In this work, the multiphase mathematical simulation (steel-slag-air) is performed in order to optimize the fluid dynamics and the homogenization temperature in an asymmetric delta-type billet caster tundish. The performance of the tundish emulates, when a change of ladle occurs, for which are considered the losses of heat through its frontiers as well as the temperature drop of the steel at the input by means of a user defined function (UDF). Also, a comparison is made for the removal of non-metallic inclusions using standard entrapment conditions at the steel-slag interface, as well as a user-defined function (UDF). This UDF takes into account the multiphase interaction with the critical velocity of the particles that approach this interface. For this analysis, it is necessary to determine the opening area of the slag layer. The results of the model for the temperature drop are validated by means of experimental measurements in plant, which show a good correspondence in the obtained data. Finally, the proposed design of flow modifiers favorably influences the fluid dynamics pattern, allowing a better thermal homogenization, and a substantial cleaning of the steel at its output from the tundish.