physical Overview ....................................................................................... 7
 

Calibrated Heater ................................................................................................................... 9
 

Test Chamber Liquid Selection ........................................................................................... 10
 

Relating Pressure to Energy ................................................................................................ 10
 

DIRECT MEASUREMENT AND CALIBRATION......................................................... 13
 

DESIGN DRAWINGS.......................................................................................................... 14
 

ESTIMATED UNCERTAINTIES ...................................................................................... 15
 

CONCLUSIONS ................................................................................................................... 16
 

ACKNOWLEDGEMENTS ................................................................................................. 16
 

NOMENCLATURE.............................................................................................................. 17
 

English symbols..................................................................................................................... 17
 

Greek symbols ....................................................................................................................... 17
 

Subscripts............................................................................................................................... 17
 

Abbreviations ........................................................................................................................ 17
 

REFERENCES...................................................................................................................... 19
 

APPENDIX A: TEST EQUIPMENT.................................................................................. 31
 

APPENDIX B: PARTS FOR NIST FABRICATION DIVISION.................................... 32
 

Magnet Holders: Quantity 2 ................................................................................................ 32
 

Mounting Plate...................................................................................................................... 34
 

APPENDIX C: MCE TEMPERATURE CHANGE FOR POLYNOMIALS................. 35
 

LIST OF FIGURES
 

Fig. 1 Halbach magnet with magnetic field lines (Lee, et al., 2002) ................................. 22
 

Fig. 2 Simple schematic of test apparatus........................................................................... 23
 

Fig. 3 Transient pressure pulse in test section.................................................................... 24
 

Fig. 4 Change in pressure for various water volumes for a magnetocaloric temperature 

change of 2 K, 5 K, and 10 K ................................................................................... 25
 

Fig. 5 Change in pressure for various R123 volumes for a magnetocaloric temperature
 

change of 2 K, 5 K, and 10 K ................................................................................... 26
 

Fig. 6 Example case illustrating the liquid pressure pulse for a volume of 9 cm3 and an 

applied voltage of 20 V for 34.6 μs .......................................................................... 27
 

Fig. 7 Example case illustrating the pressure change during cooling after a pulse for a
 

volume of 9 cm3 and an applied voltage of 20 V for 34.6 μs.................................. 28
 

Fig. 8 Side-view schematic of test apparatus...................................................................... 29
 

Fig. 9 Top-view schematic of test apparatus ...................................................................... 30
 

Fig. A.1 Agilent # 81104A pulse generator ......................................................................... 31
 

Fig. A.2 Model 460 3-Channel Gaussmeter........................................................................ 31
 

Fig. B.1 Bottom of Bar Magnetic Holder............................................................................ 32
 

2
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Fig. B.2 Lid for Bar Magnetic Holder ................................................................................. 33
 

Fig. B.3 Mounting Plate........................................................................................................ 34
 

LIST OF TABLES
 

Table 1: List of Test Apparatus Parts and Equipment .................................................... 20
 

Table 2: Estimated Expanded Uncertainties for Test Apparatus ................................... 21
 

3
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

INTRODUCTION 

A strict definition of the magnetocaloric effect (MCE) does not exist. Vodyanoy and Mnyukh 

(2013) define it simply as “the heat emanated or absorbed when [a] magnetic field is applied to 

[a] magnetic material.” McMichael et al. (1992) view the MCE as an intrinsic property of 

magnetic materials where a magnetic field (B) causes an adiabatic temperature change in the 

material. Gómeza et al. (2013) state that MCE is a physical property of materials whereby the 

temperature and the magnetic entropy vary in the presence of a varying magnetic field. In this 

report, the MCE is defined as the heat (energy) increase/decrease and the corresponding 

temperature increase/decrease of a magnetocaloric (MC) material in the presence of a magnetic 

field. For this definition, the adiabatic temperature change (∆ΤM) is the maximum temperature 

change for a given MC material exposed to a given magnetic field. 

Refrigeration that relies solely on the MCE for its cooling (MC refrigeration) has been identified 

as one of three alternative technologies that show the most promise for displacing the currently 

dominant vapor compression technology (Brown and Domanski, 2014). The temperature change 

that is caused by exposing a MC material to a magnetic field can be used in the same way as a 

temperature change that is produced by a conventional vapor compression system. Either 

method of converting work into heat can be used as the basis for a refrigeration or airconditioning system. 

The merits of MC refrigeration include the elimination of green house gases used currently as 

refrigerants and the potential to significantly improve the energetic efficiency of refrigeration as 

postulated in several theoretical studies; both these benefits would reduce the impact of 

refrigeration equipment on climate change. Consequently, significant research and experimental 

development efforts have occurred around the world in the last 20 years with the number of 

MCE publications and patents increasing exponentially (Yu et al., 2010). 

The major obstacle to MCE technology achieving its performance potential and commercial 

entry is the inability of currently available MC materials to generate the required temperature 

increase, i.e., temperature lift. For any cooling system, the temperature lift is dictated by the 

requirement that heat must be transferred from the cooled environment to the ambient 

environment, which is order of 30 K for a refrigerator. The typical temperature lift achieved 

with Gadolinium via the MCE is of the order of 5 K. As a consequence of this shortcoming, 

worldwide research has been focused on the development of new MC materials with larger MCE 

(Langebach et al., 2014). 

Recent discussions with a National Institute of Standards and Technology (NIST) technical 

expert on magnetocaloric materials (Bennett, 2015) indicate a pending breakthrough in material 

science that will allow for the production of magnetocaloric alloys theoretically capable of 30 K 

temperature change. This level of temperature change begins to make a practical refrigeration 

application possible. The Center for Functional Nanomaterials at Brookhaven National 

Laboratory has recommended that the technical expert’s proposal for obtaining alloy 

nanostructures should be funded to cooperatively work with NIST to investigate new MC 

nanomaterials alloys (Bennett, 2015). The small samples developed in the technical expert’s 

proposal that show strong magnetic tendencies will be tested for their MCE as a function of 

4
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

applied magnetic field. The expected result is a new magnetocaloric alloy that will provide 

sufficient temperature lift to make a magnetic refrigerator commercially feasible. 

Consequently, the goal of this investigation is to design a measurement method and a test 

apparatus that can be used to measure the MCE of newly developed MC materials that are 

expected to be available in small quantities of 5 g or less. It is the overall goal that MC materials 

can be identified that can be used to overcome the barriers to commercialization of MC 

refrigeration. Because of the small sample size, the instrument necessarily needs to be more 

sensitive than instruments that have been previously made. 

CURRENT STATE-OF-ART 

As outlined by Lee (2004), the common practice for measuring the MCE (adiabatic temperature 

change) has three main approaches. The first method is to directly measure the adiabatic 

temperature change by insulating the material and exposing it to a magnetic field. The remaining 

two methods are indirect methods for measuring the MCE that involve the measurement of the 

magnetization (magnetic moment) and the calculation of isothermal magnetic entropy change. 

The adiabatic temperature change is then calculated from the entropy change. For example, the 

second method, which Lee (2004) applies, uses magnetization measurements and zero-magnetic 

field heat capacity measurements to calculate the entropy change with Maxwell’s 

thermodynamic relations to determine the MCE. The third method relies on both zero-magnetic 

field and nonzero-magnetic field heat capacity measurements and the measured magnetic 

moment to calculate the entropy change. 

Pecharsky and Gschneidner (1999) favor the indirect measurement methods for MCE because 

the uncertainties in the direct measurement have several sources, including: thermometry (with 

additional sensor errors caused by the changing magnetic field), magnetic field, and heat losses. 

In addition, the indirect measurements result in more measured quantities than just the adiabatic 

temperature change. Nevertheless, according to Pecharsky and Gschneidner (1999), the 

uncertainty ranges associated with the indirect and direct methods are comparable, being 5 % to 

10 % and 3 % to 10 % for the direct and indirect methods, respectively. 

However, there is reason to question the validity of the indirect measurement approach. 

Vodyanoy and Mnyukh (2013) state that “there is no basis for that MCE to be a change of 

magnetic entropy.” They justify their claim with a physical argument that the MCE is the energy 

of the crystal restructuring and not due to large polarization change. One might attribute these 

conclusions as the opinion of a few researchers and regard the indirect method as still viable. 

However, we also have reasons to doubt the indirect approach due to our inability to confirm the 

derivation of the accepted expression for the adiabatic temperature change as derived from the 

magnetic entropy and given by Pecharsky and Gschneidner (1999). In their derivation, the 

magnetic term was ignored in the expression of the first law of thermodynamics that was used to 

calculate the adiabatic temperature from the magnetic entropy. This omission may be what 

Aslani et al. (2016) call “misappropriate use of Maxwell relations” and conclude that “direct 

methods for measuring adiabatic temperature change must be performed.” In addition, the 

indirect methods cannot be used to measure the hysteresis associated with the MCE (Bennett, 

2015). Consequently, considering that the direct and indirect methodologies have comparable 

5
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

uncertainties, and because the indirect method correctness has reason to be questioned, the 

present test apparatus design plans to use the direct method to measure the MCE. 

NIST TEST APPARATUS DESIGN 

The following section describes the test apparatus design by considering the physical limitations 

of the spatial, temporal, thermal, magnetic, and thermodynamic properties of materials that are 

available for its construction. First, the expected MCE is quantified in terms of magnitude and 

duration. Next, a technique is outlined to measure the MCE by measuring the pressure pulse that 

the MC material imposes on a surrounding liquid in an enclosed volume. This pressure pulse is 

then related to the energy pulse by using the first law of thermodynamics. The size of the test 

chamber that holds the liquid and the MC test sample is sized based on the properties of the 

liquid and the expected MCE. 

Design Considerations 

In order to properly design a test apparatus to directly measure the MCE, the basic mechanisms 

that govern the MCE phenomenon must be considered. Understanding what is to be measured 

and how the MCE is realized is essential for ensuring that the true effect is measured. Even 

though, as Vodyanoy and Mnyukh (2013) and de Oliveira and von Ranke (2010) point out, the 

physics of the MCE is not completely understood, a basic energy approach is sufficient for the 

test apparatus design. In addition, the obstacles to the accurate measurement of the MCE must 

be clearly identified and either eliminated or minimized. The following section outlines the 

measurement goals, difficulties and the solutions that were applied to the design of the test 

apparatus to measure the MCE. 

The response of the magnetocaloric material to a changing magnetic field is to change the 

orientation of its atoms so that the magnetic dipoles are aligned with the magnetic field. As 

discussed earlier, Vodyanoy and Mnyukh (2013) prefer to attribute the MCE to crystal 

restructuring and the resulting latent heat of the structural phase transition, and not to 

polarization change. However, all that is important for the apparatus design is that the MCE, be 

it by either the change in orientation or the crystal restructuring, manifests itself as a change in 

the internal kinetic energy of the material with no change in the internal potential energy. The 

MCE kinetic energy increase is in addition to the pre-existing kinetic energy of the atoms, due to 

translational, vibrational, and rotational kinetic energies. Temperature is a measure for the level 

of internal kinetic energy of an atom. The increase in temperature due to the additional MCE 

kinetic energy is known as the magnetocaloric effect ∆TM. The ∆TM is equal to the difference 

between the material’s original ambient temperature before the application of the magnetic field 

(Ta) and the maximum temperature the material would have reached in the absence of heat 

transfer (TM). If the material is allowed to cool back to ambient temperature while the magnetic 

field remains applied, then the translational, vibrational, and rotational kinetic energies are 

reduced leaving the internal potential energy and the MCE kinetic energy of the atom 

unchanged. Further reduction in the atom’s kinetic energy and corresponding temperature 

occurs when the magnetic field is removed. If the temperature drop occurs ideally without 

hysteresis when the magnetic field is removed, then it will be equal to ∆TM. 

The reason that the MCE is defined for an adiabatic condition is that it represents the maximum 

potential for temperature change for a given magnetic field intensity. Defined in this way, the 

MCE is a property of the material, and it is what is to be measured with the proposed test 

6
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

apparatus. However, any arbitrary amount of heat transfer during the application of the magnetic 

field will lead to a corresponding reduction in the MCE that is achieved. Heat transfer from the 

test sample represents a loss in MCE kinetic energy that is unavailable for increasing the sample 

temperature. Considering this issue, the primary measurement concern is to ensure that the 

maximum (adiabatic) MCE kinetic energy is measured and converted into something measurable 

without the potential for errors due to heat transfer. 

Difficulties for measuring the maximum magnetocaloric effect, i.e., the adiabatic temperature 

change (∆TM), arise from the limited availability of the sample material mass (Mm), which will 

be approximately 5 g. For this amount, it is estimated that the magnetocaloric heating effect for 

every 1 K change in temperature will be of the order of 1.2 J assuming that it has the same 

thermal and magnetic characteristics of gadolinium (Gd): 

J 

m pm∆ = ⋅ kg K 

Mc T 0.005kg 230 1K =1.2 J (1) ⋅

where the specific heat (cpm) of Gd is approximately 230 J kg-1 K-1 at room temperature. 

Further measurement difficulties arise from the brevity of the MCE event. The kinetic energy 

increases the instant the magnetic field is applied and the dipoles of the atoms are realigned. As 

a result, the measurement technique must have a sufficiently small response time in order to 

capture the MCE event. Consequently, the test apparatus must be designed to measure the 

entirety of an energy spike of the order of a few joules without loss so that it can be converted to 

an adiabatic equivalent. 

Test Apparatus Physical Overview 

The proposed measurement concept, to enable the measurement of an energy spike of the order 

of 1.2 J, is to use the incompressibility of liquid as an amplifier for the magnetocaloric heating 

effect. Being that the volume of the test chamber is designed to be relatively fixed (with the 

exception of the deflection of the pressure transducer diaphragm), liquid in the absence of gas 

will undergo a large change in pressure with a relatively small change in temperature. Being that 

pressure is directly related to temperature and energy, we consider this to be a “direct” 

measurement method for the MCE. 

For the purpose of calibration, we propose to simulate the MCE using an Agilent # 81104A (Fig. 

A.1 in Appendix A)2 pulse generator and a Nichrome wire heater. The pulse generator would be 

able to mock the magnetocaloric effect by delivering a voltage pulse to a resistive heater at 

prescribed durations of our choosing as small as a micro-second. Once the pressure pulse has 

been calibrated against the energy pulse, we would be able to use the calibration to test MC 

materials in the test apparatus. 

In order to produce a MCE that is as large as practically possible for a given test sample, a 

2 Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the 

experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by 

the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment 

identified are necessarily the best available for the purpose. 

7
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

magnetic field of the order of 2 T should be used (Bennet, 2015). Because the entire test 

chamber will be immersed in a constant temperature bath, permanent magnets will be used to 

generate the magnetic field. Magnetic fields of this order have been achieved with a Halbach 

array magnet shown in Fig. 1 (Lee, et al., 2002). However, as shown in Fig.1, the uniform 

magnetic field lines are confined to the center space of the magnet where the entire test apparatus 

must be placed. Considering this space limitation, the Halbach magnet is not suitable for the 

current test apparatus design. For this reason, paired bar magnets have been chosen to deliver 

the magnetic field incident to the test sample. Commercially available bar magnets of 0.8 T can 

be readily obtained in order to deliver a maximum of 1.6 T to the test sample. In addition, the 

bar magnets are planned to be placed on linear positioning devices so that the magnitude of the 

magnetic field can be varied by changing the proximity of the magnets to the test sample. The 

intensity of the magnetic field will be measured and calibrated with respect to magnet position 

by using a duplicate test section with a Hall sensor assembly in place of the test sample in order 

to measure the magnetic field as it exists in the test apparatus with the sample.3 A three-channel 

Gaussmeter is required to obtain the measurements from the Hall sensor. Specifications for the 

Gaussmeter, the Hall sensor, the bar magnets, and the positioning device are provided in Table 1. 

The linear positioners need to be custom built with nonmagnetic material. The stage and the 

driving mechanism is planned to be aluminum and bronze, respectively. In addition, a bronze 

leadscrew will be used to advance the stage to overcome the large repulsive forces produced by 

the two bar magnets. Bronze anti-backlash nuts and bearings will also be used. Aluminum 

boxes are planned to be made by the NIST Fabrication Division to encase each magnet. The side 

walls of the box will be wide and thick enough to accept holes through which it will be bolted to 

the stage of the positioners. Drawings of these magnet holders are provided in Appendix B. 

Figure 2 shows a simplified schematic of the test apparatus with the magnets and magnetic field 

lines. The entire apparatus will be submerged with the bar magnets in a constant temperature 

bath. Table 1 provides the list of parts to build the apparatus and required test equipment. The 

test chamber consists mainly of a pressure transducer and a valve. The pressure transducer and 

the liquid bath will serve as the pressure relief safety for the apparatus considering that the 

volume of incompressible fluid needs to be minimized. In this way, adding liquid volume to 

allow for plumbing a relief valve will be avoided. The body of the recommended pressure 

transducer from American Sensors Technologies is constructed of Austenitic or 316L stainless 

steel, which are both non-magnetic. All components of the pressure transducer must be nonmagnetic and it must be verified that the pressure measurements are unaffected by the magnetic 

field. A filling tee will be attached to the top of the valve so that the chamber can be evacuated 

before it is filled. It is likely that the valve will have to be attached to the pressure transducer 

with the sample in place. 

The primary design consideration for the test section was to minimize its internal volume relative 

to the volume of the test sample, and for it to be nonmagnetic. The measurement concept is to 

fill the entire space that holds the test sample with incompressible liquid. For an incompressible 

liquid in a fixed volume, an increase in temperature corresponds to an increase in the pressure of 

the liquid. The relationship between the liquid temperature and the pressure is governed by 

3 The Hall sensor will measure the magnet field that is incident to the test sample. The intensity of the magnetic 

field as it exists in the sample can be obtained if the permeability of the sample is known. 

8
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

thermodynamics. Figure 3 shows the expected transient pressure response to the MCE. At time 

zero, the magnetic field is zero and the pressure represents the equilibrium pressure of the test 

chamber fluid at the bath temperature (Tb). The MCE occurs nearly instantaneously once the 

magnetic field is applied. Consequently, the liquid pressure response will lag the increase in the 

kinetic energy of the test sample. As a result, the peak liquid pressure occurs after the end of the 

MCE event. In addition, the peak is smaller than what would have occurred had the test chamber 

been adiabatic. Because the test chamber is in a constant temperature bath, the peak pressure is 

reduced due to heat transfer to the bath. As the sample establishes temperature equilibrium with 

the bath, the pressure decreases until it is again at the initial pressure. At this point, the magnetic 

field can be removed to allow the temperature of the test sample to decrease. Again, the 

minimum temperature is greater than what it would have been had there been no heat transfer 

from the bath. As heat transfer occurs the pressure increases to the original pressure. 

Calibrated Heater 

The purpose of the calibration with the Nichrome heater is to account for the fact that the process 

outlined in Fig. 3 is not adiabatic. Both the tests and the calibrations will be done with the 

electric heater embedded within the test sample. This is to ensure that both the mass and the 

thermal properties of the sample-heater composite are identical for tests and calibration. The 

calibration will consist of joule input to the electric heater versus maximum and minimum 

pressures. In addition, the entire trace of pressure with respect to time will be recorded for the 

calibration in order to compare it to the MCE measurements for a check of any anomalous 

effects. It is expected that there may be a learning curve for reading and interpreting pressure 

traces. 

According to eq. (1), 12 J of heating is required to raise the magnetocaloric test sample 

temperature by 10 K. If the heating occurs over 36.4 μs4

, then the total power is 32.9 × 104 W. 

The length (Lw) of a 1.024 mm diameter (Dw) Nichrome wire is planned to be limited to 

approximately 1 mm and so that it can fit within the magnetocaloric test sample. Nichrome wire 

has an electrical resistivity (ρe) of 1 × 10-6 Ω-m. For a wire of circular cross-section, the 

electrical power (pe) is written in terms of supplied voltage (Ve) as: 

2 2 V D e π w pe = (2) 4Lw ρe 

Equation 2 can be solved for Ve using the values provided above yielding approximately 20 V. 

Considering that temperature sensors are likely to be affected by the magnetic field (Pecharsky 

and Gschneidner, 2001), the pressure traces can also be calibrated to provide the temperature 

change of the sample. This calibration would require a temperature sensor to be embedded in the 

test sample. The calibration will consist of sample temperature versus maximum and minimum 

pressures with the electric heater on and the magnetic field off. In this way, the temperature 

could be indirectly measured without using the temperature sensor during the test. 

4 This time interval was chosen because it was near the lower limits of what could be precisely produced and 

measured by the equipment. 

9
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Test Chamber Liquid Selection 

The next consideration in the design of the test apparatus is the choice of the fluid to surround 

the test sample in the test chamber. The importance of the fluid choice is significant because the 

fluid specific heat (cpf) and the temperature-pressure equilibrium of the fluid determine the 

magnitude of the response to the MCE. The fluid response is governed by the heat exchange 

from the mass of the magnetocaloric material (Mm) to the mass of the fluid (Mf) and the heat loss 

from the fluid to the bath (Qb). The final equilibrium temperature (Teq) that is achieved for the 

two masses is represented as: 

M ∆Tc − M (T −Tc ) = MT ( −Tc ) −Q (3) m M pm m eq b pm f eq b pf b 

Equation (3) can be rearranged to solve for the increase in the fluid temperature while neglecting 

Qb: 

T c Mm∆ M pm Teq −Tb = (4) M c + M c f pf m pm 

For an incompressible liquid, eq. (4) can be used along with the derivative of the fluid pressure 

(P) with respect to temperature at constant density to calculate the increase in the fluid pressure 

from: 

 T cpm M  m∆ M Peq − Pb = dP (Teq −Tb ) = dP   (5) dT ρ dT M c + M c ρ  f pf m pm 

Here the gradient of the fluid pressure with respect to the fluid temperature is evaluated at 

constant density (ρ). In addition, the Peq and the Pb are the liquid pressures evaluated at Teq and 

Tb, respectively. Figure 4 uses eq. (5) to illustrate the relationship between the estimated 

pressure pulse and the volume of water that fills the test chamber for a given MCE. In general, 

small water volumes and large MCE produce large pressure pulses. Three lines are used to 

represent the three different magnetocaloric temperature changes. For a fluid chamber volume 

(Vc) of approximately 9 mL, the pressure increase is estimated to be 36 kPa, 90 kPa, and 181 kPa 

for a 2 K, 5 K, and 10 K, respectively, temperature increase. Note that for a sample mass of 5 g 

the required volume for the sample is approximately 0.7 mL. 

Figure 5 shows the same analysis when repeated with R123 as the incompressible fluid. The 

resulting pressure increases for a 9 mL volume are substantially larger than that for water being 

192 kPa, 481 kPa, and 962 kPa for a 2 K, 5 K, and 10 K, respectively, temperature increase. The 

use of R123 would permit the test chamber volume to be significantly larger. Further 

investigation into the choice on fluid for the test chamber may be required. 

Relating Pressure to Energy 

A second method for determining the pressure spike that will allow calculation of the transient 

behavior of the pressure increase and the pressure decrease is to use the first law of 

thermodynamics on a control volume that consists of the fluid and the test sample with a heating 

element: 

10
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

dE 

q = +W (6) dt 

where q is the heat transferred between the fluid in the valve and the bath, E is the internal 

energy of the fluid, W is the work done on or by the fluid, and t is the variable for time. When 

the electric heater is used, work done on the fluid in the control volume is negative, i.e., W = -pe. 

Likewise, negative work occurs on the fluid when the magnetic field has been applied. The work 

is positive when the magnetic material loses kinetic energy at the moment that the magnetic field 

has been removed. Similarly, the q is negative while the fluid is transferring heat to the bath 

during the application of the magnetic field and positive when the field has been removed and 

the fluid temperature becomes less than Tb. 

Note that the presence of the test sample and its thermal properties are ignored in this control 

volume analysis. Consequently, the analysis in this way is expected to overestimate the fluid 

pressure increase because it neglects the necessity of the test sample to retain some of the 

increased energy of the control volume. This first law analysis views the test sample as a 

massless heater that passes all of its generated heat instantaneously and uniformly to the liquid, 

which is the second error of the above analysis. However, the benefit of the analysis is that it 

provides an approximate transient heat transfer behavior for the heating and the cooling of the 

liquid. 

Heat will be either convected from (-) the control volume fluid or to (+) to the control volume 

fluid: 

dT = − ( f −Tb q hA T ) = −hA (Pf − Pb ) (7) dP ρ

The temperature difference, Tf -Tb, is positive and negative when heat is convected from and to 

the control volume liquid, respectively. Consequently, because of the leading negative sign in 

eq. (7), the q is correctly negative and positive for the two cases. 

The h in eq. (7) is the convection heat transfer coefficient, which was assumed to be 500 Wm-2K 

for the preliminary analysis. The internal surface area of the test chamber (A) is presently 

unknown, but is estimated to be 6 × 10-4 m2

. The liquid temperature (Tf) is variable while the 

test chamber wall temperature is assumed to be constant and equal to the bath temperature (Tb). 

The gradient of the temperature with respect to the fluid pressure (dT/dP) is a property of the 

fluid and it is evaluated at the time dependent Pf and at constant density. 

The rate of change of the total internal energy (dE/dt) of the control volume can be rewritten in 

terms of the definition of the total enthalpy of the control volume (H) as: 

dE dH dV dP dP  dH  dP  dλ  f c f f f f f = − Pf −Vc =  −Vc  = Vc  ρf −1 (8) dt dt dt dt dt  dPf  dt  dPf 

11
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Equation (8) was simplified by using a chain rule for the enthalpy derivative and the fact that the 

test chamber volume is constant. The specific liquid enthalpy (λf) and the liquid density (ρf) 

where introduced into eq. (8) so that mass independent properties could be used. 

Substitution of eqs. (7), and (8) into eq. (6) yields: 

dT dPf  dλf	  −hA (P − Pb ) = V  ρf f c − ± 1 W (9) dP ρ dt dP  f 

Equation (9) is valid for when work is delivered to the liquid (use -W) by either the electric 

heater or the magnetic material and when the magnetic material is cooling the liquid (use +W). 

The work term is set to zero when the electric heater is off and after either the maximum pressure 

(Pp) or minimum pressure has been reached. 

By treating the property derivatives as constants, the solution for the electric heating case while 

voltage is applied to the heater and also for both the heating MCE and the cooling MCE is: 

 −hAdT   dP ρ t   dλ  f  Vc  ρf −1   f  Z dP Pf = Pb − dT	 1−e  (10) 

  hA 

dP   ρ 	   

Equation (10) is made valid for the electric heating case by setting Z to -pe and it is valid for the 

duration of the voltage pulse Ve, which is tp. Equation (10) provides the temperature increasing 

MCE solution when Z is set to -W. Similarly, the cooling MCE solution is obtained when work 

is taken as being positive and Z is set to +W. 

The time-dependent solution of eq. (9) for when the liquid is cooling to the bath temperature 

after the pressure has increased to Pp due to either the electric heater or the MCE heating effect 

is: 

dT −hA 

dP ρ t  dλ  V  ρ f −1  f  dP P = + P (PP − )e c f	 

(11) f b p b 

Here t = 0 corresponds to the beginning of the cooling period, which occurs immediately after 

the maximum pressure, Pp, has occurred. 

Figure 6 shows an example liquid pressure pulse for a volume of 9 cm3 and an applied voltage of 

20 V for 34.6 μs. The figure shows that the pressure increase is linear with respect to time and 

does not increase beyond tp. The lack of a lag between the energy input and the pressure 

response is a result of neglecting the heat transfer interaction between the test sample and the 

liquid surrounding it. Figure 3 shows a potentially more realistic pressure response where the 

pressure curve becomes nonlinear as the temperature of the test sample and the fluid come to 

12
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

equilibrium. The value of eq. (9) is that it is a useful design tool for selecting a liquid, a liquidvolume and other design parameters. 

Figure 7 uses eq. (11) to illustrate the cooling period after the pulse shown in Fig. 6. Figure 7 

shows that it takes approximately 200 s for the liquid to cool back to the bath temperature of 

300 K. 

DIRECT MEASUREMENT AND CALIBRATION 

The heating and cooling pressure-time measurements and eqs. (10) and (11) can be used to 

calibrate the relationship between the measured pressure and the internal kinetic energy 

increased by the magnetocaloric effect. As stated above, the shape of the pressure-time heating 

curve is to be determined through experimentation. However, for the purpose of demonstrating 

how the calibration will be done, the pressure-time heating curve is assumed to be linear: Pf = Pb 

+C1t, where C1 is a fitting constant. The fit of the heating pressure curve measurements can be 

substituted into the general governing eq. (9) to obtain the hA of the fluid-to-valve heat transfer 

(for use in eq. (10) and possibly eq. (11)) as: 

1  pe  dλf 

hA = −Vc  ρf −1

  (12) dT  C dP  1  f  t 

dP ρ

In a similar way, the cooling measurements that occur immediately after heating can be used to 

calculate the hA by taking the natural log of both sides of eq. (11) and solving for hA: 

 dλf  V ρ 1 c  f −  dP PP   f c 

 − b hA = ln  f (13) dT   P P p − b  t 

dP ρ

where Pp is the maximum fluid pressure just prior to cooling of the fluid. The t and the Pf can be 

fitted to eq. (13) in order to obtain the constant hA. The advantage of eq. (12) over eq. (13) is 

that the gradient of temperature with respect to pressure is obtained for the heating case from eq. 

(12), which is required for calculating the adiabatic temperature increase (∆TM). 

The ∆TM of the magnetocaloric test sample for constant dPf/dt is calculated as: 

dP p f t −1 t 

dt p hAtp dT ∆T M = W t d = ∫  M c M c m pm 0 m pm  2 dP 

 dλf 

+Vc  ρf −1 (14)

ρ  dPf 

for a linear pressure curve, dPf/dt = C1. The negative sign is a consequence of negative work. 

By using eq. (14), the MCE can be obtained with both measured and calculated quantities, 

including the heat capacity of the test sample (cpm), which will be measured with a differential 

scanning calorimetry (DSC). Equation (14) is also valid for determining the cooling MCE when 

the magnetic field is removed after the fluid and the test material have cooled to the bath 

13
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

temperature. For this case and a linear pressure with respect to time, dPf/dt will be negative 

resulting in the correct sign for ∆TM. Appendix C provides an expression for ∆TM for nonconstant pressure gradients using quadratic and cubic pressure curve fits. 

The validity of eq. (14) will be checked during calibration by comparison with the measured 

temperature from the thermistor imbedded in the test sample. Nara (2005) has quantified the 

effect that the intensity of the magnetic field (B) has on thermistors with the following 

temperature correction ∆T: 

∆ = T 0.0069B2 (15) 

where the units of ∆T and B are mK and Tesla, respectively. It is planned to use eq. (15) to 

correct the measured temperature of the magnetic material during MCE tests as a secondary 

measurement method for ∆TM. 

The MCE heating effect (J) can be calculated from a linear pressure response (constant pressure 

gradient) as: 

J 

p 

f 

0 

d 

t dP Wt 

dt = − = ∫ p 

p 2 

hAt 

t 







dT 

dP 

 dλf 

+Vc  ρf −1 (16) 

ρ  dPf 

The application of eq. (16) will be checked during calibration with the heater using the following 

equation: p 2 2 t 

V Dπ dP hAt e w f p dT ∫ pedt = tp = tp 

0 4L w e ρ dt 2 dP 

 dλf 

+Vc  ρf −1 (17) 

ρ  dPf 

Equation (17) was derived by assuming that the pulse generator delivers a constant voltage, Ve, 

for the duration of the pulse. Equation (17) will serve as a validation of the methodology and a 

check on the calculated quantities on the rightmost side of the equation. It is expected that 

correction constants may need to be developed as part of the calibration once the measurements 

have been examined in order account for the assumptions of the first law analysis. Variations of 

eq. (17) similar to those given in Appendix C may be used to account for potentially nonconstant pressure gradients. 

DESIGN DRAWINGS 

Figures 8 and 9 provide a detailed schematic of the side and top views of the test apparatus, 

respectively, which was shown with less detail in Fig. 2. The basic function of the test apparatus 

is to hold the test sample in a pressure vessel in proximity to a magnetic field. The valve and the 

pressure transducer serve as the pressure vessel and test chamber. The valve has three threaded 

ports and three shutoffs. One of the half inch National Pipe Thread (NPT) ports is for the 

pressure transducer and the magnetocaloric test sample. The second half inch NPT port is for a 

sealed wire connector for the two electrical wires of the heating element and the thermistor 

temperature sensor. The wires will be fished from one end of the valve to the other so that they 

can be embedded within the test sample. The smaller quarter inch NPT port will be used to 

evacuate and fill the valve with the test chamber liquid. The valve for this port will be the only 

valve that is to be closed. The valve/test chamber is mounted on a valve block in order to align 

the test sample with the axis of the two bar magnets. The bar magnets are each mounted on a 

14
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

micrometer driven positioning device. Special aluminum holders must be machined by the NIST 

Fabrication Division in order to securely fix the magnets to the lead screw driven positioners. 

Both of the positioners and the valve block are mounted onto a plate that will be fabricated. The 

drawings for the magnet holders and the mounting plate are provided in Appendix B. 

ESTIMATED UNCERTAINTIES 

All expanded measurement uncertainties (U) are reported at the 95 % confidence level and 

estimated with the law of propagation of uncertainty when a manufacturer’s value is not available. 

The law of propagation of uncertainty was used to estimate the uncertainty of the MCE heat effect 

(UJ) as: 

f c p 

2 2 2 

2 f f

p /

J 

f p 2 

dP hAdT dp V t dt 

U dP dP

U tU U U dt dt 

J dP t W W 

dt 

              =   +   +   +                  

(18) 

The components of uncertainty for J are: (1) the uncertainty in the measurement of the transient 

pressure gradient (UdPf/dt); (2) the uncertainty of the pulse time measurement (Utp); (3) the 

uncertainty in the heat transfer constants ( U / ); and (4) the uncertainty in the liquid volume of hAdT dp 

the test chamber (UVc). Table 2 provides the measurement uncertainties for the new apparatus, 

including those for Utp and UVc, which are ± 5 ns and ± 4.5 × 10-7 m3, respectively. The Utp was 

obtained from manufacturer specifications while the UVc was estimated from typical uncertainties 

for liquid densities. The liquid volume will be obtained by weighing the fluid in the test chamber 

and using the liquid density to obtain its volume. The U / was assumed to be a ± 3 % hAdT dp 

uncertainty. Because of the multiplying constants on U / as shown in eq. (18), this hAdT dp 

uncertainty can be as large as ± 300 % and still have a negligible effect on the value of UJ. The 

relative uncertainty of the transient pressure gradient was estimated from the uncertainties of the 

pressure and time measurements shown in Table 2 to be ± 0.006 (i.e., ± 0.6 %). If there is a large 

scatter in the pressure versus time measurement, this uncertainty will be underestimated. 

Conversely, if there is a small scatter in the data, the uncertainty will be overestimated. For a tp 

of 34.6 μs, all of the uncertainty components are negligible compared to the contribution of the 

uncertainty of the transient pressure gradient. For a tp of 34.6 μs, the estimated uncertainty for J 

for a 5 g sample and a peak pressure of 36 kPa is ± 0.6 %. 

Because heat transfer from the test sample to the liquid requires time to occur, and the first law 

analysis assumes instantaneous transfer of heat from the test sample to the liquid, the time to 

reach the peak liquid pressure (tp) is likely to be larger than 34.6 μs and comparable to the 

cooling time shown in Fig. 7, which is of the order of 3 minutes. For this situation, the 

uncertainty for J will remain ± 0.6 % for the above conditions. Just to provide an idea for the 

influence of tp on the uncertainty, if the pulse time is decreased to 0.6 μs, the uncertainty in time 

becomes the dominant uncertainty and increases the UJ to approximately ± 1 %. 

The law of propagation of uncertainty was also used to estimate the uncertainty of the adiabatic 

temperature change (U∆T) as: 

15
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

U U 

2 Ucpm 

2  U  ∆T J M =   +   +   (19) ∆T  

M  J   cpm   Mm 

By using the uncertainties provided in Table 2 for the specific heat of the test sample ( Uc ) and pm

that for the measured mass of the test sample (UM) the uncertainty of ∆TM was calculated as a 

constant ± 3 % of the measurement, which is 0.3 K for a ∆TM of 10 K. The estimate is consistent 

with the uncertainty range given by Pecharsky and Gschneidner (1999) direct methods, which is 

3 % to 10 % of the measurements. It should be noted that this methodology meets the lower end 

of the typical uncertainty while achieving it for test samples of abnormally small mass. In 

addition, the uncertainty in U∆T is mainly due to the uncertainty in the specific heat 

measurement. 

CONCLUSIONS 

NIST Engineering Laboratory is well positioned to make significant contributions to the 

development of superior room temperature magnetocaloric materials. This report presents a 

design for a novel test apparatus to directly measure the magnetocaloric effect (MCE), which 

consists of measuring the internal energy change and the adiabatic temperature change of a 

magnetocaloric material when exposed to a magnetic field. An apparatus design was presented 

to measure the MCE of test samples of 5 g with an estimated uncertainty of 0.6 % and 0.3 K for 

the energy change and the temperature change, respectively. The small uncertainties were 

achieved for the small sample by using the incompressibility of liquid as an amplifier to increase 

the sensitivity of the energy measurement. The design is expected to enable the evaluation of 

MC materials as candidates for commercial development while using only a 5 g sample. 

Drawings, parts list, and required test equipment were specified for the construction of the test 

apparatus. A calibration technique using a first law approach was outlined. 

ACKNOWLEDGEMENTS 

This work was funded by NIST Engineering Laboratory Exploratory Project. Thanks go to Prof. 

R. Brignoli of The Catholic University of America and to the following NIST personnel for their 

constructive criticism of the draft manuscript: W. Healy and P. Domanski. 

16
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

NOMENCLATURE
 

English symbols
 

A internal surface area of the test chamber (m2) 

A0 constant in eq. (C.2) (m3)
 

A1 constant in eq. (C.2) (m3-s)
 

A2 constant in eq. (C.2) (J)
 

B intensity of the magnetic field (T)
 

Cn=1..3 fitting constants for pressure-time (Pa-m-n)
 

cp specific heat (kJ-kg-1-K-1)
 

Dw wire diameter (m)
 

E internal energy of the fluid (J)
 

h convection heat transfer coefficient (W-m-2-K-1)
 

Hf total enthalpy of liquid in control volume (J)
 

J MCE heating effect defined in eq. (16) (J)
 

Lw length of Nichrome wire (m)
 

Mm sample material mass (kg)
 

P pressure (Pa)
 

pe electrical power (W)
 

Qb heat transferred to the bath (J)
 

q heat transfer rate to the fluid (W)
 

t time (s)
 

T temperature (K)
 

U expanded measurement uncertainties
 

Vc fluid chamber volume (m3)
 

Ve supplied voltage (V)
 

W work done on the fluid (W)
 

Z work parameter in eq. (10) (W)
 

Greek symbols
 

∆P pressure change (kPa)
 

∆TM adiabatic temperature change (K)
 

λf liquid specific enthalpy (kJ-kg-1)
 

ρf liquid density (kg-m-3)
 

ρe electrical resistivity (Ω-m)
 

Subscripts 

a ambient 

b bath 

eq equilibrium 

f fluid 

m magnetocaloric material, minimum 

M maximum 

p pulse, peak 

Abbreviations 

AC alternating current 

17
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

DC direct current 

MCE magnetocaloric effect 

NPT National Pipe Thread 

18 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

 

 

REFERENCES 

Aslani, A., Ghahremani, M., Zhang, M., Bennett, L. H., and Della Torre, E. 2016. Enhanced 

Magnetic Properties of Ni51Mn33.4In15.6 Heusler Alloy Nanoparticles. Journal of Magnetism and 

Magnetic Material, 401, 35-42. 

Bennet, L., 2015. Private communications. 

Brown, J. S. and Domanski, P. A. 2014. Review of alternative cooling technologies. Applied 

Thermal Engineering. 64, 252-262. 

De Oliveira, N. A., and von Ranke, P. J. 2010. Theoretical aspects of the magnetocaloric effect. 

Physic Reports 489, 89-159. 

Gómeza, J. R., Garciab, R. F., Catoiraa, A. D., Gómeza, M. Romero. 2013. Magnetocaloric 

effect: A review of the thermodynamic cycles in magnetic refrigeration, Renewable and 

Sustainable Energy Reviews, 17, 74–82. 

Langebach, R., Klaus, M., Haberstroh C., and Hesse, U. 2014. Magnetocaloric cooling near 

room temperature – a status quo with respect to household refrigeration. 15th Int. Refr. & Air 

Cond. Conf. at Purdue. 

Lee, J. S. 2004. Evaluation of the magnetocaloric effect from magnetization and heat capacity 

data. Phys. Stat. sol. 240(7) 1765-1768; doi 10.1001/pssb.20004685. 

Lee, S. J., Kenkel, J. M., Pecharsky, V. K., and Jiles, D. C. 2002. Permanent magnet array for the 

magnetic refrigerator. Journal of Applied Physics 91, 8894; doi: 10.1063/1.1451906 

McMichael, R. D., Shull, R. D., Swartzendruber, L. J., Bennett, L.H., and Watson, R. E. 1992. 

Magnetocaloric effect in superparamagnets, Journal of Magnetism and Magnetic Materials, 111, 

29-33. 

Nara, K. 2005. Study of the Magnetic Field Effect on Commercial Thermistors using a Water 

Triple Point. Japanese Journal of Applied Physics, 44(3), 1506–1507. 

Pecharsky, V. K. and Gschneidner, K. A., Jr. 2001. Some common misconceptions concerning 

magnetic refrigerant materials, J. Appl. Phys., 90(9), 4614–4622. 

Pecharsky, V. K. and Gschneidner, K. A., Jr. 1999. Magnetocaloric effect and magnetic 

refrigeration, J. Magnetism and Magnetic Materials., 200, 44-56. 

Vodyanoy, V. J., and Mnyukh, Y. 2013. The physical nature of “giant” magnetocaloric and 

electrocaloric effects. American Journal of Materials Science. 3(5): 105-109; 

doi:10.5923/j.materials.20130305.01 

Yu, B., Liu, M., Egolf, P. W., Kitanovski, A. 2010. A review of magnetic refrigerator and heat 

pump prototypes built before the year 2010. Int. J. Refrig. 33, 1029-1060. 

19
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Table 1: List of Test Apparatus Parts and Equipment 

Component Model Number/Product Description Website Link 

pulse 

generator 

Agilent # 81104A http://www.testequipmentdepot.com/agil 

ent/pulsegenerators/81110a.htm 

bar magnet B7512 

(75 x 25 x 12) mm N38 NiCuNi Plated 

Block Magnet 

http://www.gaussboys.com/store/index.p 

hp/magnet-shapes/blocks/b7512.html 

Linear 

positioner 

Deltron Slide model 1201-series 2200. 

Custom build with leadscrew and 

nonmagnetic materials. Bill Schully knows 

the details 800-245-5013 

http://linearpositioners.com/search/Micrometer_Posi 

tioning_Stages_Model.aspx?pkid=2535 

Gaussmeter Model 460 3-Channel Gaussmeter by Lake 

Shore Cryotronics 

http://www.lakeshore.com/products/Gau 

ssmeters/Model-460-3-ChannelGaussmeter/Pages/Overview.aspx 

Hall sensor HST-1 http://www.lakeshore.com/products/Hall 

-Probes/Pages/ProbeGuide.aspx 

pressure 

transducer 

(1/2” male NPT) http://www.astsensors.com/memspressure-sensor-technology.php 

valve Hoke double block & bleed gauge valve 

model-HM8322 

http://www.hoke.com/Catalogs/Catalog_ 

ENG_HOKE_HM_Series_Standard_Val 

ves_10.22.14.pdf 

temperature 

sensor 

Thermistor T320/E320 Series https://www.thermistor.com/t320e320­

series 

Data 

acquisition 

Agilent 34970A/34972A http://www.keysight.com/en/pd1000001313%3Aepsg%3Apro-pn34970A/data-acquisition-data-loggerswitch-unit?cc=US&lc=eng 

Nichrome 

wire 

Omega NI60-040-200 (18 gage = 

1.024 mm) 

http://www.omega.com/pptst/NI60.html 

Temperature 

bath 

Fluke Model 7103 http://www.tequipment.net/Fluke7103­

156.html?v=7540#tab-specifications 

Oscilloscope Rigol MSO2202A-S Mixed Signal 

Oscilloscope 200MHz 

http://www.tequipment.net/Rigol/MSO2 

202A-S/Mixed-SignalOscilloscopes/?v=7233 

20
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

Table 2: Estimated Expanded Uncertainties for Test Apparatus 

Measurement Instrument U U (%) 

Heat pulse 

duration 

Agilent # 81104A pulse generator Utp = ± 1 ns ± 0.003 % 

Heat pulse 

duration 

Oscilloscope Utp = ± 5 ns ± 0.015 % 

Voltage pulse Agilent # 81104A pulse generator ± (3 % + 150 mV) ± 3 % 

Heat pulse Agilent # 81104A pulse generator ± 3 % ± 3 % 

Linear 

positioner 

Deltron Slide model 1201-series 2200. ± 0.02 mm ± 0.1 % 

Magnetic field 

intensity 

Model 460 3-Channel Gaussmeter by 

Lake Shore Cryotronics with Hall 

Sensor 

± 0.016 T ± 1 % 

Liquid pressure pressure transducer ± 0.2 kPa ± (0.5 -2) % 

temperature 

sensor 

Thermistor T320/E320 Series ± 0.1 K ± 0.03 % 

DC voltage Agilent 34970A/34972A ± 0.004 % ± 0.004 % 

AC voltage Agilent 34970A/34972A ± 0.06 % ± 0.06 % 

resistance Agilent 34970A/34972A ± 0.01 % ± 0.01 % 

Bath 

temperature 

Fluke Model 7103 ± 0.25 K ± 0.07 % 

cpm DSC in Two Phase Heat Transfer 

Laboratory at NIST 

± 3 % ± 3 % 

Mm Mettler XS1003S in Two Phase Heat 

Transfer Laboratory at NIST 

± 0.002 g ± 0.04 % 

Vc Mettler XS1003S and density of fluid ± 9 × 10-8 m3 ± 1 % 

21
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Fig. 1 Halbach magnet with magnetic field lines (Lee, et al., 2002) 

22
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Fig. 2 Simple schematic of test apparatus 

23
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Fig. 3 Transient pressure pulse in test section 

24
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

Fig. 4 Change in pressure for various water volumes for a magnetocaloric temperature change 

of 2 K, 5 K, and 10 K 

25
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

Fig. 5 Change in pressure for various R123 volumes for a magnetocaloric 

temperature change of 2 K, 5 K, and 10 K 

26
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Fig. 6 Example case illustrating the liquid pressure pulse for a volume of 9 cm3 and 

an applied voltage of 20 V for 34.6 μs
 

27
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Fig. 7 Example case illustrating the pressure change during cooling after a pulse for a
 

volume of 9 cm3 and an applied voltage of 20 V for 34.6 μs
 

28
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Fig. 8 Side-view schematic of test apparatus 

29
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Fig. 9 Top-view schematic of test apparatus 

30
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

APPENDIX A: TEST EQUIPMENT 

Commercial test equipment and products are identified here and in Table 1 of this paper in order 

to specify the test apparatus sufficiently to facilitate its construction. Changes in the availability 

of test equipment and products may necessitate the re-specification of test equipment and 

products. In addition, changes in specifications may also arise if we become aware of better 

equipment or material at the time of test apparatus construction. This appendix is meant to serve 

as a record from which to begin the building of the test apparatus. 

Fig. A.1 Agilent # 81104A pulse generator 

Fig. A.2 Model 460 3-Channel Gaussmeter 

31
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

APPENDIX B: PARTS FOR NIST FABRICATION DIVISION 

Magnet Holders: Quantity 2 

The bar magnet holder is to be made in two parts. This first, shown below in Fig. B.1, is an 

aluminum cradle with drill-through holes to match hole positions on the stage of the positioning 

device. Each dimension of the cavity of the cradle is oversized by approximately 2 mm as 

compared to the bar magnet dimensions. The lid, shown in Fig. B.2, is an aluminum plate with 

drill through holes to match the mounting holes on the cradle. Aluminum wedges will be used to 

fix the position of the bar magnet within the cavity. 

Fig. B.1 Bottom of Bar Magnetic Holder 

32
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
The exact positioning of the holes will be determined once the linear positioner has been 

purchased. 

Fig. B.2 Lid for Bar Magnetic Holder 

33
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Mounting Plate 

The mounting plate drawing is shown in Fig. A.3. The exact positioning of the holes will be 

determined once the linear positioner has been purchased. There are eight drill through holes for 

the two positioners. The center-two holes are drill-through for the valve block. 

Fig. B.3 Mounting Plate 

34
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
 

 

 

 

 

 

 

 

 

 

APPENDIX C: MCE TEMPERATURE CHANGE FOR POLYNOMIALS 

Because the measured relationship between pressure and time may not be linear as shown in Fig. 

6, expressions are provided for calculating the ∆TM for either a quadratic or a cubic fit of 

pressure with respect to time as appropriate. A cubic relationship between pressure and time is: 

P = P +C t +Ct 2 +Ct 3 (C.1) f b 1 2 3 

Here the fitting constants are C1 through C3. The quadratic expression is obtained from eq. (C.1) 

by setting the constant C3 to zero. 

The first law of thermodynamics for the test apparatus, eq. (9), can be rewritten in terms of 

constants: 

dPf A (Pf − P ) = A1 + A (C.2) 0 b 2 dt 

Table C.1 provides the expressions for the A0 through A2 constants for the four different heat 

transfer cases that will be measured with the test apparatus. 

Substitution of eq. (C.1) and the derivative of eq. (C.1) with respect to time into eq. (C.2) and 

rearranging to solve for A2 yields: 

A = − t AC 2 ( 3 AC + ( − 2AC ) + t AC − 3AC ) + AC t (C.3) 2 11 01 12 0 2 13 0 3 

By substituting A2 for W into eq. (14), the ∆TM of the magnetocaloric test sample for a cubic 

dPf/dt fit is calculated as: 

−1 tp tp   AC   AC  AC  0 1 2 0 2 0 3 3 ∆T M = d = AC + t AC − + t AC − − t ∫W t  1 1 p  1 2  p  1 3  p  (C.4) Mc   2 m pm 0 M cm pm   3  4 

Here, tp is the time for the pressure to rise or fall from Pb to either the maximum or the minimum 

pressure, respectively. Equation (C.4) reduces to the expression for the quadratic pressure fit by 

setting C3 equal to zero. 

35
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931
Table C.1: Equation (C.2) Constants for MCE Cases 

MCE Case A0 A1 A2 

MCE heating dT hA 

dP ρ

− f 

c f 

f 

1 d V 

dP 

λ

ρ

   −   

-W 

Cooling after MCE 

heating 

dT hA 

dP ρ

− f 

c f 

f 

1 d V 

dP 

λ

ρ

   −   

0 

MCE cooling dT hA 

dP ρ

− f 

c f 

f 

1 d V 

dP 

λ

ρ

   −   

+W 

Heating after MCE 

cooling 

dT hA 

dP ρ

− f 

c f 

f 

1 d V 

dP 

λ

ρ

   −   

0 

36
 

______________________________________________________________________________________________________ 

This publication is available free of charge from: http://dx.doi.org/10.6028/NIST.TN.1931