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(\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}  
 
+  \sum_{a = \{w,o,g \}} \rho_\alpha \ c_{p \alpha} \ \epsilon_\alpha \ u_\alpha  \frac{\partial PT}{\partial l}
 
+  \sum_{a = \{w,o,g \}} \rho_\alpha \ c_{p \alpha} \ u_\alpha \frac{\partial T}{\partial l}
 
 - \nabla (\lambda_t \nabla T) =\  =   \   \frac{\delta E_H}{ \delta V \delta t}