run-out-table (rot) is located between last finishing stand and down coiler in a hot strip mill. as the hot steel strip passes from rot, water jets impact on it from top and bottom and strip temperature decreases approximately from 800-950 °c to 500-750°c. the temperature history that strip experience while passing through rot affects significantly the metallurgical and mechanical properties, such as strength, stiffness, weldability, fatigue resistance, flexibility and the flatness of the final product. consequently, the mill engineers and researchers are much interested in attaining desired mechanical and metallurgical properties of the product through controlling the cooling rate and temperature history and even with reducing amount of carbon contents. reducing carbon content, considerably improves the weldability due to reducing hardenability of the steel. in achieving this aim it is vital to develop physical models which are capable of precisely predicting the temperature history and phase transformation kinetic through rot. the heat transfer mechanisms in rot are heat conduction in steel strip, natural and force convection with air, radiation and forced convection boiling heat transfer due to impacting subcooled water jets. it is also coupled with phase transformation phenomenon, because of the heat released during decomposition of austenite into ferrite, pearlite and bainite during strip cooling. in addition to these complexities, other effects such as strip movement, changing of thermo-physical properties with steel phase mixture and temperature, the water stream on the plate and its temperature increment, have been redoubled the difficulties of developing a precise model for prediction of such behaviors. as a result, most of the developed models consider either heat transfer characteristics of impacting water jets and local heat transfer phenomenon or predicting phase transformation kinetics during strip cooling. recently, researchers began to consider the strong interaction between the heat transfer and phase evolution. in this thesis, a numerical model was developed to predict the temperature and phase transformation of strip on a run-out table (rot) in hot strip mill. furthermore this model could predict final phases produced during cooling in the term of nozzles arrangement in rot. with this feature, the mill engineers would be able to arrange nozzle configuration in order to obtain desired steel final phases. alternating direction implicit (adi) method was used to solve the heat conduction equation in both thickness and width direction in the strip. the kinetics of the diffusional transformation of austenite to ferrite had been calculated for the isothermal condition by avrami equation and additivity rule. the specific heat, thermal conductivity and density of steel had been determined in the term of phase fraction and temperature. accuracy of the phase transformation model was examined through comparing the results with the results presented in the literature and the accuracy of the proposed coupled complete model was examined through comparison of coiling temperatures obtained from the model with the actual data ones from hot strip mill in mobarake steel complex. the error of the model for predicting coiling temperature is less than 3% that indicates the capability of the model in predicting temperature and phase transformation in rot.