(\rho \,c_{pt})_p \frac{\partial T}{\partial t} 
 
- \ \phi \sum_{a = \{w,o,g \}} \rho_\alpha \ c_{p \alpha} \ \eta_{s \alpha} \ \frac{\partial P_\alpha}{\partial t}  
 
+ \bigg( \sum_{a = \{w,o,g \}} \rho_\alpha \ c_{p \alpha} \ \epsilon_\alpha \ \mathbf{u}_\alpha \bigg)  \nabla P
 
+ \bigg( \sum_{a = \{w,o,g \}} \rho_\alpha \ c_{p \alpha} \ \mathbf{u}_\alpha \bigg) \  \nabla T 
 
 - \nabla (\lambda_t \nabla T) =  \frac{\delta E_H}{ \delta V \delta t}