## 1 Introduction  
Solar energy is an abundant source of renewable energy. It can convert directly into electrical energy by a photovoltaic (PV) module, thermal energy with a solar thermal collector, and electrical and thermal energy simultaneously with a hybrid photovoltaic (PVT) collector. A hybrid PVT collector attaches a PV module on the top of a flat-plate-type thermal collector [1]. The original idea was to control the PV module temperature as low as possible to maintain the electrical performance [2]. The thermal collector takes the heat from the PV module by circulating fluids, such as water and air. Thus, the total solar energy converted to electrical and thermal energy by the PVT collector can reach 60-70% [3]. The thermal energy generated by hybrid PVT collectors is applicable for low-temperature applications, such as domestic hot water and low-temperature industrial processes, or space heating [4, 5]. Over the years, researchers have studied hybrid PVT collectors in various aspects. They have developed the design constructions, operational parameters, materials selection, system configurations, modeling simulation, and system performance [6]. The system performance of the PVT systems is still an interesting topic for researchers. Those aspects strongly influence the performance of the PVT system. The market expects the PVT system to be more applicable and cheaper with higher performance. Concerning the thermal efficiency \(\eta_{t}\) of PVT collector [7, 8], formulated as;  
\[\eta_{t}=F_{R}\tau\alpha-F_{R}U_{L}\frac{(T_{i}-T_{a})}{I} \tag{1}\]The PVT is influenced by heat removal factor \(F_{R}\), transmittance \(\tau\), absorptance \(\alpha\), optical efficiency \(\eta_{o}\) or \(\tau\alpha\), overall loss coefficient \(U_{L}\) (in W/m\({}^{2}\).\({}^{\circ}\)C), inlet water temperature \(T_{i}\) (in \({}^{\circ}\)C), ambient air temperature \(T_{a}\) (in \({}^{\circ}\)C), and irradiance \(I\) (in W/m\({}^{2}\)). The collector system has high performance, indicated by the high \(\tau\alpha\) and low \(U_{L}\) (see Equation (1)). The energy gain part is \(F_{R}(\tau\alpha)\), while the energy loss part is \(F_{R}U_{L}(T_{i}-T_{a})/I\). It is assumed that the PV cell in the PVT collector provides thermal resistance when electricity is not generated [9]. It is essential to determine the correlation between the PV cell without electricity generation and its resistance effect [10]. The thermal performance of the PVT system is influenced by the Joule heating when simultaneously generating electrical and thermal energy (PVT-mode) [11; 12]; there is an important factor involved. Specifically, in an effective region [13], the PVT thermal efficiency in PVT-mode is higher than in T-mode. Joule heating has the effect of improving the thermal efficiency up to 13%. Joule heating appears when the PV panel works at a high electrical current during maximum power point tracking (MPPT) at higher irradiation. Joule heating induces a lower increase in the cell temperature. Joule heating is the heat generated when the electrical current passes through the resistive material. A part of the electrical energy in PV cells becomes thermal energy. At the zero reduced temperature, the PVT thermal efficiency in the PVT-mode is higher than in T-mode when generated heat only. With the conditions, \(T_{i}\approx T_{a}\) or \(I\) is high. The thermal performance of PVT collectors still attracts the attention of researchers to this day. Various thermal efficiency models have obtained more accurate results. Several numerical models have been used to evaluate the performance of PVT systems in more detail up to three dimensions, assisted by simulations with various conditions, such as steady state, transient, and real time [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. [PERSON] et al. [14] developed a novel three-dimensional numerical model for the thermal efficiency of the PVT system and tested the flow adopting the usual k-epsilon model. The model applied the symmetric convection and boundary conditions for the PVT cooling system.