This paper reports on a mathematical model which is developed for understanding the effect of combined radiation and convection in forming a stable solidified layer inside a nozzle necessary for clean melt processing. An integral method is employed to reduce the complicated boundary value problem to a nonlinear ordinary differential equation which is then solved using the standard Runge-Kutta method. The obtained results are found to agree well with a limiting case where the emissivity approaches zero. Radiation is found to play an important role in maintaining a stable solidified layer.