## 2 Materials and Methods
### Organic Rankine Cycle (ORC) System  
In this section, the investigated ORC system is presented in detail. A schematic, and T-s diagram of the ORC system are presented in Figure 4a,b, respectively. The ORC system consists of an evaporator, a condenser, a pump and a turbine. A heat exchanger is used as the ORC evaporator. The heat absorbed by the solar dish collector is transferred to the ORC working fluid by the heat exchanger at constant pressure of 2.5 MPa (during process 2-3 in Figure 4). The ORC working fluid phase changes to a saturated or superheated fluid in the heat exchanger. The saturated or superheated fluid enters the turbine for power generation at isentropic conditions (during process 3-4 in Figure 4). Afterwards, the ORC working fluid is cooled by the condenser at constant pressure (during process 4-1 in Figure 4). It should be mentioned that the condenser operates at a constant temperature of 38 \({}^{\circ}\)C. Finally, the cooled organic fluid is pressurized by the pump at isentropic conditions (during process 4-1 in Figure 4). It should be noted that methanol is used as the ORC's working fluid. REFPROP.8 software [34] is used to determine the working fluid's thermodynamic properties. It should be mentioned that thermodynamic analyses were conducted using the Maple and REFPROP.8 software [14]. For simplicity, the internal irreversibility, the heat exchanger and pipeline pressure drop and the heat loss from the pipelines are neglected. Furthermore, it is assumed that each component of the ORC operates as a steady-flow system. Irreversibility acts as a barrier for conversion of thermal energy into work in a real system. Therefore, irreversibility affects the efficiency of a cycle and can be used to determine the efficiency. The total irreversibility rate can be approximated with [35]:  
\[\dot{I}_{total}=\sum_{j}\dot{I}_{j}\cong\dot{m}_{ORC}T_{\infty}\left[-\frac{h_ {3}^{*}-h_{2}^{*}}{T_{H}}+\frac{h_{4}^{*}-h_{1}^{*}}{T_{L}}\right] \tag{32}\]  
In the following, a list of the equations is presented for performing the thermodynamic analysis [36]. _Evaporator:_  
\[\dot{Q}_{exp}=\dot{m}_{ORC}(h^{*}{}_{3}-h^{*}{}_{2}) \tag{33}\]  
The mass flow rate of the ORC working fluid is evaluated as shown in Equation (34):  
\[\dot{m}_{ORC}=\frac{\dot{Q}_{exp}}{(h^{*}{}_{3}-h^{*}{}_{2})} \tag{34}\]  
in which  
\[\dot{Q}_{exp}=\dot{Q}_{net} \tag{35}\]  
_Turbine:_  
\[\dot{W}_{T}=\dot{m}_{ORC}(h^{*}{}_{3}-h^{*}{}_{4}) \tag{36}\]  
_Condenser:_  
\[\dot{Q}_{c}=\dot{m}_{ORC}(h^{*}{}_{4}-h^{*}{}_{1}) \tag{37}\]  
_Pump:_  
\[\dot{W}_{P}=\dot{m}_{ORC}(h^{*}{}_{2}-h^{*}{}_{1}) \tag{38}\]  
Figure 4: (**a**) A schematic of the ORC system, and (**b**) The \(T\)-s diagram of the ORC system for methanol. The net power generation can be calculated as shown below:  
\[\dot{W}_{net}=\dot{W}_{T}-\dot{W}_{P} \tag{39}\]  
The overall efficiency of the solar ORC system is defined in Equation (40):  
\[\eta_{overall}=\big{(}\dot{W}_{T}-\dot{W}_{P}\big{)}/\dot{Q}_{solar} \tag{40}\]  
Table 4 shows the input data of the solar ORC system. Input data were selected based on the reported optimal data by Ref. [37]. The aim of this study is to consider the effects of turbine inlet temperature (TIT) of the ORC working fluid, different shapes of the cavity receiver and different nanofluids as the solar working fluid of the ideal solar ORC system. The efficiency of the pump and heat exchanger is therefore assumed equal to 100%. The ORC working fluids can be categorized as dry fluids, wet fluids, and isentropic fluids. Selection of the appropriate working fluid is needed to achieve maximum efficiency. Note that methanol was selected for this study, because of its high thermodynamic performance as reported in Ref. [36]. As concluded in Ref. [36], methanol resulted highest thermodynamic performance with lowest irreversibility as the ORC working fluid among some examined organic fluids including R113, R601, R11, R141b, ethanol, and methanol.