# When can the thermal and mechanical energies of a fluid control volume be considered separately?

For a fixed control volume of a fluid, the conservation of energy equation is typically written as something like $$\dot{Q} - \dot{W} = \frac{\text{d}}{\text{d}t}\iiint_{CV} \left( \hat{u} + \frac12 V^2 + gz \right) \rho \,\text{d}V + \iint_{CS} \left( \hat{h} + \frac12 V^2 + gz \right) \rho \, \mathbf{V}\cdot\hat{\mathbf{n}} \, \text{d}A.$$

Is there any criteria for which we can reasonably decouple this into separate conservation equations for thermal and mechanical energy? That is, into the form $$\begin{cases} \dot{Q} = \frac{\text{d}}{\text{d}t}\iiint_{CV} \hat{u} \rho \,\text{d}V + \iint_{CS} \hat{h} \rho \, \mathbf{V}\cdot\hat{\mathbf{n}} \, \text{d}A, \\ -\dot{W} = \frac{\text{d}}{\text{d}t}\iiint_{CV} \left( \frac12 V^2 + gz \right) \rho \,\text{d}V + \iint_{CS} \left( \frac12 V^2 + gz \right) \rho \, \mathbf{V}\cdot\hat{\mathbf{n}} \, \text{d}A. \end{cases}$$

I know that for some common types of analysis the mechanical terms are negligible compared to the thermal and ignored entirely. Does this imply that a separate mechanical energy conservation equation can be posed?

I suspect this depends on the relative magnitude of the viscous dissipation function. Is there some dimensionless number that quantifies this?