Abstract
Thermal conductivity of frost is not only related to density, but also affected by its microstructure and environmental conditions, and it will continuously change with the formation and growth of frost. Images of frost formation and growth on the cryogenic surface in various shapes at different stages were obtained by experimental measurements, and a numerical simulation of frost formation and growth was carried out based on Diffusion Limited Aggregation (DLA) model of fractal theory in this paper. Based on the frost structure obtained by experiment, the fractal dimension of pore area distribution and porosity of frost layer on the cryogenic finned-tube vaporizer were calculated by using fractal method, and combined with heat conduction model of frost layer obtained by thermal resistance method, the thermal conductivity of frost on the cryogenic surface was calculated. The result shows that the thermal conductivity calculated by the fractal model coincides with the range of the experimental data. Additionally, comparison with other heat conduction models indicated that it is feasible to introduce the fractal dimension of pore area distribution into heat conduction model to deduce the thermal conductivity of frost.
Highlights
Finned-tube vaporizer will be frosted once its surface temperature is below the dew point of surrounding humid air, and lower than 0°C
Based on the frost structure obtained by experiment, the fractal dimension of pore area distribution and porosity of frost layer on the cryogenic finned-tube vaporizer were calculated by using fractal method, and combined with heat conduction model of frost layer obtained by thermal resistance method, the thermal conductivity of frost on the cryogenic surface was calculated
The consistent of the fractal dimension of the simulation image d1 with that of the experimental image d2 shows the rationality of the numerical simulation and provides a powerful evidence for further deriving the fractal model of heat conduction in frost layer
Summary
Finned-tube vaporizer will be frosted once its surface temperature is below the dew point of surrounding humid air, and lower than 0°C. Le Call R [11] modified the boundary conditions and the permeability coefficient of water vapor in Tao Y X model, and focused on the effective diffusion coefficient of water vapor, he got the distribution of density, temperature, thermal conductivity in frost. The formation and growth of frost is a complicated process, it is very difficult to obtain an equation of thermal conductivity based on a theory. Based on simulating the frost crystal structure which has fractal growth characteristics, Cai L [13] set up an equilibrium equation at each node and predicted the thermal conductivity of frost by using the DLA model. The detailed algorithm of simulating frosting and simulation results have been reported previously [16]
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