## 4 Discussion  
A simple, steady-state, one-dimensional thermal efficiency model has constructed the proposed thermal efficiency model with the influence factors. The result was validated and tested during T-mode and PVT-mode using the original experimental data [13]. Based on the results, OMF can explain the crossing of thermal efficiency lines between T-mode and PVT-mode. For more details, let us discuss some findings here. First, to understand the most decisive component of OMF we compare PVT-mode with T-mode. As shown in Table 2, \(K_{SA,pt}/K_{SA,t}\)= 4.06 and 5.51, then \(U_{L,pt}/U_{L,t}\) = 1.30 and 1.41 for wind loss effect and without wind loss effect, respectively. \(K_{SA}\) changes more significantly than \(U_{L}\). In other words, \(K_{SA}\) was the most decisive component in OMF, which gives \(OMF_{pt}/OMF_{t}\)= 1.36 and 1.33 for with and without wind loss effect, respectively. The reason for the \(K_{SA}\) changes is as follows: during steady-state, when a load variation took place with the ambient air temperature remaining constant, the different loads had an effect on the overall conduction coefficient. Then, the temperature gradient across the PV surface would change, which means that the overall thermal conductivity of the PVT collector changed. Based on formula and value, OMF might correlate to \(F_{R}\). The empirical relation between \(F_{R}\) and OMF may need to be studied further [32]. For the cases of wind loss effect and without wind loss effect, the RMS (sim.) value of PVT-mode of 10.6% was smaller than the T-mode of 15.2%. Second, the PVT-mode thermal efficiency is greater than T-mode in the effective region, as shown in Figure 6b through \(K_{SA}/U_{L}\) (refer to Equations (12) and (13), and \(K_{SA}/U_{L}=Q_{u,th}(T_{5}-T_{a})/Q_{L,tot}(T_{5}-T_{i})\)). As shown in Table 2, the \(K_{SA}/U_{L}\) of T-mode and PVT-mode for the wind loss effect are 1.57 and 4.92, or 2.0 and 7.81 for the without wind loss effect. The reasons why \(K_{SA}/U_{L}\) for PVT-mode was bigger than T-mode (in the effective region) can be explained as follows. Apart from heating, radiation entering a solar cell separates the electrons from their atomic bond. It produces the electron-hole pairs due to the PV conversion of a photoelectric current flow in the circuit. The bandgap decreases with temperature. Through thermal activation, more electrons cross the energy gap. These cause the dark current to increase. The open-circuit voltage decreases. Then, the thermal  
Figure 7: Simulation of thermal efficiency vs. reduced temperature: (a) Without wind loss effect; (b) wind loss effect. resistance of the absorber decreases, though the thermal conductivity increases. Finally, the electrical and thermal efficiency increase. As assumed in the Materials and Methods section, the PV cell in the PVT collector provided thermal resistance due to the additional thermal mass of the PV layer [9]. Therefore, there is heat from the internal heating \(Q_{ih,th}\) as expressed in Equation (5). For T-mode, \(Q_{ih,th}=0\). Third, we see the relation between OMF and \(F_{R}\). Referring OMF to Equation (17) and \(F_{R}\) (see Equation (6.7.3) in [33]), OMF may represent \(F_{R}\) at Equation (1) for T-mode, but not for PVT-mode. OMF was more triggered by the operation mode (PVT-mode and T-mode) [13], while \(F_{R}\) was more influenced by the geometrical design and construction parameters [32; 34]. They might be interrelated at the mass flow rate as the effect of decreasing PV temperature, thereby optimizing PV output [35], which maintains Joule heating. By formula, OMF and \(F_{R}\) did not seem directly related to each other. However, by involving the previous analysis, OMF and \(F_{R}\) might be related to each other. In PVT-mode, the material absorber in \(K_{SA}\) might become more conductive or less resistive. Then, from the beginning, it already had the approach to consider the condition with and without wind loss effects.