Abstract: Analytical solutions of the freezing of phase change material (PCM) in annular space are presented. Firstly, approximate integral method and numerical simulation are used to analyze the heat transfer process during the freezing of the PCM in annular space with internal boundary cooled and external boundary insulated.Secondly, a comparison is made between the results obtained by approximate integaral method and the numerical solution. Then, the effects of all kinds of parameters on the freezing process are discussed. Finally, two important conclusions are summarized:1.when the ratio of the inside diameter to the outside one of the PCM is not less than 0.6, we can assume a quadratic temperature distribution in PCM instead of a log arithmic one so as to cut down the efforts used in solving process, and the error will not exceed 1.5%;2. approximate integral method is not apropriate for solving those solid-liquid phase change problems which possess a low Stefan number.

Key words: Solid-liquid phase change, Annular space, Freezing process, Approximate integral method, Enthalpy formulation