A well-mixed water tank with an inlet flow and an outlet flow is used to collect solar thermal energy. Both the inlet and the outlet flow rates are the same: F (kg/s). The water in the tank has a volume of V [m'], and its surface area for collecting solar heat is S [m'). Across this surface solar heat flux to the tank is at a constant rate of/ [W/m2). The imperfect insulation leads to loss of heat from the tank Qioss a(T;-T) [W], where a is a constant, T, and T are temperature ["C] in the tank and the ambient, respectively. The water density and heat capacity are assumed to be constant: p [kg/m'), and c, [kJ/kg/"C]. The inlet water temperature is T, ["c). %3D Develop a mathematical model for the purpose of predicting the change of the temperature af the water in the tank (T;) given system input F.