## 2 Materials and Methods
### Numerical Modeling
#### 2.3.2 Thermal Simulation Details  
The thermal simulations in this study were performed using SolidWorks v.2014-2015 and COMSOL 5.2 software [35; 36]. Both of these tools are widely used, with proven validity and reliability [18; 27; 37]. SolidWorks is a well-established simulation software extensively employed in various research studies focusing on energy systems, particularly in the context of solar thermal collectors [28; 30]. This program facilitates design processes and allows separate or simultaneous simulations of flow, optical and thermal characteristics. COMSOL is a readily available software that applies finite element methods for solving multi-coupled physics problems. COMSOL is a software tool employed in research studies concerning both non-concentrating [16; 38] and concentrating solar collectors [39]. The authors developed a novel method for the thermal simulation that was applied in this study. The innovative aspect of this method stems from its consideration of the enclosed air between the reflector and glass while excluding it from the numerical simulation, leading to substantial reductions in computational time. Specifically, the simulated inclusion of enclosed air was accomplished by imposing boundary conditions that specified the temperature and equivalent value of the convective coefficient (\(h\)) on the absorber boundary areas, as well as on the interior surfaces of the cover and reflector. Several simulations were carried out, varying the enclosed air temperature while keeping the convective heat transfer coefficient constant in each simulation. The purpose was to determine the appropriate value of the enclosed air temperature that would result in the heat losses that come from the absorber being similar to those from the external faces of the solar unit. This condition ensured that the solution would converge at each operational state, as the thermal equilibrium of the solar unit needed both losses to be equivalent. The total thermal losses were accurately calculated by considering both the radiative and convective contributions. In the beginning, an arbitrary temperature value within the range of the inlet fluid temperature and the ambient air temperature was assigned to all the surfaces within the cavity to compute heat losses due to convection. Once the numerical solution was obtained, the total thermal losses from the absorber and the corresponding losses from the external faces of the solar unit were established. In the event that the receiver's thermal losses exceeded those of the exterior surfaces, a greater temperature rate was assigned to the air gap. Increasing this temperature led to a decrease in overall losses for the receiver while causing the outer surfaces to reach higher temperatures, increasing their overall losses. This iterative process was repeated until an equilibrium was achieved. This method was implemented for a subset of the examined operating points, revealing that it yields results that are comparable to those obtained by linearly interpolating between two observation points, with a \(1\) K variance in the temperature estimated within the air cavity. In order to illustrate the step-by-step implementation of the proposed method, a flowchart has been developed (Figure 3). The flowchart visually captures the sequence of actions and decisions involved in each phase of the method. By referring to this flowchart alongside the following textual description, a holistic understanding of the analysis of the thermal performance of the ACPC-PVT collector can be obtained. Figure 3: Flowchart of the proposed method. Regarding the overall chosen solution approach, it should be noted that steady-state analysis was employed during the thermal analysis. This selection was deliberate, as the study aims to mainly investigate the inlet temperature increment impact on the thermal and exergy efficiency. Furthermore, the assumption of laminar flow as the flow regime was made.