A semi-empirical model of frost formation on a cryogenic surface cooled from ambient temperature under forced convection condition

In most practical occasion, frost is formed on cold surface which is cooled from the ambient temperature. Although the initial cooling stage may account for a small proportion in the whole frosting process, the effects of the initial cooling on frosting characteristics could not be overlooked. In this paper, a semi-empirical model of cryogenic frosting involving the initial cooling process under forced convection is established by employing frost properties correlations and heat and mass balance analysis. The frost thickness calculated by the proposed semi-empirical model showed good agreement with experimental data within a maximum error of 15 %. Within the constraints of correlation validity, this model is applicable to conditions where ambient temperatures range from 10 °C to 30 °C, air flow Reynolds numbers span from 7 × 10⁴ to 1.5 × 10⁵, air humidity varies between 3.5 g/kg and 18 g/kg, and initial cooling durations extend from 15 min to 40 min, and the final wall temperature is decreased to about 80K. The results indicate that frost thickness increases with rising ambient temperature, air humidity, and airflow velocity. Notably, higher rates of frost growth are observed during the initial cooling under conditions of elevated air humidity or increased airflow velocity. The trend in frost mass closely mirrors that of frost thickness, however, a more pronounced increase in frost mass occurs with increasing ambient temperature. Furthermore, extending the duration of initial cooling could accelerate the frost growth rate and cause a higher frost surface temperature.