We seek to quantitatively understand heat transfer, fluid flow and mass transfer during materials processing, particularly welding, chemical vapor deposition and metals processing. Much of our work involves numerical calculations of temperatures, velocities and concentrations using computers. The computed results provide detailed insight about the process and reveal how the composition and structure of the processed materials evolve. Our work focuses on overcoming two major problems of the current generation of models. First, the model predictions do not always agree with the experimental results because some process parameters or materials properties cannot be accurately prescribed. Second, and more important, these unidirectional models cannot determine multiple sets of process variables that can lead to a particular materials or process attribute. Our work shows that the computational convective heat and mass transfer models when combined with a genetic algorithm can overcome the aforementioned difficulties. The reliability of the models can be significantly improved by optimizing the values of the uncertain input parameters from a limited volume of experimental data. Furthermore, the procedure can calculate multiple sets of process variables, each leading to the same target materials or process attributes by conducting a global search within a phenomenological framework of the equations of conservation of mass, momentum and energy. This computational procedure was applied to gas tungsten arc welding of several alloys to calculate various sets of welding variables to achieve a specified weld geometry. Each set of welding parameters resulted in a specified geometry showing the effectiveness of the computational procedure.