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The three-fluid heat exchanger is a multi-stream heat exchanger that provides three streams at different temperatures for certain usage objectives. Recently, optimizing heat exchangers generally and three-fluid heat exchangers especially have received great attention in the energy field. The current study objective is to get the optimal mass flow rate of the three streams to minimize the entropy generation number and maximize effectiveness. Optimization is performed on the inserted coiled tube type for 24 cases with different usage objectives and different mass flow rate constraints. The optimization is done using an analytical approach for the temperature profiles and a regressed model for the overall heat transfer coefficients. Single-objective and multi-objective genetic algorithms are the optimization algorithms. The result shows that cooling the hot fluid is the most efficient usage objective; however, heating the intermediate-temperature fluid is the less efficient usage objective. Also, the study shows that the entropy generation number is dependent on the mass flow rate constraint. The maximum effectiveness of 0.693 occurs when the usage objective is cooling the hot fluid. In this case, the mass flow rate of the cold and the intermediate-temperature fluids are maxima while the mass flow rate of the hot fluid is minimum. The minimum entropy generation number 0.0486 occurs when the mass flow rate of the cold fluid is maximum while the mass flow rate of the hot fluid and intermediate-temperature fluid are minimal. [Display omitted] • Heat transfer of a three-fluid heat exchanger is investigated. • A model for optimizing the inserted coiled tube three-fluid heat exchanger is developed. • The maximum errors for the regression models of heat transfer coefficients are 1.72% and 2.81%. • The maximum effectiveness reached about 0.69323. [ABSTRACT FROM AUTHOR]