Viscous dissipation, mechanical energy balance

This equation is based on the assumption that the change of state resulting from the process is accomplished reversibly. However, the viscous nature of real fluids induces fluid friction that makes changes of state in flow processes inherently irreversible because of the dissipation of mechanical energy into internal energy. In order to correct for this, we add to the equation a friction term F. The mechanical-energy balance is then written ... 

The four terms on the right hand side of this result can be identified as the shaft work, the fiow work, the reversible work and the irreversible work (viscous dissipation). The shaft work Is a very Important quantity In many practical problems and it can only be Included in the analysis by means of a moving control volume. In addition, the use of the kinematical relation given by Eq, 2-18 has allowed us to represent the rate of work done by the body force b in terms of an accumulation and flux of potential energy. It should be clear that the concepts of kinematics and stress are essential elements of the derivation that led originally from Eq. 1-2 to the macroscopic mechanical energy balance given by Eq. 2-23. 

Of course, in any real process with friction, viscous effects, mixing of components, and other dissipative phenomena taking place which prevent the complete conversion of one form of mechanical energy to another, allowances will have to be made in making a balance on mechanical energy for these losses in quality. 

The mechanism of viscous flow is discussed as follows. For this mechanism, matter transport is governed by the concept of Frenkel s energy balance, i.e., the rate of energy dissipation by the viscous flow is equal to the rate of the energy gained by the reduction in surface area, i.e., (Rate)jjjj = (Rate)g jj. 

The mechanical energy dissipated by the agitator is converted into viscous friction energy and finally altered into thermal energy. In most cases this term may be neglected when compared to the heat released by a chemical reaction. But with viscous reaction masses, as for example with polymerization reactions, this term must be integrated in the heat balance. It can be estimated from Equation (8). 

Solution. Based on the description of the cone-and-plate rheometer in Section 3.3 we can consider the flow to be as shown in Figure 5.4. Based on the dimensions given, the height, H, at the edge is 0.125 cm. An energy balance is performed on the slab of thickness Ay and unit width. It is assumed that heat is generated by viscous dissipation, which is the conversion of mechanical energy into heat. The viscous dissipation per unit volume is... 

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