Mathematical modeling of a three-dimensional PVT system is considered and solved using the FEM. Numerical simulation is applied to explore the influence of solar irradiance on the thermal energy, electrical power, and total efficiency of this system. Water is considered HTF. The solar irradiance, inlet fluid mass flow rate, ambient temperature, and partial shading are all chosen in the range of 200-500 W/m2, 30-180 L/h, 10-37 °C, and 0-30%, accordingly based on the weather condition of Bangladesh. The effects of irradiance, fluid flow rate, ambient temperature, and partial shading on temperatures of cell and output fluid, electrical power and thermal energy, electrical efficiency-thermal efficiency, and total efficiency of this system are examined. Numerical results show that increasing each 100 W/m2 solar irradiance enhances the cell and outlet temperatures and electrical and thermal energy by 2.17 and 0.54 °C and 20.7 and 113.3 W, respectively, and devalues the electrical, thermal, and overall efficiencies approximately 0.17, 0.67, and 0.83%, respectively. The cell and output water temperature reduce almost 0.6 and 0.83 °C, respectively; electrical and thermal energy rise by 0.30 and 3.07 W, respectively, and the electrical, thermal, and overall efficiencies escalate about 0.04, 0.4, and 0.44% for every 10 L/h mass flow rate increment. Due to each 10 °C increment of ambient temperature, cell and output water temperature increase 1.7 °C and 0.05 °C, electrical energy decreases to 0.9 W, thermal energy increases to 9.89 W, and electrical efficiency reduces about 0.1%.