This paper presents a conduction based model for solving the phase change heat transfer problem around a vertical cylinder submersed in the phase change medium. The energy equation is coupled to the how problem by an energy balance. The system of equations is solved numerically by using the average control volume technique and the ADI approach. The results show the effects of the variation of the Blot number, Stefan number, the inlet fluid temperature and the ratio of the outer to the inner tube radius on the solidified mass fraction, NTU, effectiveness and the time for complete solidification. (C) 1997 by John Wiley & Sons, Ltd.211312231239