An analytical model of freezing a liquid inside a vertical pipe is described. Natural convection in the liquid is included by incorporating an integral solution for the heat transfer coefficient for convection driven by a heated vertical plate. The resulting model can be applied to different pipe sizes, temperatures and liquids and was used to predict the formation of an ice plug under varying freezing conditions. A method of scaling the effect of pipe diameter and initial water temperature on natural convection during freezing is proposed. The factors which limit the situations in which the model can be applied are discussed.