Formulations for the energy equation exist in variety in fundamental and applied texts and monographs on fluid dynamics. It is often difficult to establish the set of conditions leading to a given formulation. More deleterious is the fact that in some cases an energy equation as point of departure does not have the generality implied by the accompanying text.
Dubbelday, Peter S., "Formulation Of The Energy Equation In Fluid Dynamics" (1975). Ocean Engineering and Marine Sciences Faculty Publications. 18.