This work is devoted to the development of a zero-dimensional semi-empirical sub-grid model (or sub-model) which predicts the size and temperature of a solid particle undergoing a phase change inside a gaseous phase. Specifically, two sub-grid models are developed, one for a solid spherical particle and another for a solid cylindrical particle. The models can be implemented as a sub-grid model in Euler-Lagrange numerical models for particulate flows with solid particles undergoing phase changes. They can be used as scale-bridge relations to create a bridge between the scales in Euler-Lagrange models, to relate the heat transfer occurring at the interfacial scale to the macro heat transfer conservation equation written for the gaseous phase. The input parameters in our model are the particulate Reynolds number (Re), the Grashof number (Gr), the Stefan number (Ste) and the Prandtl number (Pr). The model has been validated against experimental results obtained by authors and existing experimental results produced by Janna and Jakubowski (1990). Good agreement is observed between our model predictions and both experimental results. The importance of a thin water film around the melting ice particle is discussed. The emissivity of the water film has been found to be influential in determining the melting rate of the ice particle. (C) 2017 Elsevier Ltd. All rights reserved.