A theoretical model is developed to analyze the thermal storage and heat transfer characteristics in a phase change material outside a circular tube with heat transfer fluid inside the tube. A new method, the alternative iteration between temperature and thermal resistance method, is presented to analyze the variation of the phase change radius, the axial temperature variation in the heat transfer fluid and the thermal storage in the circular tube. Dimensionless formulae are developed using theoretical and numerical analysis. The present solutions agree well with those in the literature. The dimensionless correlations are not limited to one condition, so they provide a basis for tube heat transfer design and optimization over a wide range of conditions.