This paper researches the heat transfer equation and thermal balance equation of a shell-and-tube evaporator; constructs an accurate mathematical model for the evaporator; and derives equations including detailed and accurate calculation methods for all heat transfer coefficients, such as the refrigerant side heat transfer coefficient, water side heat transfer coefficient, refrigerant kinematic viscosity, density, and specific enthalpy. Adopting this approach involves fitting the relationships between the density, thermal conductivity, kinematic viscosity, and enthalpy of R134a refrigerants in saturated vapor and liquid states. The relationships between superheated gas enthalpy, density, and temperature were also assessed, and heat transfer coefficients were obtained through calculation methods and microelement heat transfer relationships in both the single-phase and two-phase zones, matching empirical formulas concerning the relationship between superheated enthalpy and temperature. Notably, the research utilizes the Simulink approach without relying on M files and S functions to establish the evaporator’s two-phase and superheated zones, as well as an overall simulation model which provides intuitive internal coupling relationships and the coefficient calculation process in the formulas and uses the function “Algebraic Constraint” instead of “memory” or “1/z” to solve algebraic loops, thereby avoiding computation deviations introduced by delays and iterations. Finally, simulation calculations were conducted, and an experimental platform was designed and built for experimental verification which can validate the derived mathematical models. The simulation results, including the evaporator pressure, and chilled water outlet temperature with variation in chilled water mass flow rate, closely matched the experimental outcomes. The simulation model is concise and intuitive. Modifying parameters such as the thermal conductivity of the model material is straightforward, thereby alleviating the workload for researchers. It also facilitates an understanding of model principles for beginners. Moreover, the database generated from the model allows for fault analysis, diagnosis, and decision evaluation.