Islam A Hassan

Ramy H Mohammed

Haitham S Ramadan

Mohamed A Saleh

Fermin Cuevas

Daniel Hissel

Performance evaluation of a novel concentric metal hydride reactor

Keywords: Hydrogen, Storage, Metal Hydride, Phase change material, Heat transfer, Reactor

Introduction

Energy storage is a promising solution to the discontinuity problem of energy production from renewables. Hydrogen has a great potential for storage of excess renewable energy, such as solar or wind energy, especially for long-term storage. Hydrogen storage is a key parameter in achieving hydrogen economy. According to Hirscher et al. [START_REF] Hirscher | Materials for hydrogen-based energy storage-past, recent progress and future outlook[END_REF], metal hydrides (MHs) have provided ample opportunities in applications such as hydrogen storage, MH compressors, thermal energy storage, electrochemical integration, and hydrogen storage in forklifts. MHs have many advantages over other storage methods, such as high safety level, reliability, high volumetric density, relatively low cost, and operation capability at normal pressure and temperature conditions [START_REF] Barthelemy | Hydrogen storage: recent improvements and industrial perspectives[END_REF][START_REF] Sakintuna | Metal hydride materials for solid hydrogen storage: a review[END_REF][START_REF] Hassan | Hydrogen storage technologies for stationary and mobile applications: Review, analysis and perspectives[END_REF]. AB 5 -type metal hydrides have great potential in hydrogen-based applications.

The performance of MH reactor depends on the heat transfer rate to or from the reactor core. Active heat exchange involves heat transfer fluid passing through the reactor to exchange heat with MH bed.

Different configurations are candidates for MH reactors, such as straight, helical, spiral cooling tubes as well as heat pipes. The effect of key parameters such as overall heat transfer coefficient, cooling fluid flow rate and its inlet temperature as well as supply or drain pressure on reactor behavior was experimentally [START_REF] Mellouli | A novel design of a heat exchanger for a metal-hydrogen reactor[END_REF][START_REF] Dhaou | Experimental study of a metal hydride vessel based on a finned spiral heat exchanger[END_REF][START_REF] Visaria | International Journal of Heat and Mass Transfer Coiled-tube heat exchanger for High-Pressure Metal Hydride hydrogen storage systems -Part 1 . Experimental study[END_REF] and numerically [START_REF] Wu | Magnesium based metal hydride reactor incorporating helical coil heat exchanger: simulation study and optimal design[END_REF][START_REF] Visaria | Coiled-tube heat exchanger for high-pressure metal hydride hydrogen storage systems-Part 2. Computational model[END_REF] investigated for spiral heat exchanger. In addition, Muthukumar [START_REF] Muthukumar | Parametric studies on a metal hydride based hydrogen storage device[END_REF][START_REF] Muthukumar | Study of heat and mass transfer in MmNi4. 6Al0. 4 during desorption of hydrogen[END_REF] numerically studied the effect of these parameters on the straight tube reactor performance. Regarding fin integration into reactor, Dhaou et al. [START_REF] Dhaou | Experimental study of a metal hydride vessel based on a finned spiral heat exchanger[END_REF] experimentally indicated faster kinetics and less critical peak temperature in case of finned spiral heat exchanger. Askri et al. [START_REF] Askri | Optimization of hydrogen storage in metal-hydride tanks[END_REF] predicted up to 80% improvement in absorption time utilizing HTF tube surrounded by fins.

According to Gkanas et al. [START_REF] Gkanas | Efficient hydrogen storage in up-scale metal hydride tanks as possible metal hydride compression agents equipped with aluminium extended surfaces[END_REF], reactor having 60 plain cooling tubes exhibited the same behavior as one having only 12 cooling tubes with longitudinal fins. Moreover, multiple studies [START_REF] Gkanas | Efficient hydrogen storage in up-scale metal hydride tanks as possible metal hydride compression agents equipped with aluminium extended surfaces[END_REF][START_REF] Freni | Finite element-based simulation of a metal hydride-based hydrogen storage tank[END_REF] discussed the effect of the number of cooling tubes on the reactor performance. Unfortunately, the utilization of heat transfer fluids in reactor cooling is associated with significant energy losses as it dissipates reaction heat through absorption and requires heat during desorption process as well as the energy consumption to circulate the heat transfer fluid through MH reactor. On the other hand, thermal conductivity of MH was improved employing copper wire matrix [START_REF] Nagel | Effective thermal conductivity of a metal hydride bed augmented with a copper wire matrix[END_REF], encapsulated powders [START_REF] Kim | Thermal analysis of the Ca0. 4Mm0. 6Ni5 metalhydride reactor[END_REF], expanded natural graphite [START_REF] Chaise | Enhancement of hydrogen sorption in magnesium hydride using expanded natural graphite[END_REF], and metal foam [START_REF] Laurencelle | Simulation of heat transfer in a metal hydride reactor with aluminium foam[END_REF][START_REF] Mellouli | Hydrogen storage in metal hydride tanks equipped with metal foam heat exchanger[END_REF][START_REF] Tsai | On the selection of metal foam volume fraction for hydriding time minimization of metal hydride reactors[END_REF].

The association of phase change materials (PCM) to MHs represents an alternative and promising heat management approach. Garrier et al. [START_REF] Garrier | A new MgH2 tank concept using a phase-change material to store the heat of reaction[END_REF] proposed the integration of PCM into MgH 2 compact discs reactor. Stored hydrogen was equivalent to 21 kWh and could be recovered in 3 h. Reactor behavior and storage efficiency were experimentally assessed at different conditions while connection with fuel cell. Ye et al. [START_REF] Ye | Numerical simulation on the storage performance of a phase change materials based metal hydride hydrogen storage tank[END_REF] numerically investigated PCM integration in MH reactors in two structures: PCM sandwiched between MH layers and PCM surrounding MH. Sandwiched design completed absorption in 1074 s. Thermal conductivity, latent heat and melting temperature of PCM are crucial properties governing the reactor thermal behavior. The effect of these properties on PCM behavior in MH-PCM reactors was intensively discussed [START_REF] Maad H Ben | Heat and mass transfer in a metal hydrogen reactor equipped with a phase-change heat-exchanger[END_REF][START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF]. El Mghari et al. [START_REF] El Mghari | Analysis of hydrogen storage performance of metal hydride reactor with phase change materials[END_REF][START_REF] El Mghari | Selection of phase change materials, metal foams and geometries for improving metal hydride performance[END_REF] investigated multiple PCMs to determine the optimal PCM quantity and metal foam amount. Among utilized PCMs, LiNO 3 •3H 2 O exhibited the best reactor performance. According to Mellouli et al. [START_REF] Mellouli | Numerical analysis of metal hydride tank with phase change material[END_REF], time required for 80% absorption for a spherical reactor was 22% better than that for a cylindrical one.

To overcome the low thermal conductivity of PCM, Mellouli et al. [START_REF] Mellouli | Impact of using a heat transfer fluid pipe in a metal hydride-phase change material tank[END_REF] introduced the integration of a heat transfer pipe into MH-PCM reactor in either MH only or in both MH and PCM. Different fluids and flow rates were investigated. Compared to the reference case, absorption time was reduced for only MH design by 94%, while only 72% improvement was obtained in both MH and PCM scenarios. Tong et al. [START_REF] Tong | Case Studies in Thermal Engineering Performance estimation of dehydriding process in metal hydride hydrogen storage tank with coiled-tube heat exchanger[END_REF][START_REF] Tong | ScienceDirect Hydrogen release from a metal hydride tank with phase change material jacket and coiled-tube heat exchanger[END_REF] discussed the effect of heating water temperature, discharge pressure, and heat transfer coefficient for coiled tube heat exchanger (CTHE), reduced CTHE, and CTHE assisted with PCM. Ye et al. [START_REF] Ye | Enhanced hydrogen storage of a LaNi5 based reactor by using phase change materials[END_REF] proposed a finned tube heat exchanger assisted with PCM layer.

PCM layer reduced absorption time by 50%. Alqahtani et al. [START_REF] Alqahtani | Thermal performance analysis of a metal hydride reactor encircled by a phase change material sandwich bed[END_REF][START_REF] Alqahtani | ScienceDirect Cyclic behaviors of a novel design of a metal hydride reactor encircled by cascaded phase change materials[END_REF] proposed two novel designs in which the MH layer was sandwiched between either two concentric single PCM cylinders or between four concentric cascaded layers of two different PCMs. The improvement in time of absorption and desorption was 81.5% and 73%, respectively, for single PCM design. Compared to single PCM sandwiched, cascaded sandwich design improved absorption and desorption durations by 26% and 51%, respectively.

Metal foam (MF), being a cellular metallic structure with high porosity [START_REF] Liu | Materials for phase change material at high temperature[END_REF], is a promising candidate for increasing effective thermal conductivity as a passive strategy to enhance heat transfer. Several PCMs suffer from low thermal conductivity. Therefore, highly conductive materials, such as metal foam [START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF][START_REF] El Mghari | Selection of phase change materials, metal foams and geometries for improving metal hydride performance[END_REF][START_REF] Darzi | Absorption and desorption of hydrogen in long metal hydride tank equipped with phase change material jacket[END_REF][START_REF] Lewis | Analysis of Heat and Mass Transfer During Charging and Discharging in a Metal Hydride -Phase Change Material Reactor[END_REF], expanded graphite [START_REF] Yao | A continuous hydrogen absorption/desorption model for metal hydride reactor coupled with PCM as heat management and its application in the fuel cell power system[END_REF], and fins [START_REF] Yao | A continuous hydrogen absorption/desorption model for metal hydride reactor coupled with PCM as heat management and its application in the fuel cell power system[END_REF], could host PCM. Recently, Chibani et al. [START_REF] Chibani | Numerical investigation of heat and mass transfer during hydrogen desorption in a large-scale metal hydride reactor coupled to a phase change material with nano-oxide additives[END_REF][START_REF] Chibani | Thermodynamics and kinetics analysis of hydrogen absorption in large-scale metal hydride reactor coupled to phase change material-metal foam-based latent heat storage system[END_REF][START_REF] Chibani | The performance of hydrogen desorption from a metal hydride with heat supply by a phase change material incorporated in porous media (metal foam): Heat and mass transfer assessment[END_REF][START_REF] Chibani | Heat and mass transfer characteristics of charging in a metal hydride-phase change material reactor with nano oxide additives: The large scale-approach[END_REF] proposed a shell and tube heat exchanger in a large-scale MH-PCM system where PCM performance was enhanced by employing either MF [START_REF] Chibani | Thermodynamics and kinetics analysis of hydrogen absorption in large-scale metal hydride reactor coupled to phase change material-metal foam-based latent heat storage system[END_REF][START_REF] Chibani | The performance of hydrogen desorption from a metal hydride with heat supply by a phase change material incorporated in porous media (metal foam): Heat and mass transfer assessment[END_REF] or nano-oxides (NO) [START_REF] Chibani | Numerical investigation of heat and mass transfer during hydrogen desorption in a large-scale metal hydride reactor coupled to a phase change material with nano-oxide additives[END_REF][START_REF] Chibani | Heat and mass transfer characteristics of charging in a metal hydride-phase change material reactor with nano oxide additives: The large scale-approach[END_REF]. Time of absorption and desorption were reduced to 500 s and 700 s in MF scenario while 550 s and 700 s in NO scenario. To confirm the effectiveness of MH-PCM system, the exergy efficiency of MH-PCM system was 98.8% [START_REF] Quoc | ScienceDirect Thermal management of metal hydride hydrogen storage using phase change materials for standalone solar hydrogen systems : An energy / exergy investigation[END_REF]. In Ref. [START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF], copper foam showed an improvement in absorption time by approximately 34%. According to ElMghari et al. [START_REF] El Mghari | Selection of phase change materials, metal foams and geometries for improving metal hydride performance[END_REF], MF's thermal conductivity enhancement is significantly affected by the base material, while marginal enhancement was achieved with porosity change. Integration of PCM in MH reactors represents an effective heat management system. MH-PCM reactor approaches high sustainability and improves capital and operating costs to advance this technology toward commercialization. However, low thermal conductivity represents a severe challenge.

Multiple studies in literature have focused on heat transfer pipe integration which raises the cost and complexity of the system. Several scientific papers concentrated on the mass of PCM, while rare studies focus on the distribution of PCM in the reactor, especially for LaNi 5 . In this paper, a new design of MH-PCM reactor is investigated and geometrically optimized for LaNi 5 -H 2 . This design divides the quantity of metal hydride into multiple cylindrical layers separated by phase change material. Each layer of MH is sandwiched between two layers of PCM to quickly remove the heat generated during the hydrogen absorption and provide heat to accelerate the desorption process. The principle of alternative layers of both materials increases the contact area, decreases the heat transfer distance, and splits the single large heat source into several limited heat sources. This study utilizes LaNi 5 owing to its great potential in Hydrogen based applications [START_REF] Joubert | LaNi5 related AB5 compounds: Structure, properties and applications[END_REF]. The mathematical model is built in COMSOL Multi-physics software depending on finite element technique. The model is used for studying the performance of the suggested reactor for different design parameters. The effect of the number of layers, thermal conductivity of PCM, and various typical PCMs on the system performance is investigated. Moreover, the volume of the proposed reactor is optimized to achieve volume reduction in addition to faster absorption/desorption processes. The results can be considered guidelines for designing an efficient hydrogen storage system that can be adopted for commercialization.

Description of the proposed reactor

The proposed reactor is a mutual design in which layers of MH and PCM are arranged alternately, as shown in Fig. 1. In other words, each layer of MH is sandwiched between two layers of PCM to enhance the dissipation rate of heat generated during the absorption process. This concentric design is covered by a shell (cylinder) with an opening at its top for Hydrogen to get in and out during the absorption and regeneration processes, respectively. The shell (container) has an inner diameter of 9 cm and a height of 10 cm with gap height of 2 cm. These dimensions are fixed throughout this study except while studying the reactor volume. The gap above the layers is large enough for Hydrogen to reach each MH layer even after the expansion of PCM and metal hydride. Hydrogen pipe is connected to the gap to allow hydrogen gas to enter or exit from reactor in loading and discharge processes. Fig. 1 Schematic diagram for a cross-sectional view of the 3D proposed reactor

Numerical Work

This section discusses the development of the mathematical model for the suggested reactor.

Governing equations, assumptions, and initial and boundary conditions describing the behavior of the reactor are provided. Mesh sensitivity and model validation studies are performed as well.

Computational Domain

The computational domain of the reactor proposed in Fig. 1 can be simplified as a 2D axisymmetric domain to reduce the computational time without scarifying the solution accuracy. The shell thickness is not considered in the computational domain and the reactor is well-insulated. The gap is designed to be large enough to feed the MH. Therefore, its influence on the system performance is negligible. The selected domain has a length (R) of 4.5 cm and a height (H) of 8 cm. These dimensions (i.e., reactor volume) are fixed during the parametric study. The numbers of MH layers are varied by changing their thickness or the thickness of PCM layers.

Several assumptions are considered to establish the mathematical model of heat and mass transfer within MH and PCM [START_REF] Alqahtani | Thermal performance analysis of a metal hydride reactor encircled by a phase change material sandwich bed[END_REF][START_REF] Prasad | Design and performance analysis of an annular metal hydride reactor for large-scale hydrogen storage applications[END_REF]:

1. Hydrogen gas is considered an ideal gas.

2. Local thermal equilibrium between Hydrogen and MH is assumed.

3. The reactor external surface is perfectly insulated.

4. The thermal-physical properties of MH and PCM are constant during the absorption process.

5. The thermal resistance and thermal capacity of MH and PCM layers interfaces are neglected.

6. Convection through PCM is negligible owing to the high viscosity and small characteristic length leading to a low Grashof number.

7. The effect of expansion/contraction during the phase change of PCM [START_REF] Maad H Ben | Heat and mass transfer in a metal hydrogen reactor equipped with a phase-change heat-exchanger[END_REF] and the absorption process of MH [START_REF] Yao | A continuous hydrogen absorption/desorption model for metal hydride reactor coupled with PCM as heat management and its application in the fuel cell power system[END_REF] is neglected.

Governing Equations

The governing equations are extracted from relevant references [START_REF] Maad H Ben | Heat and mass transfer in a metal hydrogen reactor equipped with a phase-change heat-exchanger[END_REF][START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF][START_REF] El Mghari | Analysis of hydrogen storage performance of metal hydride reactor with phase change materials[END_REF], which describe the behavior of both MH and PCM.

Mass conservation equation

The continuity equation is solved in the MH layers to find the pressure and velocity fields of hydrogen gas in these domains, expressed as:

(1) [START_REF] Barthelemy | Hydrogen storage: recent improvements and industrial perspectives[END_REF] where is the porosity of MH, is the hydrogen density and subscript g refers to the gas phase, is the mass source term of Hydrogen, is the Darcy velocity, is the permeability inside the MH bed, is the dynamic viscosity of Hydrogen, and is the pressure gradient.

The conservation of mass states that the magnitude of absorbed Hydrogen equals the magnitude of the decrease in MH density, , and vice versa in the desorption process. This relation could be described as:

(

where subscript s refers to the solid phase.

Energy conservation equation

Energy equation in MH and PCM layers are formulated and solved to estimate the temperature fields. It can be written for the MH as: [START_REF] Hassan | Hydrogen storage technologies for stationary and mobile applications: Review, analysis and perspectives[END_REF] where is the enthalpy of absorption reaction, is the temperature inside the MH reactor. The term represents the energy source term.

The effective heat capacity and effective thermal conductivity of MH domain are calculated on a volume basis as: and

For the PCM layers, the convection heat transfer in the liquid phase could be neglected because the PCM possesses high viscosity in the liquid phase. As a result, the energy equation for the PCM layer can be formulated as: [START_REF] Dhaou | Experimental study of a metal hydride vessel based on a finned spiral heat exchanger[END_REF] where the effective heat capacity and thermal conductivity of PCM are calculated as:

(7) (8)
where is melting fraction and L is the latent heat of fusion of PCM. The variables and are obtained as: and (9)

Reaction kinetics

The mass source term that appears in the continuity equation (Eq. 1) is calculated as: [START_REF] Muthukumar | Parametric studies on a metal hydride based hydrogen storage device[END_REF] where is the kinetics constant for absorption reaction, is the activation energy, is the universal gas constant, is the metal hydride density, is the metal hydride density at its maximum hydrogen content, and is the plateau pressure, which is calculated from Van't Hoff equation as: [START_REF] Muthukumar | Study of heat and mass transfer in MmNi4. 6Al0. 4 during desorption of hydrogen[END_REF] where is the reaction enthalpy for the M to MH transition, is the reaction entropy for the M to MH transition, and R is the gas constant. and depend on MH alloy [START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF].

To enhance the reliability of the model, the empirical fits of the P-C-T curves for LaNi 5 are utilized throughout this study except in the validation section. The plateau pressure is calculated as given in

Refs. [START_REF] Nishizaki | Coefficients of performance of hydride heat pumps[END_REF][START_REF] Cho | Dynamic modeling and simulation of hydrogen supply capacity from a metal hydride tank[END_REF]: [START_REF] Askri | Optimization of hydrogen storage in metal-hydride tanks[END_REF] where a, b, , , , and are constants whose values are 13.44, 3780 [K], 0.038, 0, 1, 0.5 and 0.137 respectively [START_REF] Nishizaki | Coefficients of performance of hydride heat pumps[END_REF][START_REF] Cho | Dynamic modeling and simulation of hydrogen supply capacity from a metal hydride tank[END_REF]. The symbol expresses absorption and desorption processes, respectively.

The standard atmospheric pressure and temperature of metal hydride are denoted by and .

Reacted fraction of MH represents the ratio between Hydrogen absorbed mass and saturation absorbed Hydrogen. This value is determined as in [START_REF] Nishizaki | Coefficients of performance of hydride heat pumps[END_REF][START_REF] Cho | Dynamic modeling and simulation of hydrogen supply capacity from a metal hydride tank[END_REF]: [START_REF] Gkanas | Efficient hydrogen storage in up-scale metal hydride tanks as possible metal hydride compression agents equipped with aluminium extended surfaces[END_REF] where is the metal density (hydrogen-free MH density)

Mathematical model of phase change material

The energy equation, effective heat capacity and effective thermal conductivity of PCM are defined as follows

(14) (15)
and ( 16)

Boundary and Initial Conditions

Appropriate boundary and initial conditions are set to model the 2D axisymmetric domain shown in Fig. 2, solve the governing equations, and get reliable results. Metal hydride and PCM layer thicknesses are denoted by w MH and w PCM , respectively. The depth of PCM layer underneath the MH domains is denoted by d. These geometric parameters are investigated below. The model has been validated using the data presented in ref. [START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF] at the same operating and design conditions. Plateau pressure is determined through Van't Hoff equation, Eq. 11. Initially, the distribution of temperature, pressure, and hydrogen concentration within the reactor is set to be uniform. The initial temperature of the MH and PCM domains is set to be 293.15 K. The initial pressure and density of MH are set to be 0.147 MPa and 7164 kg/m 3 . The initial and loading pressure are selected based on the absorption isotherm of LaNi 5 [START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF] PCM Metal hydride

r w PCM w MH H h w MH /2 z R d 1 2 2 2 3 3 3 4 4

Fig. 2 2D axisymmetric computational domain

For the boundary conditions, face ( 1) is assumed to be axis-symmetric, where the gradient in pressure, temperature, and hydrogen concentration is zero. Faces (2) are the hydrogen inlets of the MH sub-domains where the temperature is set to be 293.15 K, and the pressure changes linearly from 0.147 MPa to 0.8 MPa through 100 s and then remains constant during the absorption process. Faces (3) and ( 4) are assumed to be impermeable walls with no flow boundary condition and well-insulated where the temperature gradient is zero. The inter-phase boundary conditions of the MH and PCM are defined as a coupled wall enabling conjugate heat transfer [START_REF] Askri | Optimization of hydrogen storage in metal-hydride tanks[END_REF][START_REF] Ye | Numerical simulation on the storage performance of a phase change materials based metal hydride hydrogen storage tank[END_REF]: [START_REF] Chaise | Enhancement of hydrogen sorption in magnesium hydride using expanded natural graphite[END_REF] where is the vector normal to the wall. Thermo-chemical properties for LaNi 5 , Hydrogen, and paraffin wax RT35 are listed in Table 1. These numerical values of boundary and initial conditions are sufficient to define the domain and start the solution.

Mesh Sensitivity

The reactor consists of alternate layers of MH and PCM (paraffin RT35). It is simulated at different sizes of mesh (i.e., number of elements) to study the effect of mesh size on the solution accuracy.

Table 2 shows the mesh statistics and steady-state simulation results for different cell sizes. It is noticed that the relative error in the steady-state temperature of MH reduces as the mesh gets finer.

The extra-fine and extremely fine meshes provide a relative error of about 0.133% and 0.099%, respectively. The same trend is found for the steady-state temperature of PCM and melting fraction.

Therefore, the extra fine mesh is considered in the following investigations to simulate the proposed reactor with reasonable computational time and high accuracy.

Code Validation

In order to study the reliability of the present model, the present results are compared with those obtained in Ref. [START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF] at the same conditions. The validated reactor is composed of two concentric cylinders of MH and PCM. Height and radius are 6 cm and 2 cm for the inner LaNi 5 cylinder while 8 cm and 4.5 cm for the outer paraffin wax RT35 cylinder. Plateau pressure is determined through Van't Hoff equation, Eq. 11. Initially, the distribution of temperature, pressure, and hydrogen concentration within the reactor is set to be uniform. The initial temperature of the MH and PCM domains is set to be 293.15 K. The initial pressure and density of MH are set to be 0.147 MPa and 7164 kg/m 3 . As described in Fig. 2, face (1) is assumed to be axis-symmetric while faces (2) are the hydrogen inlets of the MH sub-domains where the temperature is set to be 293.15 K, and the pressure changes linearly from 0.147 to 0.8 MPa through 100 s and then remains constant during the absorption process. Faces (3) and ( 4) are assumed to be impermeable walls and well-insulated. The inter-phase boundary condition of the MH and PCM is defined as a coupled wall enabling conjugate heat transfer [START_REF] Askri | Optimization of hydrogen storage in metal-hydride tanks[END_REF][START_REF] Ye | Numerical simulation on the storage performance of a phase change materials based metal hydride hydrogen storage tank[END_REF]. Thermo-chemical properties for LaNi 5 , Hydrogen, and paraffin wax RT35 are listed in Table 1. Fig. 3 shows the average temporal temperature of metal hydride and the average melting fraction of PCM obtained from the present model and Ref. [START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF]. The present model is able to predict the average temperature and average melting fraction of PCM. Analysis of these curves indicates that the maximum relative error in the melting fraction of PCM and temperature of MH is less than 4% and 1%, respectively. Consequently, the present model could be used for predicting the absorption behavior of Hydrogen in MH with acceptable error.

Results and Discussion

After establishing mesh sensitivity and code validation, the present model is employed to simulate the absorption characteristics of a hydrogen reactor consisting of multi-concentric layers. The influence of the number of layers on the reactor performance is studied. The effect of phase change material thermal conductivity on the thermochemical behavior of the reactor is investigated for a four layers reactor for thermal conductivity ranging from 0.2 to 3 W/m.K. In addition, typical PCMs are employed to examine the effect of available commercial types of PCMs on reactor performance.

Finally, the effect of reactor volume reduction on the reactor performance is discussed in the case of utilizing lithium nitrate trihydrate as PCM. The depth of PCM underneath MH is investigated for values ranging from 2 cm to zero. Reactor radius is varied from 4.5 to 2.5 cm. The average hydrogen storage capacity, average MH temperature, and average melting fraction of PCM are presented and discussed for all simulated cases.

Effect of the number of PCM layers

Conventional MH-PCM reactor design, investigated in code validation, is composed of an inner MH cylinder encircled with a concentric PCM cylinder. Throughout the paper, this reactor is defined as single-layer reactor since it includes only one layer of MH. Effect of the number of layers for PCM on the thermal behavior of the MH reactor is studied while keeping the total volume of MH and PCM fixed to establish a fair comparison. Table 3 lists the dimensions of the four studied cases.

Compared to a single-layer reactor (i.e., one layer of MH and one layer of PCM), hydrogen absorption time reduces to about one-third of its initial value for all multi-layer cases, as shown in Fig. 4a. As heat management plays a vital role in the absorption process, absorption time required for MH to reach its 90% storage capacity, t 0.9 , significantly reduces to 3555, 4560, 5640 s for four, three, two layers reactor, respectively, compared to 16290 s for the one layer reactor. Thanks to the discretization of MH and PCM into multi-layers, the contact area between MH and PCM increases, and the heat transfer resistance decreases, as well as splitting the main heat source in MH and heat sink in PCM into smaller ones in the different layers. Therefore, this design accelerates the absorption process. The utilization of four layers has the best hydrogen storage performance. MH reacted fraction does not achieve 1 owing to the utilization of empirical fits of the P-C-T curves, which require high pressure for complete absorption. Increasing the number of layers reduces the thickness of the MH layer and hence decreases its thermal resistance. As a result, the heat generated during the absorption process is conducted efficiently to the PCM, leading to a faster decline in MH temperature, as presented in Fig. 4b. The peak temperature in MH during the absorption process is reduced to 328.1, 329.61, and 331.33 K for four, three, and two layers reactor, respectively, instead of 334.26 K for the single layer (see Fig. 4b). The heat accumulation rate inside the reactor slows down, and the steady-state temperature is attained very fast. PCM melting fraction increases to 1 in the multi-layers reactor faster than for the one-layer reactor, as shown in Fig. 4c. The melting process continues for a long period after approaching maximum absorption owing to the poor thermal conductivity of paraffin wax RT35. This phenomena decrease as the number of layers increases. The

Effect of the PCM thermal conductivity

The thermal conductivity of PCM could be increased by using metal additives or packed in metal foam [START_REF] Lafdi | Experimental study on the influence of foam porosity and pore size on the melting of phase change materials[END_REF][START_REF] Mesalhy | Numerical study for enhancing the thermal conductivity of phase change material (PCM) storage using high thermal conductivity porous matrix[END_REF][START_REF] Lafdi | Graphite foams infiltrated with phase change materials as alternative materials for space and terrestrial thermal energy storage applications[END_REF][START_REF] Mesalhy | Carbon foam matrices saturated with PCM for thermal protection purposes[END_REF][START_REF] Zhu | Experimental and numerical study of metal foam composites in innovative application of thermal energy storage[END_REF]. Herein, the effect of the PCM's thermal conductivity on the four-layer reactor's performance is investigated. Fig. 5 demonstrates that superior reactor performance is achieved as the thermal conductivity of PCM increases. High thermal conductivity allows efficient heat transfer between MH and PCM adjacent layers. Therefore, lower peak temperature, faster steady-state achievement, and quicker melting fraction growth are observed, as shown in Fig. 5. Absorption time required for MH to reach its 90% storage capacity, t 0.9 , significantly reduces to 675 s at a PCM thermal conductivity of 3 W/m.K, compared to 3555 s at 0.2 W/m.K (~5.33 times reduction), as shown in Fig. 5a. MH reacted fraction does not achieve 1 owing to the utilization of empirical fits of the P-C-T curves which require high pressure for complete absorption. The peak temperature in MH bed during absorption reduces from 328.11 to 325.31 K as the thermal conductivity increases from 0.2 to 3 W/m.K, as presented in Fig. 5b. Although steady-state melting fraction reaches 1 for all simulated cases, the time to reach this value decreases as the PCM thermal conductivity increases, as

shown in Fig. 5c. The duration between approaching the maximum hydrogen storage capacity and reaching the steady melting fraction significantly decreases as the thermal conductivity of PCM increases. As described in [START_REF] Rahman | Experimental characterization of inward freezing and melting of additive-enhanced phase-change materials within millimeter-scale cylindrical enclosures[END_REF], thermal conductivity plays an important role in the loading and discharging rates in case of 100% phase change thermal cycles.

Effect of using different PCMs

PCM with high latent heat and high thermal conductivity produces the highest performance. PCM

k = 0.2 W/m.K (base case) k = 0.5 W/m.K k = 1 W/m.K k = 2 W/m.K k = 3 W/m.K
melting temperature shall be close to the average temperature between the two equilibrium temperatures corresponding to loading and discharging pressures [START_REF] Garrier | A new MgH2 tank concept using a phase-change material to store the heat of reaction[END_REF][START_REF] Alqahtani | ScienceDirect Cyclic behaviors of a novel design of a metal hydride reactor encircled by cascaded phase change materials[END_REF]. The selection of latent heat considers available space, while thermal conductivity choice depends on required absorption and desorption rates. In addition, economic, corrosion, and environmental issues are considered in PCM selection. However, no commercially available PCM fulfills these desired thermo-physical properties. Therefore, typical PCMs are employed in this section. Table 4 lists the thermo-physical properties of different PCMs investigated in this study. For instance, paraffin wax RT28 has the advantage of having a low melting temperature and a relatively high latent heat, but its thermal conductivity is low. In this section, HC refers to high capacity corresponding to high latent heat. Fig. 6 shows the performance of four layers reactor using various PCMs. All salt hydrates (lithium nitrate trihydrate, sodium sulfate decahydrate, and sodium carbonate decahydrate) exhibit similar behavior because they have comparable thermo-physical properties. Though, lithium nitrate trihydrate has slightly better performance due to its higher latent heat. In contrast, the poor thermal conductivity of paraffin PCMs leads to slow kinetics and hence low hydrogen storage performance.

Parrafin wax RT35 is characterized by the lowest latent heat, resulting in the lowest rate of hydrogen absorption, the highest steady-state temperature, and the melting fraction of unity, as presented in Fig. 6. Analysis of the curves indicates that the absorption time needed for MH to have 90% storage capacity is between 176 and 220 s for salt hydrates. The best t 0.9 is calculated to be 176 s using lithium nitrate trihydrate. The t 0.9 increases to 528, 650 and 3555 s for paraffin wax RT28 HC, RT35

HC and RT35, respectively (see Fig. 6a). Thermal conductivity of these three paraffins is the same.

Therefore, the effect of latent heat could be predicted through comparing the behavior of RT35 and RT35 HC. The t 0.9 for RT35 HC is greatly lower than that of RT35. Accordingly, as latent heat increases, absorption time would decrease. The difference between latent heat of RT28 HC and RT35

HC is relatively small. Based on neglecting this difference, the t 0.9 for RT28 HC, having lower melting temperature, is lower than that of RT35 HC showing that absorption time would decrease as melting temperature decreases. However, this decrease would affect desorption process as MH-PCM reactors undergoes thermal cycles in consequent absorption-desorption cycles. Using lithium nitrate trihydrate, the steady-state temperature and steady-state melting fraction are 302.64 K and 0.22, as presented in Fig. 6b andc. From the analysis, the best performance is achieved using lithium nitrate trihydrate as a PCM for four layers reactor. Therefore, it is considered in the next subsection.

Although lithium nitrate trihydrate has superior performance in terms of heat transfer, several studies [START_REF] Kenisarin | Salt hydrates as latent heat storage materials:Thermophysical properties and costs[END_REF][START_REF] Milian | Advances in the development of latent heat storage materials based on inorganic lithium salts[END_REF][START_REF] Aridi | Review on the sustainability of phase-change materials used in buildings[END_REF] reveal that its cost is relatively high at 4.71 $/kg [START_REF] Aridi | Review on the sustainability of phase-change materials used in buildings[END_REF]. Therefore, it is rarely utilized in practical thermal systems in addition to being classified as a laboratory reagent in terms of commercial availability [START_REF] Milian | Advances in the development of latent heat storage materials based on inorganic lithium salts[END_REF]. On the other hand, Fernandez et al. [START_REF] Fernández | Thermophysical properties of low cost lithium nitrate salts produced in northern Chile for thermal energy storage[END_REF] investigated the production of relatively cheap lithium nitrate trihydrate in Chile. Moreover, Wen et al. [START_REF] Wen | Direct production of lithium nitrate from the primary lithium salt by electrodialysis metathesis[END_REF] recommend lithium nitrate production utilizing the electrodialysis metathesis strategy, which significantly decreases the cost. Consequently, lithium nitrate trihydrate could be commercialized soon. Contrary to lithium nitrate trihydrate, paraffins could be an adequate option for thermal energy storage applications owing to its availability, wide melting temperature range, affordable costs as well as low supercooling tendency [START_REF] Aridi | Review on the sustainability of phase-change materials used in buildings[END_REF]. However, paraffins have low thermal conductivity. To enhance their low thermal conductivity, metal foam, metallic and carbon structures could be utilized. Finally, PCM selection process considers cost, thermal behavior, environmental and safety issues. The duration between approaching the maximum hydrogen storage capacity and reaching the steady melting fraction significantly decreases as the thermal conductivity of PCM increases which is obvious for salt hydrates. MH reacted fraction does not achieve 1 owing to the utilization of empirical fits of the P-C-T curves, which require high pressure for complete absorption.

Effect of the overall volume of the proposed reactor

Herein, the total volume of four layers reactor is changed by varying the PCM thickness underneath MH and the thickness of PCM layers in the radial direction. Lithium nitrate trihydrate is utilized through the process of reactor volume reduction. This investigation aims to reduce the reactor volume while maintaining its superior performance. Such a study is needed due to the presence of large quantities of unmelted PCM (low average melting fraction) at the steady-state conditions, as shown in Fig.

. This means that PCM thickness underneath the MH layers does not participate efficiently in the reactor performance, leading to a bulky system. The effect of this thickness is examined in the following sub-section.

a. Effect of PCM thickness underneath MH layers

The effect of PCM layer thickness below the MH on the reactor behavior is discussed. Fig. 8 shows that this layer thickness has no significant impact on reactor performance. This trend is because the contact area between the adjacent layers of MH and PCM is much larger than the contact area between the MH and PCM underneath it. Therefore, the heat generated in MH during the absorption process is mainly conducted in the radial direction, not in the axial one. As shown in Fig. 8a, t 0.9 slightly changes between 170 and 184.5 s when the depth (d) changes between 2.0 and 0.0 cm, which proves the little importance of this PCM quantity, especially when the thermal conductivity of PCM is low. As PCM quantity decreases with decreasing the PCM depth underneath MH, the melting fraction rises faster, and more heat is absorbed, leading to reactor rapid cooling, which accelerates hydrogen absorption. Therefore, reactors with 1.5 and 1.0 cm PCM depths reach 90% absorption capacity after 170 and 175.8 s, while reactors with 2.0 cm depth achieve 90% absorption capacity after 176.2 s. Further decrease in PCM quantity would slightly delay the reactor cooling, and t 0.9 would increase as in 0.5 and zero depths. In addition, the peak temperature is 314.81 K for d=2 cm and ranges from 314.9 to 316.1 for the rest cases (see Fig.

). The steady-state melting fraction increases from 0.218 to 0.374 as the d value decreases from 2 to 0 cm, as presented in Fig. 8c.

b. Effect of the thickness of PCM layers

This part examines the effect of the thickness of PCM layer on the behavior of the four layers reactor (see Fig. 9). It can be seen that the hydrogen absorption rate and the steady hydrogen storage capacity are almost the same for reactors with an outer radius of more than 3 cm, as presented in Fig. 9a. The value of t 0.9 increases from 185 to 222 s for reactors with an outer radius of 4.5 and 3.5 cm respectively. Reactors having an outer radius of 3.0 cm attain 90% of hydrogen absorption after 530 s with lower steady hydrogen absorption capacity than reactors with greater outer radius. The reactor with an outer radius of 2.5 cm reaches only about 46.35% of the full loading, indicating that the PCM quantity is not enough to absorb the heat generated during the absorption process for full loading achievement. As a result, the temperature of MH increases to 331.1 K for the reactor of 2.5 cm outer radius and maintains at this high temperature, as plotted in Fig. 9b. This increase in the MH temperature value is responsible for the incomplete absorption process. In turn, an increase in the MH temperature at the beginning of absorption process is noticed for the reactors of an outer radius of more than 3 cm. Afterward, the MH temperature steadily reduces, facilitating the absorption process. Heat is generated during the absorption process, and PCM absorbs this heat and melts. Thus, a reactor with less PCM volume exhibits a higher melting fraction, as observed in Fig. 9c. This trend highlights the significant effect of PCM layer thickness (PCM volume) on the reactor response. The

Evaluation of the proposed reactor capacity

In this sub-section, two evaluation parameters are suggested to estimate the capacity of the proposed reactor, taking into account its total mass and volume. In other words, the reactor's absorption rate per unit mass and volume are assessed. The first parameter is the specific capacity rate (SCR), which represents how many grams of Hydrogen could be absorbed per 1 kg of the system per minute. The second indicator is the volumetric capacity rate (VCR), which denotes the mass of Hydrogen absorbed by 1 m 3 of the system per minute. The two parameters reflect how bulky and heavy the reactor is. They would be effective in storage system design for mobile and stationary applications.

The evaluation parameters are estimated using the following equations:

where represents the amount of Hydrogen absorbed by MH at t 0.9 , m r and V r are the overall As previously discussed, sodium carbonate decahydrate and lithium nitrate trihydrate PCMs have comparable performance, while the latter has a higher density. A reactor with an outer radius of 3.5 cm and zero PCM depth has the best performance. The capacity of this reactor is estimated and compared with previously published one, as listed in Table 5. In Ref. [START_REF] Afzal | Design of a large-scale metal hydride based hydrogen storage reactor: simulation and heat transfer optimization[END_REF], 20% expansion volume was selected to allow the expansion of MH, while up to 15.6 % is required for the expansion of certain PCMs, as stated in Ref. [START_REF] Pan | Energy density and volume expansion in solid-liquid phase change, for energy applications[END_REF]. Therefore, this study considers 25% of the volume as a gap for MH and PCM expansion process and reactor walls. It can be seen that the suggested reactor has better capacity than previously reported reactors in open literature. Ref. [START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF] Ref. [START_REF] El Mghari | Selection of phase change materials, metal foams and geometries for improving metal hydride performance[END_REF] Ref. [START_REF] Alqahtani | Thermal performance analysis of a metal hydride reactor encircled by a phase change material sandwich bed[END_REF] Ref. [START_REF] Ye | Numerical simulation on the storage performance of a phase change materials based metal hydride hydrogen storage tank[END_REF] MH LaNi 5 LaNi 5 LaNi 5 Mg 2 Ni Mg PCM Lithium nitrate trihydrate (1) Parrafin wax RT35 (2) Lithium nitrate trihydrate (3) NaNO 3 [START_REF] Hassan | Hydrogen storage technologies for stationary and mobile applications: Review, analysis and perspectives[END_REF] Mg 69 Zn [START_REF] Mellouli | Impact of using a heat transfer fluid pipe in a metal hydride-phase change material tank[END_REF] (1) After reactor volume reduction (jacket bed with R= 3.5 cm and H= 6 cm) (2) This study used copper foam for pool bed. (3) utilizing 94% porosity copper foam with pool bed (4) sandwich bed (5) Compact discs of MH are stacked by steel brackets and PCM is sandwiched between MH.

Conclusion

The present work proposes a multi-layer cylindrical reactor, which consists of layers of MH and PCM arranged alternatively. A numerical model is built, and a parametric study is carried out to investigate the effect of various design parameters on the reactor's performance. The key results could be summarized as follows:

1. A cylindrical reactor with four alternating layers of MH and PCM has a much better capacity rate than that with one layer.

2. Although the steady-state melting fraction of PCM reaches 1 for the majority of simulated cases, the time to reach this value decreases as the PCM thermal conductivity increases. This trend reveals the significant effect of the conductive thermal resistance of the MH on the reactor performance.

3. Lithium nitrate trihydrate, sodium sulfate decahydrate, and sodium carbonate decahydrate produce similar performance because they have comparable thermo-physical properties.

However, lithium nitrate trihydrate is slightly better due to its relatively higher latent heat.

4. During the absorption process, the heat generated in MH is conducted mainly in the radial direction, not in the axial one. Thus, the PCM layer underneath the MH is found to be useless.

The SCR and VCR of the proposed four layers reactor, after reactor volume reduction, are calculated to be 1.51 g H2 /min/kg sys and 3016 g H2 /min/m

Fig. 3

 3 Fig. 3 Comparison between results obtained in the present model and that ofTong et al. [24]

  layer of PCM adjacent to MH absorbs heat during three stages. In the first stage, PCM temperature rises to melting temperature and then PCM undergoes phase change process in the second stage. In the third stage, PCM absorbs sensible heat which raises the temperature of liquid PCM. This sensible heat transfers to the solid PCM which increases the melting fraction. The heat transfer inside PCM takes much more time especially for high thickness PCM films such as single layer design or quantity of PCM underneath the metal hydride.

Fig. 4

 4 Fig. 4 Temporal variation of (a) hydrogen storage capacity, (b) temperature of MH, and (c) melting 302 fraction of PCM for different layers reactor. 303

Fig. 5

 5 Fig. 5 Temporal variation of (a) hydrogen storage capacity, (b) temperature of MH, and (c) melting fraction of four layers reactor at different thermal conductivities of PCM.

Fig. 6

 6 Fig. 6 Temporal variation of (a) hydrogen storage capacity, (b) temperature of MH, and (c) melting fraction of four layers reactor at different commercial PCMs.

Fig. 7

 7 Fig. 7 Steady-state results of (a) hydrogen storage capacity, (b) temperature of MH, and (c) PCM melting fraction.

Fig. 8

 8 Fig. 8 Temporal variation of (a) hydrogen storage capacity, (b) temperature of MH, and (c) melting fraction of four layers reactor at different underneath thicknesses of PCM.

Fig. 9

 9 Fig. 9 Temporal variation of (a) hydrogen storage capacity, (b) temperature of MH, and (c) melting fraction of four layers reactor at different outer diameters of reactor

Table 1

 1 Thermo-chemical parameters for LaNi 5 , H 2 , and paraffin RT35[START_REF] Tong | Thermal management of metal hydride hydrogen storage reservoir using phase change materials[END_REF][START_REF] Nishizaki | Coefficients of performance of hydride heat pumps[END_REF][START_REF] Cho | Dynamic modeling and simulation of hydrogen supply capacity from a metal hydride tank[END_REF].

	Parameter	Interpretation	Value	Parameter	Interpretation	Value
	ε [-]	porosity	0.5	k MH	MH thermal	2.4
				[W/m.K]	conductivity
	ρ M [kg/m 3 ]	Metal (hydrogen-free	7164	k H2	Hydrogen thermal	0.1815
		MH) density		[W/m.K]	conductivity
	ρ ss [kg/m 3 ]	MH density at maximum 7259	R u	Universal gas constant 8.314

Table 2

 2 Statistics and steady-state simulation results for different mesh sizes.

	Parameter	Normal Fine	Mesh size Finer Extra fine Extremely fine
	No. of elements	352	552	1139	3692	14300
	Average element quality	0.8806 0.9041 0.915	0.939	0.950
	Steady-state MH temperature (K) 316.55 319.77 322.39	322.82	323.14
	Relative change in T MH (%)	-	1.007 0.813	0.133	0.099

Table 3

 3 Geometric parameters for the multi-layer MH-PCM reactor

	No. of PCM layers	H (cm)	h (cm)	w PCM (cm)	w MH (cm)	R (cm)
	One	8	6	2.5	4.0	4.5
	Two	8	6	1.661	0.786	4.5
	Three	8	6	1.150	0.420	4.5
	Four	8	6	0.875	0.286	4.5

Table 4

 4 Thermo-physical properties of the investigated PCMs

		Chemical	T m (K)	(kg/m 3 )	k (W/m.K)	C p (J/kg.K)	L
		formula		l	s	k l	k s	C p,l	C p,s	(kJ/kg)
	Paraffin wax RT 35 Paraffin wax RT 35 HC Paraffin wax RT 28 HC	C n H 2n+2 / CH 3 (CH 2 )nCH 3	308 308 301	760 760 760	880 880 880	0.2 0.2 0.2	0.2 0.2 0.2	2400 2400 2400	1800 1800 1800	157 240 245
	Calcium
	chloride	CaCl 2 .6H 2 O	302.6	1562	1802	0.54 1.09	2310	1430	192
	hexahydrate
	Sodium sulfate decahydrate	Na 2 SO 4 .10H 2 O	305.5	1420	1485	0.54 1.23	2570	1440	251
	Sodium
	carbonate	Na 2 CO 3 .10H 2 O	305	1442	1460	0.56 1.25	3350	1880	267
	decahydrate
	Lithium
	nitrate	LiNO 3 .3H 2 O	303	1780	2140	0.58 1.32	2770	1730	296
	trihydrate

  Table 5 includes studies that were based on simulations. Nevertheless, Ye et al. [22] validated the deduced numerical model against experimental results. The SCR of the proposed reactor, 4 layer design utilizing lithium nitrate trihydrate investigated in section 4.3, is 1.013 and 0.975 g H2 /min/kg sys while using sodium carbonate decahydrate and lithium nitrate trihydrate, respectively. An inverse trend is shown for the VCR, which means that the reactor using sodium carbonate decahydrate is more bulky but lighter than the reactor employing lithium nitrate trihydrate for the same hydrogen content. The VCR values are 1437 and 1722 g H2 /min/m 3 sys while using sodium carbonate decahydrate and lithium nitrate trihydrate, respectively. Therefore, reactors utilizing lithium nitrate trihydrate and sodium carbonate decahydrate are recommended for stationary and mobile applications, respectively. The study focuses on stationary applications. Therefore, the geometric parameters of the reactor employing lithium nitrate trihydrate are optimized. The SCR and VCR of the optimized reactor are 1.51 g H2 /min/kg sys and 3015.76 g H2 /min/m 3 sys , respectively.

Table 5

 5 Performance of the present reactor in comparison with recently published ones

	Study	study Present	Previous studies *

  Values are estimated based on the best presented results.

							Al 3 (5)
	SCR (g H2 /min/kg sys )	1.51	0.107	0.074	0.117	0.44
	VCR (g H2 /min/m 3	sys )	3016	106	138	218	967

*

  3 sys using lithium nitrate trihydrate as a PCM material. These values are much higher than those presented in the open literature, indicating the superiority of the suggested reactor.

	ρ	Density, [kg/m 3 ]
	Symbols
	C a	Kinetics constant, [1/s]
	C p	Specific heat, [J/kg. K]
	E	Activation energy, [J/mol]
	HC	High capacity PCM
	Κ	Permeability, [m 2 ]
	k	Thermal conductivity, [W/m.K]
	L	Latent heat of PCM, [kJ/kg]
	M H2	Hydrogen Molecular weight, [kg/mol]
	P	Pressure, [MPa]
	R u	Universal gas constant, [J/mol. K]
	SCR	Specific capacity rate, [	/min/kgsys]
	T m	Melting temperature of PCM, [K]
	VCR	Volumetric capacity rate [	/min/m 3 sys]
	w	Layer width, [m]
	Nomenclature
	Abbreviations
	MH	Metal hydride
	MHR	Metal hydride reactor
	PCM	Phase change material
	Greek symbols
	∆H	Enthalpy change, [J/mol H 2 ]
	∆S	Entropy change, [J/mol. K]
	ε	Porosity, [-]
	θ	Melting fraction, [-]