Frost is a material composed of ice and air. Frosting is the vapor-to-solid phase change process in which airborne water vapor becomes frost on a cooled surface. Frost forms on cold surfaces when the surface temperature is below 0°C and below the dew point of the water vapor contained in a surrounding body of air. Supercooled water droplets first form on the cold surface. These droplets subsequently freeze to form a thin ice layer and frost begins to grow on this ice layer. Hayashi et al. (1977) defined three chronological periods of frost formation.
In this period, ice crystals grow in a direction perpendicular to the cold surface to form frost with widely-spaced distinct ice needles.
Branches grow on the above ice needles until the upper frost layer becomes almost flat. During this period, part of the water vapor flux from the environment causes increased frost depth and part enters the frost layer by vapor diffusion, causing densification to occur.
The outer frost surface reaches a temperature of 0°C and fluctuates close to this temperature. In this period, heat transfer rates remain almost constant as the frost layer thickens because increased thermal resistance due to increased frost depth is offset by resistance reductions due to frost density increases. In this period, density is believed to increase due to soakage and subsequent freezing of liquid water from the surface entering the frost layer.
Frost depth increases approximately in proportion to the square root of time prior to the quasi-steady growth period. [Schneider (1978)]. Hayashi et al. (1977) classified frost into types A, B, C and D, with type A frost being more needle-like and less dense at all stages of chronological development and Type D being most dense. Type A frost generally forms with high vapor concentration differences between the air and the cold surface and at low surface temperatures.
Sensible heat transfer through a growing frost layer is supplemented by the release of latent heat of evaporation as water vapor becomes ice within and at the surface of the frost layer. The thermal resistance of the frost layer formed on heat exchange equipment may be calculated by knowing frost depth and the frost effective conductivity. At a particular depth position in the layer, the local frost effective thermal conductivity is defined as
where includes sensible and latent heat transfer.
Frost effective conductivity may take values between that of air, 0.024 W/m K and that of ice, 2.3 W/m K. A generalized correlation of frost thermal conductivity has been presented by Dietenberger (1983) who considers frost conductivity to depend on: frost density; local frost temperature; cold wall temperature; air temperature; air relative or specific humidity and ambient total air pressure. Conductivity is particularly sensitive to frost density.
Frost density is not uniform through the frost layer thickness. Density is influenced by the conditions under which the frost forms and may have values from 50 kg/m3 for Type A frost at the earliest stages of development up to the value for ice, 917 kg/m3, for very mature frost.
Calculation of frost layer thermal resistance requires mathematical modelling using numerical techniques. A finite-difference transient 1-dimensional model for heat transfer and frost growth has been developed by Monaghan and Oosthuizen (1990) which is capable of calculating heat transfer, frost depth and frost mass or density over time when the environmental conditions and wall temperature are given but varying. For single tubes in a steady environment and for rows of tubes in an unsteady outdoor environment, Monaghan and Oosthuizen's model was found to be within +/– 25% in prediction of overall thermal conductance in a wide range of conditions.
Tests of typical refrigeration heat exchangers under frosting conditions have been carried out by Kondepudi and O'Neal (1989). In these tests, Kondepudi and O'Neal found that: rate of frost mass accumulation and pressure drop increased with air humidity, cold refrigerant temperatures and higher fin densities; and latent energy contributed about 30%-40% of total heat transfer.
Dietenberger, M. A. (1983) Generalised Correlation of the Water Frost Thermal Conductivity, Int. J. of Heat Mass Transfer, 26, 607.
Hayashi, Y., Aoki, A., Adachi, S. and Hori, K. (1977) Study of Frost Properties Correlating with Frost Formation Types, J. Heat Transfer, 99, 239.
Kondepudi, S. N. and O'Neal, D. L. (1989) The Performance of Finned Tube Heat Exchangers under Frosting Conditions, ASME Winter Annual Meeting, San Francisco.
Monaghan, P. F. and Oosthuizen, P. H. (1990) Mathematical model of frost growth on a single cylinder in steady crossflow. In Heat Transfer 1990, Proc. of 9th Int. Heat Transfer Conference, IHTC9, Jerusalem, ISRAEL, 3, 115-120, Hemisphere Publishing Corp., Washington, USA.
Schneider, H. W, (1978) Equation of the Growth Rate of Frost Forming on Cooled Surfaces, Int. J. Heat Mass Transfer, 21, 1019. DOI: 10.1016/0017-9310(78)90098-4