Effective Thermal Conductivity of Frost Consideringmass Diffusion and Eddy Convection

Abstract

A physical model for the effective thermal conductivity of water frost is proposed for application to the full range of frost density. The proposed model builds on the ZehnerSchlunder one-dimensional formulation for porous media appropriate for solid-to-fluid thermal conductivity ratios less than about 1000. By superposing the effects of mass diffusion and eddy convection on stagnant conduction in the fluid, the total effective thermal conductivity of frost is shown to be satisfactorily described. It is shown that the effects of vapor diffusion and eddy convection on the frost conductivity are ofthe same order. The results also point out that idealization ofthe frost structure by cylindrical inclusions offers a better representation of the effective conductivity of frost as compared to spherical inclusions. Satisfactory agreement between the theory and the measurements for the effective thermal conductivity of frost is demonstrated for a wide range of frost density and frost temperature.

Frost growth and densification on a flat surface in laminar flow with variable humidity

“…It incorporates the water frost density correlation presented in [9]. The frost thermal conductivity model is taken from [11], which is based on the point contact model of Zehner and Schlunder [12,13], and regards the frost as made up of cylindrical particles. The ZehnerSchlunder model is known to be appropriate for the frost circumstances which involve ice to air conductivity ratio (of about 100) is less than 1000 [13,14].…”

Correlation of Water Frost Porosity in Laminar Flow Over Flat Surfaces

“…Generally, the frost thermal conductivity is correlated with frost density (Ostin and Anderson, 1991), with additional dependence on the frost surface temperature and atmospheric variables including air velocity, air humidity, and air temperature. Whereas several theoretical models have been proposed for the prediction of frost thermal conductivity as a function of frost density (or frost porosity) and frost surface temperature (Kandula 2010), published work on the frost density dependence is relatively small. Inaccuracies in the frost porosity could lead to significant errors and uncertainties in the predicted frost thickness and frost surface temperature.…”

Frost growth and densification in laminar flow over flat surfaces

“…The effective thermal conductivity of frost k f is obtained from the work of the author [25] on the basis of a porous packed bed model of Zehner-Schlunder [26] considering a unit cell approach and one-dimensional heat flow (see Hsu et al [27], Cheng and Hsu [28]):…”

“…The constant C is taken as 2.5 for cylindrical particles (Zehner-Schlunder [26]), which were found to represent frost structure and resulting frost them1al conductivity satisfactorily [25). A detailed comparison of Zehner-Schlunder model with data (for spherical particles) for ice to air thermal conductivity ratio ranging from 8 to 1200 and for various values of solids fraction was recently presented by the author [29).…”

“…In the presence of mass diffusion and eddy convection, the effective thermal conductivity of air k w'c is expressed as (Kandula [25])…”