Heat transfer entropy creation

As an example, let us consider a feedwater heater, such as illustrated by Component No. 6 in Figure No. 1. Let Z represent the annualized capital cost (say in dollars per year) of owning and operating the feedwater heater (including maintenance, overhead, etc., as well as interest). Also, let X represent the unit cost of each type of lost work, while T0 represents the lost work, where represents the rate of entropy creation (or production) corresponding to each type of lost work in the feedwater heater (2, 6,7). Then let A, Ag, and Ah represeht the unit costs of lost work Td a T0 b, and T h due respectively to head loss (pressure drop) in the feedwater A, head loss in the condensing steam B, and heat transfer (temperature drop) from the condensing steam.to the feedwater, denoted by H, so that the total annualized cost T attributable to the feedwater heater is,... 

In addition to the entropy creation due to heat transfer, there are entropy creations A and B due to viscous friction in the fluid in the tubing and on the shell side of the exchanger respectively. For example (32,33),... 

The entropy creation A due to head loss in the tubes is related to the heat transfer area A via the hydraulic diameter D = 4AcLN/A. Since the mass rate M is given by M = pvAcN = mAcN, Eqn. (9) yields ... 

The paradox involved here can be made more understandable by introducing the concept of entropy creation. Unlike the energy, the volume or the number of moles, the entropy is not conserved. The entropy of a system (in the example, subsystems a or P) may change in two ways first, by the transport of entropy across the boundary (in this case, from a to p or vice versa) when energy is transferred in the form of heat, and second,... 

In contrast to thermodynamic properties, transport properties are classified as irreversible processes because they are always associated with the creation of entropy. The most classical example concerns thermal conductance. As a consequence of the second principle of thermodynamics, heat spontaneously moves from higher to lower temperatures. Thus the transfer of AH from temperature to T2 creates a positive amount of entropy ... 

Returning to the former case, the irreversibility lies in the fact that the system has been restored to its original condition only at cost of transferring heat from it into a heat bath. Thus the inevitable result of an irreversible process is the creation of entropy, and the system can be restored to its original condition only by the removal of heat. That is to say, the created entropy must be transferred to some other body, such as a heat bath, w hich thereby undergoes a... 

Since dS must be positive or zero, T > and thus the heat flows from the hotter to the cooler body, in agreement with experience. The creation of entropy in the system continues for as long as exceeds and the state of equilibrium requires equality of these temperatures. This is in accordance with the mecming of temperature as discussed in 1 4. A reversible transfer of heat thus requires that there shall be only an infinitesimal temperature difference. Thus if 2s<-2i is an infinitesimal, the increase of entropy in the above equation becomes equal to dqdT/T and is of the second order of smallness. 

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