Dissipated energy and entropy

The energy equation (3.71), clearly shows that the internal energy in a fluid element is changed by the influx of heat and the performance of work. In the case of multicomponent mixtures, as shown in (3.75), a further term for the energy fed into the system with the material is added. 

The work done consists of the reversible part and the dissipated work. We want to calculate these contributions individually with the help of an entropy balance. For the sake of simplicity we will only consider pure substances. According to Gibbs fundamental equation, we have 

Inserting the energy equation (3.71) and the continuity equation (3.21) yields 

3 Convective heat and mass transfer. Single phase flow 

The first term on the right hand side of (3.78) represents the entropy fed in with the heat. This is known as the entropy flux. The two remaining terms represent the production of entropy. The second term stems from the finite temperature differences in thermal conduction, the third from the mechanical energy. We call 

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