The analysis of the process of frost formation on a cold surface exposed to humid air yields a system of differential equations. In this study, the orthogonal collocation method is used to help solve the system of equations resulting from the flow of humid air over heat exchanger fins maintained at a temperature below both the dew-point temperature of water vapor in air and the freezing point. The temporal dependence of the frost growth creates a moving boundary that is addressed using a front-fixing method. This proposed method allows solving for important variables such as frost thickness, temperature distribution, and heat flux through the frost layer. Model results were found to agree closely with available experimental data. In all data sets modeled, it was found that super saturation at the frost-air interface must be included in the model to accurately predict frost growth. (C) 2019 Elsevier Ltd. All rights reserved.