A mathematical model for frost growth and densification on flat surfaces

Cheikh, Amne El; Jacobi, Anthony M.

doi:10.1016/j.ijheatmasstransfer.2014.05.054

Cited by 61 publications

(10 citation statements)

References 15 publications

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“…In fact, results for horizontal plate did not allow the authors of the present study to conclude for the impact of relative humidity on frost density. For vertical plate, results obtained for the two authors Ro, 2002 andEl Cheikh andJacobi, 2014) are in agreement. In fact, frost density is found to increase with lower relative humidity.…”

Section: Impact Of Environmental Parameterssupporting

confidence: 67%

State-of-the-art review of frost deposition on flat surfaces

Léoni

Mondot

Durier

et al. 2016

International Journal of Refrigeration

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A B S T R A C TThis paper presents a comparative study of predictive methods of frost growth and densification on horizontal, vertical and parallel flat surfaces. The study treats two aspects of frost formation: thickness and density. It focuses on the comparison between four different existing theoretical models or empirical correlations and a database gathering almost 382 test points available in the literature for average frost thickness. Furthermore, five correlations are compared to 149 data points for average frost density. Impacts of air velocity, relative humidity and wall temperature are studied. The latter is found to have a significant impact on frost development. Quantitative and qualitative analyses of the predictive methods are proposed. This study leads to the identification of the main issues in the field of modelling of frost deposition on horizontal, vertical and parallel flat plates. DensityThickness Correlation Model Synthèse de l'état de l'art du dépôt de givre sur des surfaces planes

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Section: Impact Of Environmental Parameterssupporting

confidence: 67%

State-of-the-art review of frost deposition on flat surfaces

Léoni

Mondot

Durier

et al. 2016

International Journal of Refrigeration

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“…where D f = Dε/δ is the effective diffusivity of the water vapor in air, δ is the tortuosity of the frosted medium, and λ is the desublimation coefficient obtained from the solution of Equation ( 4) subjected the following boundary conditions: ω(x = 0) = ω w , (dω⁄dx) x = 0 = 0 and ω(x = x f ) = ω s , yielding Ha = x f (λD f ) 1/2 = cosh −1 (ω s ⁄ω w ), where Ha is the Hatta number, representing the ratio between the time scale of diffusion and desublimation. Albeit a saturation boundary condition was used in this approach, more sophisticated models rely on supersaturated boundary conditions at the air-frost interface [49,51,56].…”

Section: Frost Build-upmentioning

confidence: 99%

Evaporator Frosting in Refrigerating Appliances: Fundamentals and Applications

et al. 2021

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Modern refrigerators are equipped with fan-supplied evaporators often tailor-made to mitigate the impacts of frost accretion, not only in terms of frost blocking, which depletes the cooling capacity and therefore the refrigerator coefficient of performance (COP), but also to allow optimal defrosting, thereby avoiding the undesired consequences of condensate retention and additional thermal loads. Evaporator design for frosting conditions can be done either empirically through trial-and-error approaches or using simulation models suitable to predict the distribution of the frost mass along the finned coil. Albeit the former is mandatory for robustness verification prior to product approval, it has been advocated that the latter speeds up the design process and reduces the costs of the engineering undertaking. Therefore, this article is aimed at summarizing the required foundations for the design of efficient evaporators and defrosting systems with minimized performance impacts due to frosting. The thermodynamics, and the heat and mass transfer principles involved in the frost nucleation, growth, and densification phenomena are presented. The thermophysical properties of frost, such as density and thermal conductivity, are discussed, and their relationship with refrigeration operating conditions are established. A first-principles model is presented to predict the growth of the frost layer on the evaporator surface as a function of geometric and operating conditions. The relation between the microscopic properties of frost and their macroscopic effects on the evaporator thermo-hydraulic performance is established and confirmed with experimental evidence. Furthermore, different defrost strategies are compared, and the concept of optimal defrost is formulated. Finally, the results are used to analyze the efficiency of the defrost operation based on the net cooling capacity of the refrigeration system for different duty cycles and evaporator geometries.

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“…As the frost crystals continue to expand and interact with each other, a porous frost layer with a rough surface eventually forms. During the process of frost growth, moist air either deposits on the frost surface to increase the frost thickness or diffuses into the frost layer to increase the frost density [16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Variation of Frost Roughness on a Flat Plate Under Forced Convection

Tongxin

O’Neal

McClain

2020

Journal of Thermal Science and Engineering Applications

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Experiments were conducted on a cold flat plate to characterize the variation of frost roughness over both time and location on the surfaces. The testing conditions included air temperatures from 8 to 16°C, wall temperatures from −20 to −10°C, relative humidities from 60 to 80%, and air velocities from 0.5 to 2.5 m s−1. A 3-D photogrammetric method was employed to measure the variation in frost root-mean-square height and skewness by location and time. These data were used to develop the equivalent sand-grain roughness for the frost at different locations and time. The experimental results showed that frost roughness varied by location and changed with time. For the environmental conditions in this study, relative humidity and air temperature were the most important factors determining changes in the peak frost roughness. For example, at an air temperature of 12ºC and surface temperature of −15ºC, the frost roughness peaked at about 40 minutes for a relative humidity of 80% and 90 minutes for a relative humidity of 60%. Empirical correlations were provided to describe the relationships between the environmental conditions and the appearance of the peak frost roughness.

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A mathematical model for frost growth and densification on flat surfaces

Cited by 61 publications

References 15 publications

State-of-the-art review of frost deposition on flat surfaces

State-of-the-art review of frost deposition on flat surfaces

Evaporator Frosting in Refrigerating Appliances: Fundamentals and Applications

Variation of Frost Roughness on a Flat Plate Under Forced Convection

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