Volumetric rate of entropy production

If the local entropy production, <, is integrated over the volume, it is called the volumetric rate of entropy production... 

Equation (3.314) shows the volumetric rate of entropy production. Both the flows and the forces may change with time, while they remain constant at the system boundaries at stationary state only. The time variation of P is... 

The time derivative of entropy production is called the rate of entropy production, and can be calculated from the laws of the conservation of mass, energy, and momentum, and the second law of thermodynamics expressed as equality. If the local entropy production, a, is integrated over the volume, it is called the volumetric rate of entropy production. ... 

Second-law analysis can determine the level of energy dissipation from the rate of entropy production in the system. The entropy production approach is especially important in terms of process optimality since it allows the entropy production of each process to be determined separately. The map of the volumetric entropy production rate identifies the regions within the system where excessive entropy production occurs due to irreversible processes. Minimizing of excessive irreversibilities allows a thermodynamic optimum to be achieved for a required task. Estimation of the trade-offs between the various contributions to the rate of entropy production may be helpful for attaining thermodynamically optimum design and operation. 

Example 5.4 Minimization of entropy production For a fixed design, the minimization of the rate of entropy production may yield optimal solutions in some economic sense. Such a minimization comes with certain set of constraints. For a single force-flow system, the local rate of volumetric entropy production is... 

Figure 4.4 shows the temperature profile for T2 = 300 K and -2.0 < Br < 8.0. The rise of temperature in the middle part of the Couette device is considerably large for high values of Br. Inserting Eqs. (4.26) and (4.29) into Eq. (4.23) yields an expression for the volumetric entropy production rate for a Couette flow. 

Here, the terms on the right side of the above equation show the entropy production due to heat transfer and fluid friction, respectively hence, the entropy production expression has the following basic form , Sprod =, Yprod Ar +, S prod A/,. The volumetric entropy production rate is positive and finite as long as temperature or velocity gradients are present in the medium. 

An evolution criterion can be obtained from the rate of change of volumetric entropy production P = fXJXdV > 0 as follows ... 

When the chemical reaction reaches equilibrium, affinity vanishes A = —St /za, = 0. The entropy generated per unit time and unit volume is called the rate of volumetric entropy production or the entropy source of density ... 

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