Entropy generation transfer

The same property of entropy generation holds for other processes. In electrical conductance, charged particles move from higher to lower electrical potentials. In diffusion phenomena, all chemical entities are transferred from higher to lower chemical potentials. 

In Section 3.3, we have shown that the entropy generation rate in the case of heat transfer in a heat exchanger is simply the product of the thermodynamic driving force X = A(l/T), the natural cause, and its effect, the resultant flow / = Q, a velocity or rate. Selected monographs on irreversible thermodynamics, see, for example, [1], show how entropy generation also has roots in other driving forces such as chemical potential differences or affinities. 

The ideal, unrealistic, but basic limit of the thermodynamic efficiency of a process is that of the reversible process where all work available and entering the process is still available after the process. Work has simply been transferred from one carrier to another. Driving forces are infinitesimally small and the process is "frictionless" no barriers have to be taken. As a result, there is neither entropy generation nor loss of available work. The work requirements of the process can be accurately calculated from the thermodynamic properties of the equilibrium states that the process passes through. 

For the establishment of the realistic limit, one has to take account of the rates of processes in which mass, heat, momentum, and chemical energy are transferred. In this so-called finite-time, finite-size thermodynamics, it is usually possible to establish optimal conditions for operating the process, namely, with a minimum, but nonzero, entropy generation and loss of work. Such optima seem to be characterized by a universal principle equiparti-tioning of the process s driving forces in time and space. The optima may eventually be shifted by including economic and environmental parameters such as fixed and variable costs and emissions. For this aspect, we refer to Chapter 13. 

When a chemical reaction occurs in a steady-state system, products must be transferred out of the system and reactants must be transferred into the system. To avoid additional entropy generation, we take these transfers as being transfers by diffusion to reservoirs at material equilibrium with the system. The entropy generated in the system by the chemical reaction is then, by Eq. (9), the entropy increase of the reservoirs ... 

The entropy generation for the direct heat-transfer process is ... 

Since heat transfer with respect to the surroundings is the negative of heat transfer with respect to the system, ( surr = —Q. Therefore the rate of entropy generation 5,otai is defined as... 

The rate of entropy generation and the lost work for each of the individual ] of the process are calculated by Eqs. (16.1) and (16.15). Since the flow rate of methane is not given, we take 1 kg of methane entering as a basis. The rates S, W m, and Q are therefore expressed not per unit of time but per kg of entering meth The heat transfer for the compression/cooling step is calculated by an enc balance ... 

The. thermodynamic efficiency of the power plant is 27.3 percent, and the major source of inefficiency is the fumace/boiler. The combustion process itself accounts for most of the entropy generation in this unit, and the remainder is the result of heat transfer across finite temperature differences. 

The above equation implies that the extremum is a minimum. Thus, with a constant transfer coefficient, the distribution of the driving force that minimizes the entropy generation under the constraint of a specified duty is a uniform distribution. The minimal dissipation for a specified duty implies the equipartition of the driving force and entropy generation along the time and space variables of the process. 

The final term, representing the rate of entropy generation Sq, reflects the second-law requirement that it be positive for irreversible processes. There are two sources of irreversibility (a) those within the control volume, i.e., internal irreversibilities,and (b) those resultingfrom heat transfer across finite temperature differences between system and surroundings, i.e., external thermal irreversibilities. In the limiting case where Sq = 0, the process must be completely reversible, implying ... 

The entropy balance cannot be used directly to provide useful information since the entropy generation due to heat transfer cannot be evaluated at this stage in the calculation. However, we can use the fapt that for a system in which M, U, and V are cpnstant, at equilibrium the entropy is a maximum with respect to the independent variations within the system. The final entropy of the system is... 

Entropy distributes more or less quickly over the entire body from the point where it is created. This process is also connected with the generation of entropy even if it is not directly obvious (see Sect. 3.14). All of these entropy generating processes are irreversible. If entropy was created in this way we will not get rid of it again, unless we could transfer it in the surroundings. But this is inhibited by the thermal insulation. 

In the first part of the second law (2.3.8), we introduced a heat transfer term Qgxt that represents the amount of heat entering or leaving a system at the external side of its boundary. This is in contrast to the heat Q, which is the amount of heat that actually enters or leaves the system. These two terms, Qgxt and Q, may differ, depending on the amount of entropy generated in the boundary however, in many applications, the two will have similar magnitudes. 

If the device transfers heat from the lower temperature to the higher temperature, Ql must be positive, that is, the heat is added to the cycle from Tl, and the cycle eventually delivers Qh to the reservoir at higher temperature Th. Since entropy generation cannot be negative, the process is possible only if the device exchanges work. Solving for this work,... 

Comments The amount of heat that is exchanged between the two streams does not enter in the calculation of the entropy generation because it is internal to the system. The contribution of this transfer is taken into account indirectly, through its effects on the affected streams. The heat must be accounted in the entropy balance only when it involves a bath, because in this case the bath is a closed system and its entropy change cannot be calculated as an entropy change of flow streams. The next two examples explore variations of this problem. 

To estimate the entropy generation we must make some assumptions about the stream that absorbs this heat. This stream must be no hotter than 150 °C to allow for practical rate of heat transfer, we will take its temperature to be at 145 °C, and will treat it as a bath ... 

Application of the EGM method to the entropy generated by heat transfer at the surface (which should be maximum in a spray-cooUng appUcatiOTi), identifies the temperature as the parameter to be accounted for in the optimization process. Here, the derivative of (21.7) produces a single solution for the optimization of the wall temperature as 7 ,v,opt = 7b + 27 f, which can be interpreted with respect to the superheating degree (ATwb.opt = T w.opt - Ty,) as... 

MicroChannel heat sinks, such as a microchannel of square cross section with internal longitudinal fins, are an integral part of most devices used for thermal management in electronic equipment cooling. A thermodynamic analysis may help optimize the height of fin and thermophysical parameters, based on the minimizing the entropy generation rates due to heat transfer and fluid flow within the microchannel. 

Entropy generation of forced convection heat transfer of liquid fluid over the horizontal surface with embedded open parallel microchannels at constant heat flux boundary conditions may be formulated by an integral of the local entropy generation. Embedded open parallel microchannels within the surface can sufficiently reduce both friction and thermal irreversibilities of liquid fluid through slip-flow conditions (Kandlikar et al., 2006 Yarin et al., 2009). 

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