| Glaser[28] | $ \left[\begin{array}{c}{\boldsymbol{g}}_{\mathrm{v}} \\{\boldsymbol{q}}\end{array}\right]=\left[\begin{array}{cc}\delta_{\mathrm{v}} & 0 \\0 & \lambda\end{array}\right] \nabla\left[\begin{array}{c}p_{\mathrm{v}} \\T\end{array}\right] . $ |
gv为气态水的质量扩散通量，q为能量扩散通量，λ为多孔材料的有效导热系数，δv为水蒸气渗透系数，
pv为水蒸气分压力，T为温度. |
Philip &
de Vries[31] | $\left[\begin{array}{cc}1 & 0 \\ 0 & \rho c_{p}\end{array}\right] \dfrac{\partial}{\partial \tau}\left[\begin{array}{l}{\rho_\mathrm{w}} \\ T\end{array}\right]=\nabla \cdot\left(\left[\begin{array}{cc}{D_\mathrm{w}} & D_\mathrm{T} \\ h_{1 \mathrm{at}} D_{\mathrm{w} \mathrm{v}} & \lambda\end{array}\right] \nabla\left[\begin{array}{l}{\rho_\mathrm{w}} \\ T\end{array}\right]\right). $ |
ρ为材料密度，cp为比定压热容，ρw为含湿量（水质量浓度），hlat为水的蒸发潜热，Dwv为与含湿量梯度相关的气态水
扩散系数，Dw或DT为与含湿量或温度梯度相关的水分扩散系数（含气态水与液态水）. |
| Luikov[34] | $\begin{aligned} & {\left[\begin{array}{cc}1 & 0 \\ 0 & \rho c_{p}\end{array}\right] \dfrac{\partial}{\partial \tau}\left[\begin{array}{c}{\rho_\mathrm{w}} \\ T\end{array}\right]=\nabla \cdot\left(\left[\begin{array}{cc}D_\mathrm{w} & D_\mathrm{T} \\ h_{\mathrm{lat}} D_{\mathrm{w} \mathrm{v}} & \lambda+h_{\mathrm{lat}} D_{ \mathrm{Tv}}\end{array}\right] \nabla\left[\begin{array}{l}{\rho_\mathrm{w}} \\ T\end{array}\right]\right),} \\ & {\left[\begin{array}{cc}1 & 0 \\ -\rho \sigma h_{\mathrm{lat}}-\gamma & \rho c_{p}\end{array}\right] \dfrac{\partial}{\partial \tau}\left[\begin{array}{l}{\rho_\mathrm{w}} \\ T\end{array}\right]=\nabla \cdot\left(\left[\begin{array}{cc}D_\mathrm{w} & D_\mathrm{T} \\ 0 & \lambda\end{array}\right] \nabla\left[\begin{array}{l}{\rho_\mathrm{w}} \\ T\end{array}\right]\right) (\text { 简化后 }).}\end{aligned} $ |
| σ为相变因子，γ为吸附热，DTv为与温度梯度相关的气态水扩散系数. |
| Künzel[9] | $ \left[\begin{array}{cc}\varsigma & 0 \\ 0 & \rho c_{p}+{\rho_\mathrm{w}} c_{p, 1}\end{array}\right] \dfrac{\partial}{\partial \tau}\left[\begin{array}{c}\varphi \\ T\end{array}\right]=\nabla \cdot\left(\left[\begin{array}{cc}\delta_{\mathrm{v}} p_{\mathrm{sat}}+D_\mathrm{w} \varsigma & \varphi \xi \delta_{\mathrm{v}} \\ h_{\mathrm{lat}} p_{\mathrm{sat}} \delta_{\mathrm{v}} & \lambda+h_{\mathrm{lat}} \delta_{\mathrm{v}} \varphi \xi\end{array}\right] \nabla\left[\begin{array}{c}\varphi \\ T\end{array}\right]\right).$ |
φ为相对湿度，cp,l为液态水的比定压热容，psat为饱和水蒸气压力，ς为含湿量-相对湿度曲线斜率，
ξ为水蒸气饱和压力-温度曲线斜率. |
| 陈友明等[44] | $\left[\begin{array}{cc}\varsigma l & 0 \\ 0 & \rho c_{p}+{\rho_\mathrm{w}} c_{p, 1}\end{array}\right] \dfrac{\partial}{\partial \tau}\left[\begin{array}{c}p_{\mathrm{c}} \\ T\end{array}\right]=\nabla \cdot\left(\left[\begin{array}{cc}\delta_{\mathrm{v}} p_{\mathrm{sat}} l+K_1 & \varphi \xi \delta_{\mathrm{v}} \\ h_{1 \mathrm{at}} p_{\mathrm{sat}} \delta_{\mathrm{v}} l-h_{1 \mathrm{at}} K_1 & \lambda+h_{1 \mathrm{at}} \delta_{\mathrm{v}} \varphi \xi\end{array}\right] \nabla\left[\begin{array}{c}p_{\mathrm{c}} \\ T\end{array}\right]\right). $ |
| pc为毛细压力，Kl为液态水渗透系数，l为相对湿度-毛细压力曲线的斜率. |
| 黄建恩等[50] | $\left[\begin{array}{cc}1 & -\varphi \xi \\ 0 & \rho c_{p}\end{array}\right] \dfrac{\partial}{\partial \tau}\left[\begin{array}{c}p_{\mathrm{v}} \\ T\end{array}\right]=\nabla \cdot\left(\left[\begin{array}{cc}p_{\mathrm{sat}} \delta_{\mathrm{v}} /(\varsigma \rho) & 0 \\ h_{ \mathrm{lat}} \delta_{\mathrm{v}} & \lambda\end{array}\right] \nabla\left[\begin{array}{c}p_{\mathrm{v}} \\ T\end{array}\right]\right). $ |
| Qin等[52] | $\left[\begin{array}{cc}\rho c_{\mathrm{m}} & 0 \\ -\rho c_{\mathrm{m}}\left(\sigma h_{\text {lat }}+\gamma\right) & \rho c_{p}\end{array}\right] \dfrac{\partial}{\partial \tau}\left[\begin{array}{c}\rho_{\mathrm{v}} \\ T\end{array}\right]=\nabla \cdot\left(\left[\begin{array}{cc}\delta_{\mathrm{v}} & \delta_{\mathrm{v}} \varepsilon \\ 0 & \lambda\end{array}\right] \nabla\left[\begin{array}{c}\rho_{\mathrm{v}} \\ T\end{array}\right]\right). $ |
| cm为比湿容，ρv为气态水密度，ε为与气态水密度梯度相关的气态水扩散系数. |
| Budaiwi等[53] | $\left[\begin{array}{cc}1 & -\varphi \mathrm{d} w_{\mathrm{a}, \text { sat }} / \mathrm{d} T \\ 0 & \rho c_{p}\end{array}\right] \dfrac{\partial}{\partial \tau}\left[\begin{array}{c}w_\mathrm{a} \\ T\end{array}\right]=\nabla \cdot\left(\left[\begin{array}{cc}w_{\mathrm{a}, \text { sat }} \delta_{\mathrm{v}} R \rho_{\mathrm{a}} T /\left(M_{\mathrm{w}} \varsigma \rho\right)+D_\mathrm{w} & 0 \\ h_{1 \mathrm{at}} \delta_{\mathrm{v}} R \rho_{\mathrm{a}} T / M_{\mathrm{w}} & \lambda\end{array}\right] \nabla\left[\begin{array}{c}w_{\mathrm{a}} \\ T\end{array}\right]\right). $ |
| wa为空气中水质量分数，wa,sat为空气中饱和水质量分数，R为理想气体常数，ρa为空气密度，Mw为水的摩尔质量. |