# Exergy Analysis of a Parallel-Plate Active Magnetic Regenerator with Nanofluids

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}O

_{3}nanofluids as heat transfer fluids. A 1D numerical model has been extensively used to quantify the exergy performance of a system composed of a parallel-plate regenerator, magnetic source, pump, heat exchangers and control valves. Al

_{2}O

_{3}-water based nanofluids are tested thanks to CoolProp library, accounting for temperature-dependent properties, and appropriate correlations. The results are discussed in terms of the coefficient of performance, the exergy efficiency, and the cooling power as a function of the nanoparticle volume fraction and blowing time for a given geometrical configuration. It is shown that while the heat transfer between the fluid and solid is enhanced, it is accompanied by smaller temperature gradients within the fluid and larger pressure drops when increasing the nanoparticle concentration. It leads in all configurations to lower performance compared to the base case with pure liquid water.

## 1. Introduction

^{−1}for gadolinium at room temperature [1]. A heat transfer fluid, typically water, is then used as a heat transfer medium to remove heat. This process (Brayton cycle) produces cold and reaches steady-state conditions after a number of repeated cycles.

## 2. One-Dimensional Numerical Method

#### 2.1. Description of the System

_{HHEX}), the valve opens to keep the temperature constant. Third, the magnetic field is removed and the magnetic entropy increases. As a result of the demagnetization, the temperature of the MCM goes down below its original value. For the last step, the refrigerant is pumped from the hot to the cold end, referred as a hot blow. It follows that the temperature in the cold reservoir decreases. In a similar way to the cold blow, the valve now opens if the temperature drops below T

_{CHEX}. Hence, heat is absorbed to maintain the same temperature level.

#### 2.2. Numerical Modeling

#### 2.2.1. Assumptions

- The system operating near room temperature, adiabatic conditions may be assumed. It has been carefully checked that including losses to the surroundings leads to similar results.
- The plates are made of gadolinium (Gd), which is the most common material used in magnetic refrigeration near room temperature. To model the magnetocaloric effect (MCE), the experimental data of Dankov et al. [18] are used showing better results compared to the Weiss-Debye-Sommerfeld model. The properties of Gd are temperature- and pressure-dependent thanks to Coolprop library.
- The magnetic field is applied in the y-direction (Figure 1). As a first step, the demagnetization is neglected. The reader can refer to the works of Nielsen et al. [19], Engelbrecht et al. [20] and Mugica et al. [15] for details on the impact of the demagnetization effect on the performance of the AMR.
- The magnetic field is assumed equally applied throughout the entire length of the regenerator. The parasitic losses are neglected. Their influence on the AMR performance has been discussed in [20].
- The time for magnetization or demagnetization is fixed to t
_{mag}= t_{demag}= 0.01 s and no idle time between each step of the cycle is considered. - The flow is supposed to be laminar, fully-developed and steady-state with only one uniform velocity component V in the streamwise direction. The impact of flow maldistribution discussed in [20] is not taken into account here.
- Nanofluids are assumed to be single-phase fluids with constant volumetric concentration in nanoparticles $\varphi $ throughout the domain. Their thermophysical properties depend on the fluid and nanoparticle properties, $\varphi $ and the local temperature T.

#### 2.2.2. Energy Equations

_{P}(or c) and λ represent the density (kg·m

^{−3}), the heat capacity (J·kg

^{−1}·K

^{−1}) and thermal conductivity (W·m

^{−1}·K

^{−1}) of the materials respectively. Note that the solid is subjected to an instantaneous increase in temperature due to magnetization since the magnetic work term is neglected in Equation (2). The heat capacity of the solid depends also on the applied magnetic field.

^{−2}·K

^{−1}) is evaluated through: h = Nu D

_{h}/λ

_{f}, where D

_{h}is the hydraulic diameter defined by D

_{h}= 4 e

_{f}l/(2e

_{f}+ l), for a parallel-plate regenerator. As the flow between two plates is symmetric, e

_{f}is half the fluid thickness only and l represents the width of one plate. The heat transfer coefficient h is evaluated using the Nusselt number for constant laminar flow in rectangular ducts (see in [21]):

^{−3}is the aspect ratio of the duct leading to Nu = 8.2831. The maximum value of the Reynolds number is obtained here for pure liquid flow: Re = ρ

_{f}V D

_{h}/μ

_{f}~ 40 confirming the laminar nature of the flow. During the magnetization and demagnetization phases, Nu = 4 as suggested in [17].

#### 2.2.3. Heat Transfer Fluid Properties

_{2}O

_{3}nanofluids are used in Section 3. The main advantages of alumina nanoparticles are their very low price and the absence of corrosion in thermal systems. Their properties are evaluated using the common relations for the density ρ and heat capacity C

_{p}[23] as follows:

_{2}O

_{3}-water-based nanofluids with a mean particle diameter of 47 nm, Equations (8) and (9) provided by Maïga et al. [24] then used by Mintsa et al. [25] have proven to be accurate in most configurations as shown by Sekrani et al. [26] for laminar flows in an uniformly heated pipe. Equations for the dynamic viscosity μ and the thermal conductivity λ of the nanofluid write:

_{np}= 3900 kg·m

^{−3}, C

_{p,np}= 775 J·kg

^{−1}·K

^{−1}and λ

_{np}= 40 W·m

^{−1}·K

^{−1}.

_{μ}/C

_{λ}was introduced as a kind of merit function by Prasher et al. [27] to recommend or not a given nanofluid. In the present case, this ratio, which slightly varies both with temperature and nanoparticle concentration, remains close to 3.537 ± 0.1%. It means that the increase in viscosity is always larger than the increase in thermal conductivity when the nanoparticle concentration increases but as C

_{μ}/C

_{λ}remains lower than 4, it can be recommended as a heat transfer fluid after [27].

#### 2.2.4. Numerical Method and Parameters

#### 2.3. Thermodynamic Analysis

_{mot}= 0.90, η

_{Fou}= 0.95, η

_{hys}= 0.97. The formula to evaluate work power (W) is:

_{p}= 0.95, F is the flow rate (m

^{3}·s

^{−1}) and t

_{blow}the blowing time (s).

_{0}) and the source temperatures (T

_{HS}and T

_{CS}). The exergy (E

_{x}) produced at each end is the product of the Carnot efficiency (Ɵ) with the heat transfer rate ($\dot{Q}$):

_{HX}= T

_{HS}− T

_{0}= T

_{0}− T

_{CS}(Figure 1). Finally, COP and exergy efficiency η

_{ex}are defined as:

## 3. Results and Discussion

_{0}= 293 K and P

_{0}= 10

^{5}Pa. The parameter L and e

_{s}represent the length and half the thickness of one plate, respectively.

_{f}F ${c}_{p,f}{t}_{blow}/\left({m}_{s}{c}_{s}\right)$. It is a dimensionless parameter classically used to characterize the conditioning of the system [2], which depends on the volumetric flow rate F and the blowing time ${t}_{blow}$ among other parameters. The cycle frequency is given by f = 1/[2(t

_{blow}+ t

_{mag})] and will be varied between 0.125 Hz and 0.495 Hz. The fluid and solid properties are averaged values over the temperature range. Rowe [29,30] introduced also the parameter R defined as: R = 1 + UF, which is the ratio of total thermal mass to the solid thermal mass. As it will be shown in the following sections, UF remains relatively small in the present study such that R ≈ 1.

#### 3.1. Influence of the Nanoparticle Concentration

_{blow}= 1 s (f = 0.495 Hz) and F = 10

^{−6}m

^{3}·s

^{−1}. Note that, on this figure, UF slightly varies from one nanoparticle concentration to another, from UF = 0.0473 at $\varphi $ = 0% to UF = 0.0467 at $\varphi $ = 5%. The COP and the exergy efficiency decreases quadratically with $\varphi $, while the absorbed power decreases linearly with the volume fraction in nanoparticles $\varphi $. For examples, for pure water: COP = 4.87, η

_{ex}= 16.81% and ${\dot{Q}}_{abs}$ = 55.29 W and for $\varphi $ = 5%, COP = 1.88, η

_{ex}= 6.93% and ${\dot{Q}}_{abs}$ = 49.44 W. Introducing nanoparticles increases rapidly the pressure drop and as a consequence, the pumping power $\dot{{W}_{p}}$ required to operate the system. It increases then the total work power $\dot{W}$ and then decreases the COP (Equation (11)). At the same time, the presence of nanoparticles leads to an increase of the cold source temperature. Though the weak increase of the mass flow rate, it is accompanied by a global decrease of the absorbed power ${\dot{Q}}_{abs}$ and so of the exergy efficiency η

_{ex}(Equation (11)).

^{2}/m

^{3}), i.e., the ratio between the heat transfer area and the total volume of the regenerator.

_{conv}contributes to 87.71% of the total generated entropy S

_{gen}. It may be attributed to the particularly high surface area density of the present regenerator. The other contributions come from the viscous losses S

_{viscous}(10.12%), the conduction within the MCM S

_{Scond}(2.05%) and the conduction within the fluid S

_{Fcond}(0.12%).

_{2}O

_{3}nanoparticles dispersed in water have on the system. It does not only increase the viscous losses greatly, but the entropy generated by conduction within the fluid domain increases more rapidly than the one associated to convection. In this case, an increase of S

_{conv}means a higher heat transfer between the fluid and solid domains. This result was expected as the thermal conductivity of the fluid increased by adding the nanoparticles. This increase is regarded as a positive effect, as S

_{conv}can be lowered by shifting to a hybrid Brayton-Ericsson cycle by lowering F and increasing t

_{blow}at the same time (see for example the work of Plaznik et al. [32]). Nonetheless, the increase of S

_{Fcond}points out that more heat is travelling in the longitudinal direction of the regenerator, destroying to some extent the temperature difference attained in the case with pure water.

#### 3.2. Influence of the Blowing Time

_{blow}are modified, even if UF is kept constant. Thus, the objective of the present section is quantify the influence of the blowing time t

_{blow}(or cycle frequency f) both at a constant volumetric flow rate (such UF will vary) and at constant UF (such that F is changed accordingly to the blowing time variations). Changing the blowing time is expected to enable the nanofluid to catch more or less thermal energy from the MCM.

^{−6}m

^{3}·s

^{−1}. The variations of UF directly represent the variations of t

_{blow}. The absorbed power increases almost linearly with the blowing time up to a maximum value at t

_{blow}= 3 s, while the COP and the exergy efficiency decrease at the same time. It confirms the results of Rowe [30] at R ≈ 1, which obtained also a decrease of the efficiency and an increase of the cooling power when UF increases. The main result here is that, for this range of utilization factor (UF = [0.0467, 0.187]), introducing nanoparticles into the base fluid leads to lower overall performance of the system, whatever the value of $\varphi $.

_{ex}. The linear increase of the absorbed power ${\dot{Q}}_{abs}$ up to UF ≈ 0.14 (t

_{blow}= 3 s or f = 0.166 Hz) is directly connected to a linear decrease of the cold source temperature when UF is increased.

_{ex}and ${\dot{Q}}_{abs}$ exhibit the same profile and increase when the blowing time is increased. The rejected heat exhibits a non monotonous profile for all cases (not shown here), with a decrease (in magnitude) up to t

_{blow}= 1.5 s and then it increases up to t

_{blow}= 5 s. Tagliafico et al. [8] obtained a decrease of the COP for increasing values of the cycle frequency for a gadolinium AMR (m = 395 g, B = 1.7 T) for an utilization factor that maximizes the refrigeration capacity. However, the amplitude of its decrease was lower for f = [0.1–0.6] Hz in their case. The results of Lei et al. [16] confirmed this trend whatever the geometry considered (packed bed spheres, parallel plates or pack screen bed). However, they showed also that COP could also increase with the cycle frequency for large aspect ratios depending on the geometry and hydraulic parameter.

_{blow}= [1, 5] s, f = [0.1, 0.495] Hz, F = [0.4, 2.03] × 10

^{−6}m

^{3}·s

^{−1}and UF = [0.0467, 0.189]. These ranges do not correspond to any marketable AMR device but have been considered in the literature. The main result obtained here is that whatever the nanoparticle concentrations and the operating conditions, adding alumina nanoparticles to water lead to lower performance in terms of COP, exergy efficiency and cooling power compared to pure water.

## 4. Conclusions

_{blow}= 3 s. At constant utilization factor, COP, exergy efficiency and cooling power are found to increase with the blowing time.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Bouchekara, H. Recherche sur les Systèmes de Réfrigération Magnétique: Modélisation Numérique, Conception et Optimisation. Ph.D. Thesis, Institut National Polytechnique de Grenoble, Grenoble, France, 2008. (In French). [Google Scholar]
- Kitanovski, A.; Tušek, J.; Tomc, U.; Plaznik, U.; Ožbolt, M.; Poredoš, A. Magnetocaloric Energy Conversion: From Theory to Applications, Green Energy and Technology; Springer: New York, NY, USA, 2015. [Google Scholar]
- Pecharsky, V.V.; Cui, J.; Johnson, D.D. (Magneto) caloric refrigeration: Is there light at the end of the tunnel? Philos. Trans. R. Soc. A
**2016**, 374. [Google Scholar] [CrossRef] [PubMed] - Trevizoli, P.V.; Christiaanse, T.V.; Govindappa, P.; Niknia, I.; Teyber, R.; Barbosa, J.R., Jr.; Rowe, A. Magnetic heat pumps: An overview of design principles and challenges. Sci. Technol. Built Environ.
**2016**, 22, 507–519. [Google Scholar] [CrossRef] - Yu, B.; Liu, M.; Egolf, P.W.; Kitanovski, A. A review of magnetic refrigerator and heat pump prototypes built before the year 2010. Int. J. Refrig.
**2010**, 33, 1029–1060. [Google Scholar] [CrossRef] - Tusek, J.; Kitanovsky, A.; Zupan, S.; Prebil, I.; Poredos, A. A comprehensive experimental analysis of gadolinium active magnetic regenerators. Appl. Therm. Eng.
**2013**, 53, 57–66. [Google Scholar] [CrossRef] - Trevizoli, P.V.; Nakashima, A.T.; Peixer, G.F.; Barbosa, J.R., Jr. Performance assessment of different porous matrix for active regenerators. Appl. Energy
**2017**, 187, 847–861. [Google Scholar] [CrossRef] - Tagliafico, G.; Scarpa, F.; Canepa, F. A dynamic 1-D model for a reciprocating active magnetic regenerator; influence of the main working parameters. Int. J. Refrig.
**2010**, 33, 286–293. [Google Scholar] [CrossRef] - Tura, A.; Nielsen, K.K.; Rowe, A. Experimental and modeling results of a parallel plate-based active magnetic regenerator. Int. J. Refrig.
**2012**, 35, 1518–1527. [Google Scholar] [CrossRef] - Wu, J.; Liu, C.; Hou, P.; Huang, Y.; Ouyang, G.; Chen, Y. Fluid choice and test standardization for magnetic regenerators operating at near room temperature. Int. J. Refrig.
**2014**, 37, 135–146. [Google Scholar] [CrossRef] - Nielsen, K.; Tušek, J.; Engelbrecht, K.; Schopfer, S.; Kitanovski, A.; Bahl, C.; Smith, A.; Pryds, N.; Poredoš, A. Review on numerical modeling of active magnetic regenerators for room temperature applications. Int. J. Refrig.
**2011**, 34, 603–616. [Google Scholar] [CrossRef] [Green Version] - Trevizoli, P.V.; Nakashima, A.T.; Barbosa, J.R., Jr. Performance evaluation of an active magnetic regenerator for cooling applications—Part II: Mathematical modeling and thermal losses. Int. J. Refrig.
**2016**, 72, 206–217. [Google Scholar] [CrossRef] - Niknia, I.; Campbell, O.; Christiaanse, T.V.; Govindappa, P.; Teyber, R.; Trevizoli, P.V.; Rowe, A. Impacts of configuration losses on active magnetic regenerator device performance. Appl. Therm. Eng.
**2016**, 106, 601–612. [Google Scholar] [CrossRef] - Roy, S.; Poncet, S.; Sorin, M. Sensitivity analysis and multiobjective optimization of a parallel-plate active magnetic regenerator using a genetic algorithm. Int. J. Refrig.
**2017**, 75, 276–285. [Google Scholar] [CrossRef] - Mugica, I.; Poncet, S.; Bouchard, J. Entropy generation in a parallel-plate active magnetic regenerator with insulator layers. J. Appl. Phys.
**2017**, 121, 074901. [Google Scholar] [CrossRef] - Lei, T.; Engelbrecht, K.; Nielsen, K.K.; Veje, C.T. Study of geometries of active magnetic regenerators for room temperature magnetocaloric refrigeration. Appl. Therm. Eng.
**2017**, 111, 1232–1243. [Google Scholar] [CrossRef] - Roudaut, J. Modélisation et Conception de Systèmes de Réfrigération Magnétique autour de la Température Ambiante. Ph.D. Thesis, Université de Grenoble, Grenoble, France, 2012. (In French). [Google Scholar]
- Dankov, S.Y.; Tishin, A.; Pecharsky, V.; Gschneidner, K. Magnetic phase transitions and the magnetothermal properties of gadolinium. Phys. Rev. B
**1998**, 57, 1–13. [Google Scholar] [CrossRef] - Nielsen, K.K.; Smith, A.; Bahl, C.R.H.; Olsen, U.L. The influence of demagnetizing effects on the performance of active magnetic regenerators. J. Appl. Phys.
**2012**, 112, 094905. [Google Scholar] [CrossRef] [Green Version] - Engelbrecht, K.; Tusek, J.; Nielsen, K.K.; Kitanovski, A.; Bahl, C.R.H.; Poredos, A. Improved modelling of a parallel plate active magnetic regenerator. J. Phys. D
**2013**, 46, 255002. [Google Scholar] [CrossRef] - Rohsenow, W.M.; Hartnett, J.P.; Cho, Y.L. Handbook of Heat Transfer; McGraw-Hill: New York, NY, USA, 1998. [Google Scholar]
- Garby, L.; Larsen, P.S. Bioenergetics: Its Thermodynamic Foundations; Cambridge University Press: Cambridge, UK, 1991. [Google Scholar]
- Bianco, V.; Manca, O.; Nardini, S.; Vafai, K. Heat Transfer Enhancement with Nanofluids; CRC Press: New York, NY, USA, 2015. [Google Scholar]
- Maïga, S.E.B.; Palm, S.M.; Nguyen, C.T.; Roy, G.; Galanis, N. Heat transfer enhancement by using nanofluids in forced convection flows. Int. J. Heat Fluid Flow
**2005**, 26, 530–546. [Google Scholar] [CrossRef] - Mintsa, H.A.; Roy, G.; Nguyen, C.T.; Doucet, D. New temperature dependent thermal conductivity data for water-based nanofluids. Int. J. Therm. Sci.
**2009**, 48, 363–371. [Google Scholar] [CrossRef] - Sekrani, G.; Poncet, S. Further investigation on Laminar forced convection of nanofluid flows in a uniformly heated pipe using direct numerical simulations. Appl. Sci.
**2016**, 6, 1–24. [Google Scholar] [CrossRef] - Prasher, R.; Song, D.; Phelan, J.W. Measurements of nanofluid viscosity and its implications for thermal applications. Appl. Phys. Lett.
**2006**, 89, 133108. [Google Scholar] [CrossRef] - Kitanovski, A.; Egolf, P.W. Application of magnetic refrigeration and its assessment. J. Magn. Magn. Mater.
**2009**, 321, 777–781. [Google Scholar] [CrossRef] - Rowe, A. Thermodynamics of active magnetic regenerators: Part I. Cryogenics
**2012**, 52, 111–118. [Google Scholar] [CrossRef] - Rowe, A. Thermodynamics of active magnetic regenerators: Part II. Cryogenics
**2012**, 52, 119–128. [Google Scholar] [CrossRef] - Trevizoli, P.V.; Barbosa, J.R., Jr. Entropy generation minimization analysis of oscillating-flow regenerators. Int. J. Heat Mass Transf.
**2015**, 87, 347–358. [Google Scholar] [CrossRef] - Plaznik, U.; Tusek, J.; Kitanovski, A.; Poredos, A. Numerical and experimental analyses of different magnetic thermodynamic cycles with an active magnetic regenerator. Appl. Therm. Eng.
**2013**, 59, 52–59. [Google Scholar] [CrossRef] - Li, P.; Gong, M.; Yao, G.; Wu, J. A practical model for analysis of active magnetic regenerative refrigerators for room temperature applications. Int. J. Refrig.
**2006**, 29, 1259–1266. [Google Scholar] [CrossRef]

**Figure 1.**Simplified scheme of the active magnetic regenerative refrigeration (AMRR) and its power balance.

**Figure 2.**Influence of the nanoparticle concentration $\varphi $ on the Coefficient of Performance (COP), exergy efficiency and absorbed power ${\dot{Q}}_{abs}$. Results obtained for UF around 0.047 (t

_{blow}= 1 s or f = 0.495 Hz and F = 10

^{−6}m

^{3}·s

^{−1}).

**Figure 3.**Evolution of the generated entropy according to the nanoparticle concentration $\varphi $ for utilization factor (UF) around 0.047 (t

_{blow}= 1 s or f = 0.495 Hz, F = 10

^{−6}m

^{3}·s

^{−1}). The results are normalized by their values for $\varphi $ = 0% (S

_{conv}= 16.95 J·m

^{−2}·K

^{−1}, S

_{Fcond}= 0.023 J·m

^{−2}·K

^{−1}, S

_{Scond}= 0.396 J·m

^{−2}·K

^{−1}, S

_{viscous}= 1.956 J·m

^{−2}·K

^{−1}).

**Figure 4.**Variations of the COP, exergy efficiency η

_{ex}and absorbed power ${\dot{Q}}_{abs}$ (

**a**,

**b**,

**c**) as a function of the utilization factor UF (at constant flow rate F = 10

^{−6}m

^{3}·s

^{−1}) and (

**d**,

**e**,

**f**) as a function of the blowing time (at constant utilization factor UF = 0.095).

Material | B | L | e_{f} | e_{s} | ∆T_{HX} |
---|---|---|---|---|---|

0.2 kg (Gd) | 1.5 T | 0.1 m | 0.15 mm | 0.5 mm | 5 K |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mugica, I.; Roy, S.; Poncet, S.; Bouchard, J.; Nesreddine, H.
Exergy Analysis of a Parallel-Plate Active Magnetic Regenerator with Nanofluids. *Entropy* **2017**, *19*, 464.
https://doi.org/10.3390/e19090464

**AMA Style**

Mugica I, Roy S, Poncet S, Bouchard J, Nesreddine H.
Exergy Analysis of a Parallel-Plate Active Magnetic Regenerator with Nanofluids. *Entropy*. 2017; 19(9):464.
https://doi.org/10.3390/e19090464

**Chicago/Turabian Style**

Mugica, Ibai, Steven Roy, Sébastien Poncet, Jonathan Bouchard, and Hakim Nesreddine.
2017. "Exergy Analysis of a Parallel-Plate Active Magnetic Regenerator with Nanofluids" *Entropy* 19, no. 9: 464.
https://doi.org/10.3390/e19090464