## 1 Introduction
[PERSON] et al. [15] developed the numerical models for electrical and thermal efficiency using MATLAB simulation. They compared the electrical and thermal performance between a classical PV generator and water glazed PVT collector under northern Sahara climatic conditions. [PERSON] et al. [18] developed and validated a numerical model of thermal and electrical performance through experimental results indicated in the previous literature. The numerical model took the heat balance equations and different thermal and electrical parameters for each configuration. [PERSON] et al. [19] developed a model to simulate a hybrid photovoltaic-thermal collector under a transient regime. The model used a control volume approach. The collector is divided into small elemental volumes where the energy equation is solved using a bidimensional finite difference method. [PERSON] et al. [20] developed a novel 2D irradiance temperature coupling model for the performance of flat-plate PVT systems. [PERSON] et al. [21] developed a nonlinear state-space model of a hybrid photovoltaic/thermal (glazed and unglazed PVT) system to couple the electrical and hydraulic circuits. The proposed model was used to predict, monitor, diagnosis, and increase the life span. [PERSON] et al. [22] developed the 1D (dimensional) steady-state numerical model and performed the bifluid using MATLAB. It used a commercial WISC PVT collector by adding an air channel, an aluminum absorber with fins, and a layer of thermal insulation. [PERSON] et al. [23] established and verified a theoretical model of 22 designs for a concentrating PVT dual-fluid solar collector with 1D steady-state energy-balance equations. The air and water mass flow rates were varied to predict the system performances. [PERSON] et al. [24] developed a theoretical model of the heat transfer in the PVT collector with different parallel cooling channels that was established to evaluate the effect on the thermal performance of the PVT collector. [PERSON] et al. [25] predicted the thermal efficiency of PVT collector by modifying multilayer perceptron artificial neural network (MLP-ANN), adaptive neuro-fuzzy inference system (ANFIS), and least squares support vector machine (LSSVM) approaches. [PERSON] et al. [16] developed a mathematical model based on heat transfer balance equations and electrical and thermophysical proprieties to draw the output behavior of both PV module and hybrid PVTwater-based system. [PERSON] et al. [17] developed a numerical analysis and experimental validation of the thermal and electrical behavior of the air PVT collector based on the geometric design and the Tunisia climate conditions. The thermal modeling used the heat balance equations of each component. [PERSON] et al. [26] developed a novel thermal model for a PVT system which includes the thermal contact resistance between the layers of a PVT system and individual resistance. This model provides a clear understanding of how the properties of each layer influence their overall performance. From those studies, numerical and theoretical models have predicted the thermal performance of PVT collectors with a certain complexity and flexibility. However, they have not included the effect of Joule heating, or Joule heating has not been the focus of the discussion. As a result, they have not explained the Joule heating effect on the thermal performance of a hybrid PVT collector. The commonly used thermal efficiency model has not also covered the Joule heating effect [7; 8]. A factor needs to be involved and proved empirically in the thermal efficiency model used to explain the Joule heating effect on thermal efficiency in PVT-mode. A performance analysis was carried out for the previous result in steady-state [13]. The purpose of this study is to develop the operation mode factor (OMF) by remodeling the thermal efficiency model of a hybrid PVT collector during steady state.