•A frost model that considered the crystal growth period was constructed.•The approach was verified by comparison with five experimental results.•The model can reduce the maximum thickness and density errors by 17.4 % and 10.2 %.•The factors affecting the period of nucleation were analyzed. In engineering applications, the formation and growth of frost layers can significantly affect the normal operation of equipment, leading to undesirable influences. Therefore, it is imperative to understand the frost formation mechanisms as a basis for developing effective anti-frosting and defrosting methodologies. This study proposes a model for the growth of horizontal cold surface frost layers using the classical nucleation theory and the Eulerian multiphase flow model. Compared to numerous models that investigate the frost formation issues using the computational fluid dynamics (CFD) method, our proposed model takes into account the crystal growth period (the heterogeneous nucleation process of ice). The predicted results of the proposed model were found to be in good agreement with the data collected from five related experimental studies. In this regard, the maximum frost layer thickness error was 23.9 % with a mean error of 5.1 %, and the maximum density error was 22.8 % with a mean error of 8.1 %. Compared to existing models in the literature, the proposed model can reduce the maximum thickness and density uncertainties by 17.4 % and 10.2 %, respectively. Additionally, the effects of the surface contact angle and environmental parameters on the nucleation process were analyzed using the established model. It was found that a larger contact angle, higher cold surface temperature, and lower air temperature, humidity, and velocity were unfavorable conditions for supporting the formation and growth of ice crystals. Moreover, the nucleation completion time was shortened with the increase in the moist air supersaturation degree, varying as an exponential function. The findings of this study provide an important theoretical basis for the development of optimizing strategies for anti-frosting and defrosting.