## 2 Methodology
### Numerical Simulation of Heat and Mass Transfer  
The model geometry was 180 mm wide, 230 mm tall, 80 mm deep, and its envelope was 1.14 mm thick, exactly those of a real enclosure used in the library (Figure 1). The laminar airflow was assumed to align with the width of the enclosure, infiltrating through both the envelope and the gas of the enclosure. The air can flow through the gaps to the free-flow domain inside the empty enclosure and also permeate the porous domain of the cardboard. In the storage room, the airflow velocity of supply air was approximately 0.2 m/s (the Reynolds number \(=\frac{\rho vl^{\prime}}{\mu}=\frac{1.2\times 0.2\times 0.002}{18\times 10^{-5}}=26 <2000\) laminar flow), and the temperature was between 15 and 25 \({}^{\circ}\)C. The airflow was expected to affect the convective heat and mass transfer, which consequently led to phase change and water vapor diffusion in the cardboard material. This hygrothermal response of the material was a key point to understanding the buffering effect on mitigating the hygrothermal fluctuation in the microenvironment inside the enclosure. The enclosure envelope could retain and release heat and moisture, and its hygrothermal condition was influenced by the conditions in both the micro- and macro-environments. Meanwhile, the hygrothermal conditions of both the micro- and macro-environments were interacting with each other through both the porous material and the gap. Hence, a two-way coupling was necessary in this study for the two-fold interaction with the two hygrothermal variables. Figure 2 shows the interdependence of heat and moist-air transfer. The heat and moisture balance are coupled in a way that the latent heat, moisture state, transfer characteristic, and thermal storage affect the heat transfer, while the heat transfer determines the saturated vapor pressure, moisture driving force, and storage conditions. The heat and moist-air convection balance are coupled in a way that the temperature affects the air density, and conversely, the air convective heat transfer affects the temperature field. The moisture and air convection balance are coupled in a way that the airflow determines the convective moisture transfer, and in turn the vapor permeability determines the airflow in the porous media. To consider the complexity of modeling, we selected the direct coupling method, regarding the water vapor and air as one fluid in both the free-flow domain and porous domain. The space of these two domains is continuous, and a single set of conservation equations is solved by one solver in the simulation [22]. Figure 1: Geometry diagram of the model. The Equations (1)-(3) show the mathematical description [23; 24]:  
\[\big{(}\rho C_{p}\big{)}_{eff}\frac{\partial T}{\partial t}+\rho C_{p}u\cdot \
abla T-\
abla\cdot\Big{(}k_{eff}\
abla T+L_{V}\delta_{P}\
abla(\phi p_{sat}) \Big{)}=Q \tag{1}\]  
\[\xi\frac{\partial\phi}{\partial t}+\rho u\
abla\omega_{v}-\
abla\cdot(\xi D_{W }\
abla\phi+\delta_{P}\
abla(\phi p_{sat}))=G \tag{2}\]  
\[\rho\bigg{(}\frac{\partial u}{\partial t}+u\cdot\
abla u\bigg{)}+\
abla\cdot( pI-K)=F \tag{3}\]  
where \(\big{(}\rho C_{p}\big{)}_{eff}\) is the effective volumetric heat capacity at constant pressure, \(\rho\) is moisture air density [kg/ m\({}^{3}\)], \(C_{p}\) is heat capacity [J/(kg\(\cdot\)K)]. \(u\) is moisture air velocity [m/s]. \(T\) is the temperature [K]. \(k_{eff}\) is the effective thermal conductivity [W/(m\(\cdot\)K)]. \(L_{V}\) is the latent heat of evaporation [J/kg]. \(\delta_{P}\) is vapor permeability [s]. \(\phi\) is the relative humidity. \(\omega_{v}\) is vapor mass fraction. \(p_{sat}\) is the vapor saturation pressure [Pa]. \(Q\) is the heat source [W/m\({}^{3}\)s]. \(\xi\) is the moisture storage capacity [kg/ m\({}^{3}\)], \(\xi=\frac{\partial\omega_{v}(\phi_{v})}{\partial\phi_{w}}\). \(D_{W}\) is the moisture diffusivity [m\({}^{2}\)/s]. \(G\) is the moisture source [kg/m\({}^{3}\)s]. \(p\) is the fluid pressure [N/m\({}^{2}\)]. \(I\) is the identity tensor. \(K\) is the viscous force [N/m\({}^{2}\)].