As a flow enters or leaves a control volume it takes in or takes out some amount of energy as work. This concept mathematically leads enthalpy to appear in the 1st law of thermodynamic equation for control volume; But what is the physical sensible concept of this flow work?
The attached notes show how the thermal energy equation can be derived for a single component flow system. Various specializations of the general equation reduce to common expressions of the First Law in thermodynamics. The principles used in these notes can allow one to derive the equivalent form for multi-components systems though the algebra/manipulations are more "intense"
in the total energy equation, the term Div (v.T) is responsible for the work, it contains the reversible part (related to the isotropic terms of T) and the irreversible part (related to the deviatoric part of T). The irreversible part is associated to dissipation of kinetic energy caused by the work that increases the internal energy
All answers and comments are so respectful but the concept I am looking for is neither complicated nor mathematical. I just looking for the sensible and physical concept of this matter! Thank you
there is nothing of different from the concept of work in classical physics (F ds)...the action of the force has the counterpart in the stress in the fluid, the action of the displacement has the counterpart in the velocity of the fluid. The divergence take into account for the local variation and makes the term dimensionally consistent. The infinitesimal volume of fluid makes work when it is acted upon stress and produces a diplacement.
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