A simple mathematical model for rime and glaze-ice accretion due to freezing rain on a horizontal plane surface

A mathematical model, which simualates rime and glaze-ice accretion due to freezing rain on a horizontal plane surface, is described. The thermal transients within the accreted ice are governed by local surface heat and mass transfer balances for the impacting supercooled droplets. The evolution of the rime and glaze-ice surfaces are formulated in terms of moving boundary and Stefan-type problems, respectively. During glaze accretion, the flow of unfrozen water (run-back water) is modelled in the context of the thin liquid film approximation.Analytical solutions are obtained and, in particular, the mathematical structure of the transition from rime to glaze accretion is examined, using the method of matched asymptotic expansions. Illustrative results are given for horizontal plane surfaces having circular and square cross-section.