Energy equations
Considering the total enthalpy of the phase k
$H_k=e_k+\frac{1}{2}u_k^2+\frac{P}{\rho_k}$ (13)
The energy equation is written
$\frac{\partial}{\partial t}(\alpha_k \rho_k H_{k})+\frac{\partial}{\partial x_j}(\alpha_k \rho_k H_{k}U_{k,j}) = \frac{\partial}{\partial x_j} (\alpha_k \tau_{k,ij} U_{k,i})-\frac{\partial}{\partial x_j}\alpha_kQ'_{k,j}-\alpha_k\frac{\partial P}{\partial x_i}+\alpha_k \rho_k U_{k,i} g_{i}+\Pi_k+Q_{wall→k}+I_{p→k,i}$ (14)
Where $Q'_k=\lambda_kT_k$ and $\lambda_k$ represents the thermal conductivity.
$Q{wall →k}$ denotes the heat exchange with boundaries and is described by the nucleate boiling model. It takes into account bubble creation and satisfies:
$\sum_{k=1}^{n phase}Q{wall→k}=Q_{wall}$ (15)
where $Q_{wall}$ is the total imposed heat flux.
Furthermore, $\Pi_k$ represents the bulk interface heat transfer, sum of the interface transfer between phase p and phase k, which complies with conservation relation
$\Pi_k= \sum_{p≠k} \Pi_{p→k}$ (16)
where
$\Pi_{p→k}+\Pi_{k→p}=0$ (17)
It should be noted that the code does not consider the terms and $\alpha_k \tau_{k,ij} U_{k,i}$ and $I_{p→k,i}$