## 3 Modelling and Simulation of Solid-State Hydrogen Storage Device  
The solid-state hydrogen storage unit consists of a bed in which the MH material is placed and heat exchange pipes, and its internal structure is shown in Figure 4.  
Due to the porosity of the MH and the space reserved for the expansion of the MH during design, gaseous hydrogen will be present in the hydrogen storage device, and the hydrogen storage bed can be viewed as a homogeneous mixture of the solid porous phase and the gaseous phase. In this paper, the heat and mass transfer process inside the device is simplified by making the following assumptions [20]:  
1. The gas phase follows the ideal gas law;  
2. The MH bed is considered to be homogeneous, and the porous medium is homogeneous;  
3. Neglecting the thermal radiation between the metal powders and the thermal convection between the metal powders and the hydrogen, the solid and gas phases in the tank can rapidly reach local thermal balance;  
Figure 3: Structure of the PEMFC-MH system. 4. During the reaction, the volumes of the gas and solid phases are constant, and the physical properties of the MH bed are constant;  
5. The modelled lumped parameters ignore temperature and pressure gradients inside the vessel, and the temperature and pressure inside the unit are uniform. The model of the solid-state hydrogen storage device in this paper is used to describe the heat and mass transfer process inside the device when hydrogen is absorbed or discharged from the hydrogen storage device, which specifically includes the conservation of mass, conservation of energy, reaction dynamic equations for hydrogen absorption or discharging, thermodynamic balance pressure equations, equations for the state of the ideal gases inside the device, and some auxiliary equations. (1) Conservation of mass  
The mass of solid material present inside a hydrogen storage device at a given moment during its operation consists of two components: the mass of the hydrogen storage alloy LaNi\({}_{5}\)\(m_{\text{M}}\) and the mass of the metal hydride LaNi\({}_{5}\)H\({}_{6}\)\(m_{\text{MH}}\):  
\[m_{\text{s}}=m_{\text{MH}}+m_{\text{M}} \tag{4}\]  
As the hydrogen absorption proceeds, the mass of LaNi\({}_{5}\)H\({}_{6}\) gradually increases until the mass of LaNi\({}_{5}\) is zero and the absorption is saturated, at which time the solid material mass is \(m_{\text{s}}^{\text{sat}}\). The hydrogen release process is reversed; when all the hydrogen is released from the material, the mass is \(m_{\text{s}}^{\text{emp}}\). The hydrogen concentration contained in the hydrogen storage material is defined as the SOC of the solid-state hydrogen storage device, which can be expressed as:  
\[SOC\%=\frac{m_{\text{MH}}}{m_{\text{s}}^{\text{sat}}} \tag{5}\]  
The variation in the mass of hydrogen and MH in the MHT during hydrogen absorption is expressed as:  
\[\left\{ \begin{array}{l}\frac{dm_{\text{H}_{2}}}{dt}=\dot{m}_{\text{in}}^{ \text{H}_{2}}-\dot{m}_{a}^{\text{H}_{2}}\\ \frac{dm_{\text{MH}}}{dt}=\dot{m}_{a}^{\text{MH}}\\ \frac{dm_{\text{m}}}{dt}=\dot{m}_{a}^{\text{H}_{2}}\\ \end{array} \right. \tag{6}\]  
The variation in the mass of hydrogen and MH in the MHT during hydrogen release is expressed as:  
\[\left\{ \begin{array}{l}\frac{dm_{\text{H}_{2}}}{dt}=-\dot{m}_{\text{out}}^{ \text{H}_{2}}+\dot{m}_{\text{d}}^{\text{H}_{2}}\\ \frac{dm_{\text{MH}}}{dt}=\dot{m}_{\text{d}}^{\text{MH}}\\ \frac{dm_{\text{s}}}{dt}=-\dot{m}_{\text{d}}^{\text{H}_{2}}\\ \end{array} \right. \tag{7}\]  
where \(\dot{m}_{\text{in}}^{\text{H}_{2}}\) and \(\dot{m}_{\text{out}}^{\text{H}_{2}}\) represent the hydrogen mass flow rate into and out of the MHT, respectively; \(\dot{m}_{a}^{\text{H}_{2}}\) and \(\dot{m}_{\text{d}}^{\text{H}_{2}}\) represent the hydrogen mass flow rate absorbed and released by MH, respectively; and \(\dot{m}_{a}^{\text{MH}}\) and \(\dot{m}_{\text{d}}^{\text{MH}}\) represent the mass change for the MH during  
Figure 4: Structural diagram of a solid-state hydrogen storage unit. hydrogen absorption and release, respectively.