3.2.3. Combination of Splitting

To have more information about the share of each component of a system in total exergy destruction, the two main parts discussed above can be combined. Researchers can use a combination of endogenous or exogenous parts with avoidable or unavoidable parts for a more detailed designing of the systems [30]. By combining the two main splitting parts, the exogenous/unavoidable and the endogenous/unavoidable, the exogenous/avoidable and the endogenous/avoidable rates are obtained. To reach the unavoidable endogenous rate of the kth component, the equation below is used [31,32]:

$$
\dot{E}\_{D,k}^{LIN.EN} = \dot{E}\_{P,k}^{EN} \left(\frac{\dot{E}\_{D,k}}{\dot{E}\_{P,k}}\right)^{LIN} \tag{25}
$$

In this equation, the ratio of exergy loss to exergy of product in this kth component is obtained in unavoidable conditions of the cycle, and the endogenous product exergy is obtained for the kth component when it is in hybrid cycle conditions. The unavoidable exogenous rate for the kth component is obtained from the following equation:

$$
\dot{E}\_{D.k}^{LIN.EX} = \dot{E}\_{D.k}^{LIN} - \dot{E}\_{D.k}^{LIN.EN} \tag{26}
$$

Then, the avoidable endogenous and exogenous parts of the exergy destruction for the kth component can be gained by reducing the unavoidable endogenous and exogenous exergy losses from the endogenous and exogenous exergy losses of that component, respectively.

$$
\dot{E}\_{D,k}^{AV.EN} = \dot{E}\_{D,k}^{EN} - \dot{E}\_{D,k}^{LIN.EN} \tag{27}
$$

$$
\dot{E}\_{D.k}^{AV.EX} = \dot{E}\_{D.k}^{EX} - \dot{E}\_{D.k}^{LIN.EN} \tag{28}
$$

The real potential of components in a system to improve their performances and to have the best efficiencies in a general system may be determined and analyzed by a mixture of the exergy loss sections mentioned above. There is no way to decrease the unavoidable/endogenous section of exergy loss because of technological limitations of the kth part, while avoidable/endogenous parts of the exergy destruction can be decreased by improving the efficiency of related components. The exogenous/unavoidable part of exergy loss for each component cannot be reduced because of technological constraints associated with other system components. However, the exogenous/avoidable parts may be decreased by the betterment of the total system performance, the efficiency of related components and, also, by improving the performance of other components in a system.

#### **4. Simulation, Results and Discussion**

The EES (engineering equation solver) is one of the most commonly used softwares to simulate power cycle operations. In this research, the EES was used to simulate cycle processes and to calculate properties of parameters in a system to reach cycle efficiencies. The input data and parameters for system components' working conditions of waste heat conditions used in this study are obtained from previous studies [12]. The conditions are shown in Table 3. These conditions are used for both conventional and advanced exergy analysis in this research.


**Table 3.** Heat source parameters and assumptions [12].
