In addition to variable properties of fluids, heat interaction with ambient, and axial wall conduction, the temperature distribution of a three-fluid heat exchanger, is strongly affected by Geometric and design parameters. Geometric parameters such as exchanger length and tube diameter and design parameters are fluid flow rate and ambient temperature. In this study, the effect of geometric and design parameters on the temperature distribution and effectiveness of a three-fluid heat exchanger with three thermal communication have been investigated. The governing equations on the flow, are simulated considering heat-in-leak to the cold fluid and variable properties of the fluids, and are solved based on the first law of thermodynamics and analytical methods. Cooling the hot fluid and heating the cold fluid, have been considered as the objective of the three-flow heat exchanger, in order to effectiveness investigation. The effect of ambient heat in leak is to increase the cold fluid temperature, leading to a little lift on hot fluid temperature profile, will result in an enhancement in the cold effectiveness and a reduction on hot effectiveness. Increasing ambient temperature, enhances the effects of heat in leak from ambient. An increase in the diameter of outer tube, Where the cold fluid is flowing and is in contact with the ambient, makes the hot and cold temperatures become farther apart in each cross-section, and decreases the hot and cold effectiveness. An increase in the flow rate of the cold fluid, results in a higher hot effectiveness and reduces the cold effectiveness. Due to An increase in the hot flow rate, both the hot and cold effectiveness are enhanced.