An approximate solution is proposed for the heat transfer problems of a latent heat thermal energy storage unit with a finned tube through which a coolant flows. In the actual storage unit, the temperature of the coolant changes along the axis of the tube so that the problems have been very difficult to solve. This analysis uses a dimensionless heat extraction rate or an apparent Biot number as a function of a dimensionless time, which has been obtained by analysis or experiment for the finned tube at a constant wall temperature. For this purpose, and analysis was made on the apparent the performance of a thermal energy storage unit with the finned tube and n-Octadecane as the phase change material agreed well with the experimental results.