General correlation for frost thermal conductivity on parallel surface channels

Growth of frost layer on cold fins of tube-fin heat exchangers leads to an increase in the pressure drop and a decrease in the frost thermal conductivity and thereby the heat transfer rate. There is a lack of a general model in the literature for estimating the frost thermal conductivity on parallel plate channels, including almost all parameters affecting this factor. In this study, for the first time, the general explicit semi-empirical correlations consist of dimensionless parameters are developed, which apply to parallel surface channels. The dimensionless input parameters include the wall temperature, air temperature, air velocity, frost porosity, relative humidity, specific heat of moist air, latent heat of sublimation, and operating time. The comparative results indicate that the best correlation predicts data points with an coefficient of determination, average absolute relative error, and relative root mean square error equal 0.9921, 2.755%, and 3.713%, respectively. Other available published correlations present higher deviations using the same dataset. Furthermore, to provide a good insight into this study, a sensitivity analysis is carried out employing the validated model. It is shown that the effective thermal conductivity of the frost layer is not only a function of frost density but also depends on a group of dimensionless parameters. It is observed that the thermal conductivity of the frost layer increases with the increase in the Reynolds number, Fourier number, air humidity, and it decreases with the increase in the dimensionless temperature, modified Jakob number, and porosity.