Enhancements of thermal performances of an active magnetic refrigeration device based on nanofluids

Y. Chiba*, A. Smaili**, O. Sari*** *Department of Mechanical Engineering, Faculty of Science and Technology, University of Medea, 26.000, Algeria, E-mail: Chiba.younes@univ-medea.dz **Ecole Nationale Polytechnique, Laboratoire de Génie Mécanique et Développement, P.B. 182,El-Harrach, Algiers, 16200, Algeria, E-mail: arezki.smaili@g.enp.edu.dz ***University of Applied Sciences of Western Switzerland, Avenue des sports 20, 1400, Yverdon-Les-Bains, Switzerland, E-mail: osmann.sari@heig-vd.ch


Introduction
In the past few decades, a large number of experimental and numerical studies of magnetic refrigeration devices near room temperature have been published, either in a magnetic refrigeration system or in magnetocaloric materials [1][2][3][4][5][6][7][8][9].For active magnetic regenerator refrigerator device, the heat transfer plays an important role between magnetocaloric material and carrier fluid.It is strongly desirable to increase the efficiency of rate of heat exchange due to the magnetization and demagnetization of magnetocaloric material and carrier fluid.These new advanced concepts of nanofluids offer good heat transfer characteristics compared to conventional fluid.
To do this, a new concept for intensification of heat transfer was introduced by Masuda et al. 1993 [10] and Choi 1995 [11] called nanofluids.It becomes possible to increase the efficiency of any machine and reduce the operating costs of magnetocaloric devices.Many researches dedicated to nanofluids are carried out in order to improve heat transfer by convection [12][13].
Different areas of application of nanofluids have been reported elsewhere by Saidur et al. 2011 [14], such as:  cooling and air conditioning systems;  engine cooling;  transformer cooling oil and lubrications;  nuclear systems;  solar energy and thermal storage;  drilling;  defense and space;  biomedical applications.
The main objective of this work is to propose novel method for increasing the rate of heat exchange by convection between the carrier fluid and magnetocaloric material, a new class of fluids called nanofluids containing a small particles, such as Al2O3 suspended in water, have thermal properties compared with the those of the water.The results on the performance predictions obtained by using nanofluids (Al2O3) and water are presented and discussed.
The heat transfer by using nanofluids have several advantages [14]:  more heat transfer area between fluids and particles;  high thermal conductivity by varying particles concentration;  reduced pumping power as compared to conventional fluids;  high stability.However, nanofluids possess the following chal-lenges:  long term stability of nanoparticles dispersion;  increased pressure drop and pumping power;  higher viscosity;  high cost of nanofluids;  difficulties in production process.The thermophysical properties of nanofluids; density, specific heat capacity, viscosity and thermal conductivity are dependent on the volume fraction of nanoparticles and base fluid can be defined by relationships [15]: where The calcul of viscosity and thermal conductivity based on semi-empirical correlations can be defined by following equations [15]:

Description of magnetic refrigeration cycle
Fig. 1 Schematic diagram of the AMR cycle setup [8,6] Fig. 1 shows a schematic diagram of an AMR cycle developed at HE-SO, Switzerland, which is composed of (i) a two regenerators bed (i.e.magnetocaloric material which can act as refrigerant and regenerator media); (ii) a blower to force the flow throughout the regenerator at convenient velocity; (iii) a circulating heat transfer fluid (i.e. in this study nanofluid and water).The AMR cycle consists of four steps, namely, isentropic magnetization and demagnetization processe, by application and removal of a magnetic field, as well as cold and hot blows (i.e.cooling and heating the circulating fluid).
The mains steps of AMR cycle can be described in detail as follows [2,4,16]:  isentropic magnetization process;  hot blow at applied magnetic field;  isentropic demagnetization process;  cold blow at removed magnetic field.

Thermodynamic approach
Based on the heat energy equation, the heat trans-fer through the regenerator bed of nanofluid can be written as: The heat energy equation for magnetocaloric material can be written as:

Heat transfer
The Nusselt number characterized heat transfer by convection in the case of parallel plates between the carrier fluid and the magnetocaloric material.For base fluid (water), Nusselt number has been calculated by using correlation proposed by Ghiaasiaan, 2011 [17].For constant wall temperature (boundary condition): The coefficient DB and DT can be calculated by using correlation proposed by Malvandi et al. 2014 [19]: In addition, the following correlation developed by Karimipour in 2015 can be used to determine the nanofluid Nusselt number in a microchannel as a function of:

Magnetocaloric properties
The properties of magnetocaloric material has been determined by using mean field theory based on magnetism and thermodynamic.The heat specific total capacity consists of three components; namely, the magnetic heat specific capacity, electronic heat specific capacity and lattice heat specific capacity.
The total heat specific can be expressed by the equation:

c B T c B T c T c T S B T S T S T T
where cm, cl and ce are respectively the magnetic heat spe-cific capacity, electronic heat specific capacity and lattice heat specific capacity.Magnetic entropy, lattice entropy and electronic entropy is given by relation: where where   J B  Brillouin function given by: Lattice entropy:   The magnetocaloric effect by using mean field theory can be calculated as function of heat specific and total entropy.

Resolution method
The discretization of the energy equations of the solid and the nanofluid has been carried by using the finite differences method implicit scheme as described in the equations (Eq.( 24)-( 28).
The nanofluid energy equation is given by: The solid energy equation is given by: The main steps of the resolution of the discrete equations obtained are shown in Fig. 2 as well, the system of equations obtained was resolved by using Tridiagonal Matrix Algorithm (TDMA).

Fig. 2 Numerical algorithm AMR cycle
The average cold outlet nanofluid temperature is given by the relation: Once steady cyclic state is obtained, the resulting cooling capacity and coefficient of performance can be calculated as follows: The exergy and coefficient of performance of AMR cycle can be calculated as:

Results and discussion
Table 1 shows the thermophysical properties of base fluid (water) and nanoparticles (Alumina) composed of nanofluids and used in numerical simulation of AMR device.3 Impact of nanoparticle volume fraction on thermophysical properties of nanofluids Fig. 3 shows variation of ration of thermophysical properties (thermal conductivity, specific heat, density and Prandtl number) of nanofluids as function of nanoparticle volume fraction.Fig. 3 illustrates clearly the positive impact of the increase of the volume of the particles on number of Prandtl and the thermal conductivity and negative impact on the viscosity and the specific heat.
The results presented in Fig. 4, show the variation of magnetocaloric effect under magnetic field of 2T and specific heat capacity at magnetic field of 0T and 2T as function of the temperature for magnetocaloric material Gadolinium by using molecular field theory approach.These properties have been injected in numerical model to compute the physical parameters of active magnetic refrigerator.
Fig. 4 Variation of adiabatic temperature and specific heat as function of temperature.
Fig. 5 shows impact of frequency on the evolutions of the average cold outlet temperature of nanofluid without load under magnetic field of 2T as function of cycle number.As it can be seen, all the curves exhibit sharp decreasing trends with number of cycle, then an asymptotic behaviour towards the steady state.More the frequency value is higher more is slower the convergence towards the steady state.9 show respectively evolution of cooling power as function of temperature span and cold temperature under magnetic field of 2T and operating pa-rameters; namely, mass flow rate of 0.15 kg/s and temperature of hot exchanger of 21°C.As it can be seen, differences up to 15% have been noted between nanofluid and water.Fig. 10 and Fig. 11 show respectively evolution of coefficient of performance as function of temperature span and cold temperature under magnetic field of 2T and operating parameters; namely, mass flow rate of 0.15 kg/s and temperature of hot exchanger of 21°C.As it can be seen, differences up to 15% have been noted between nanofluid and water.

Conclusion
In this paper, a numerical study on a magnetic refrigeration device operating near room temperature has been carried out.The obtained results confirm that nanofluid offers higher heat performance than water with differences about to 15% have been noted.
The potential of nanofluids is promising and can be considered for the future fluids for the enhancement and intensification of heat transfer on multi-domain.The proposed numerical model and the obtained results enable us to clarify the opportunity and utility of using and applying nanofluids in magnetic refrigeration devices.Finally, future works will be focus on experimental study to validate the numerical model and the results obtained of this model will be used again by comparing with other type of nanofluids.

Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 10 Fig. 11
Fig. 5 Variation of average temperature cold reservoir as function of cycle number at different values of frequency without load under magnetic field of 2T Fig. 6 and Fig. 7 show respectively evolution of exergy as a function of span temperature and as a function of cold temperature under magnetic field of 2T and operating parameters; namely, mass flow rate of 0.15 kg/s and

Table 1
Thermophysical properties of base fluid and nanoparticles