Mass transfer on and within a frost layer
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Na et al. [44] employed an exponential function of the dimensionless vapor pressure (pv/pv,sat) to estimate the ice-crystal growth rate, limiting the deviation in mass-transfer rate to within 25%.
“Na et al. [44] employed an exponential function of the dimensionless vapor pressure ( p v/ p v,sat) to estimate the ice-crystal growth rate, limiting the deviation in mass-transfer rate to within 25%.”
From A physics-informed quasi-steady frosting model with coupled heat–mass transfer for predicting frost layer growth (2026) · cites this paper as Na et al. [44]
The 0-D model by Na and Webb is used to model the frost formation process due to its adequate precision and simplicity for system modeling.
“Based on the suggestion of Brèque and Nemer [3], the 0-D model by Na and Webb [13] is used to model the frost formation process due to its adequate precision and simplicity for system modeling.”
From Model for cyclic frosting and defrosting of flat tube heat exchangers: Theoretical analysis and experimental validation (2023) · cites this paper as Na and Webb [13]
Previous published models describe the effects of frosting of a dry heat exchanger, neglecting the effects of water retained after defrosting.
“Previous published models describe the effects of frosting of a dry heat exchanger, neglecting the effects of water retained after defrosting.”
From Model for cyclic frosting and defrosting of flat tube heat exchangers: Theoretical analysis and experimental validation (2023) · cites this paper as [13]
Na and Webb provided a simple equation for the supersaturation degree at the frost surface that predicted their experimental data.
“Also, Na and Webb provide a simple equation for the supersaturation degree at the frost surface that was that predicted their experimental data.”
From New model for frost growth rate (2004) · cites this paper as [15]
Moderate uncertainty in the tortuosity factor has very small effect on the heat transfer rate through the frost layer and frost densification rate if rational correlations for mass diffusion prediction within the frost layer are used.
“Na and Webb [15] showed that moderate uncertainty in the tortuosity factor has very small effect on the heat transfer rate through the frost layer and frost densification rate if one uses rational correlations for the mass diffusion prediction within the frost layer.”
From New model for frost growth rate (2004) · cites this paper as [15]
Water vapor at the frost surface is supersaturated, not saturated.
“Na and Webb [13-15] have shown that the air is supersaturated at the frost surface, as opposed to the previous assumptions that the water vapor is saturated at the frost surface.”
From New model for frost growth rate (2004) · cites this paper as [15]
The densification rate is related to the water vapor diffusion rate within the frost layer, which is related to tortuosity.
“The densification rate is related to the water vapor diffusion rate within the frost layer, which is related to the tortuosity [15].”
From New model for frost growth rate (2004) · cites this paper as [15]
Na and Webb [15] showed that the assumption of saturation at the frost surface overpredicts the mass transfer rate by a factor of 4-30 in their test range.
“Na and Webb [15] showed that the assumption of the saturation at the frost surface overpredicts the mass transfer rate by the factor of 4-30 in their test range.”
From New model for frost growth rate (2004) · cites this paper as [15]
A tortuosity factor greater than 1.0 is physically impossible.
“which is physically impossible as discussed in [15].”
From New model for frost growth rate (2004) · cites this paper as [15]
The overprediction of the saturation model is because it overpredicts the mass transfer rate from the air stream to the frost surface.
“The over prediction of the saturation model is because it overpredicts the mass transfer rate from the air stream to the frost surface as discussed in [15].”
From New model for frost growth rate (2004) · cites this paper as [15]
The model of Lee et al. [11] assumed that the humid air was saturated at the frost surface, while Webb and coworker [7,12] assumed that the humid air was supersaturated at the frost surface.
“The model assumed that the humid air was saturated at the frost surface, while Webb and coworker [7,12] assumed that the humid air was supersaturated at the frost surface.”
From Numerical Simulation of Frosting on Fin-and-Tube Heat Exchanger Surfaces (2017) · cites this paper as [12]
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“More recent models for the prediction of the frost growth rate use supersaturated water vapor at the frost surface instead of saturated vapor such as Na and Webb [16,17].”
MethodA mathematical model for frost growth and densification on flat surfaces
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“In the moisture frost process, the density increases continuously with the total mass of the deposition (Na and Webb, 2004a).”
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“=3 ðD:1Þ with Lewis number Le evaluated as: Le ¼ aðjÞ sðjÞ cðjÞ DvðjÞ ðD:2Þ The air thermal diffusivity a(j) is evaluated in each row as the ratio between air conductivity ka(j) and air density and specific heat: aðjÞ ¼ kaðjÞ qaðjÞ cp;a ðD:3Þ The vapor diffusivity was evaluated according to Lee et al. [13]: DvðjÞ ¼ 0:…”
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Heat transfer—A review of 2004 literature
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“16,17 Especially, the boundary layer thickness is significantly enlarged in the random cross-linked pores owing to the strong viscous force induced by factors such as twisted channels and uneven pore size distributions (Figure 1A).”
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“Na and Webb [ 5 ] investigated fundamental phenomena related to frost deposition and growth.”
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Ma, C., Ge, X., Zheng, H., Song, M., Sheng, W., Chen, X.-Z., Fu, D.-Y., & Dang, C.-B. (2025) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2025.127205 · Cited by 5 · see citing works
Frost Formation: Optimizing solutions under a finite volume approach
Bartrons, E., Segarra, C. D. P., & Oliet, C. (2016) · Journal of Physics Conference Series · doi:10.1088/1742-6596/745/3/032062 · Cited by 5 · see citing works
Matsumoto, K., Ito, Y., Hayashi, K., Murahashi, K., Shirai, D., & Honda, M. (2012) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2012.10.003 · Cited by 5 · see citing works
Feasibility Study on Practical Application of AAV with a Defrosting Method
Kim, H.-Y., Kim, C.-H., & Han, D.-G. (2014) · Journal of Industrial and Intelligent Information · doi:10.12720/jiii.3.2.163-167 · Cited by 5 · see citing works
“Saturation and supersaturation models of frost growth [1] are compared with boundary layer analysis under Korean climate.”
MethodFrost Formation on Fan-Supplied Tube-Fin Evaporators: A Visual and Numerical Analysis
Silva, D. L. D. (2012) · Purdue e-Pubs (Purdue University System) · Cited by 5 · see citing works
Benchmarking MELCOR 1.8.2 for ITER Against Recent EVITA Results
Merrill, B. J. (2007) · doi:10.2172/924495 · Cited by 5 · see citing works
A non-iterative solution for frost growth on flat surfaces
Hollon, D., Truster, N., Byrd, L., Roman, A. J., & Wolff, M. (2023) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2023.124578 · Cited by 5 · see citing works
Bezovsky, M., Stričík, M., & Praščáková, M. (2010) · Applied Energy · doi:10.1016/j.apenergy.2010.02.031 · Cited by 4 · see citing works
“Thermo-physical properties of materials describing the defrosting speed during the defrosting processes are; specific heat capacity cp (J/kg K), which expresses the ability of materials various types to bind heat, and thermal conductivity k (W/m K), which reflects the coal ability to heat [3,4,2].”
BackgroundMethodJedlikowski, A., Skrzycki, M., Kanaś, P., & Anisimov, S. (2022) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2022.122860 · Cited by 3 · see citing works
The effect of surface wettability on frost growth and densification on flat plates
ElCheikh, A. (2013) · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign) · Cited by 3 · see citing works
Frost microstructure during the frost layer growth
MATSUMOTO, R., Oda, Y., Uesugi, K., & Hoshino, M. (2025) · Journal of Thermal Science and Technology · doi:10.1299/jtst.25-00074 · Cited by 2 · see citing works
“In the theoretical model for frost formation (Na and Webb, 2004b; Hermes et al., 2009), the mass flux of water vapor supplied from the air is divided into two components: one contributing to densification within the frost layer and the other contributing to the growth of the frost layer.”
Hao, Y., Zheng, H., Ma, C., Fu, D.-Y., Sheng, W., Chen, X.-Z., Song, M., & Dang, C.-B. (2026) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2025.128091 · Cited by 2 · see citing works
Modeling of frost accretion on microchannel evaporators for household refrigerators
Boeng, J., de Araujo, T. E. H. R. P., Machado, M. W., & Stahelin, R. (2026) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2026.131390 · Cited by 3 · see citing works
Prediction and Evaluation of Frosting Surface on Cylindrical Structure Using Growth Rate Model
Park, S., Kihara, H., & Abe, K. (2023) · International Journal of Aeronautical and Space Sciences · doi:10.1007/s42405-023-00568-6 · Cited by 2 · see citing works
Unsteady heat and mass transfer during frost formation in a fin-and-tube heat exchanger.
Lenić, K., Trp, A., & Franković, B. (2006) · Cited by 2 · see citing works
Study of frost growth on heat exchangers used as outdoor coils in air source heat pump systems
Sankaranarayanan, K. (2011) · Cited by 2 · see citing works
Safikhani, H., & Shabani, H. (2020) · International Journal of Engineering · doi:10.5829/ije.2020.33.12c.17 · Cited by 2 · see citing works
“Na and Webb [8- 10] suggested a model based on density of supersaturated water vapor in the frost layer.”
MethodInfluentialDimensionless Model of Frost Roughness on Cold Flat Plate Under Forced Convection
Zhang, T., O’Neal, D. L., McClain, S. T., & Riley, J. T. (2021) · Journal of Aircraft · doi:10.2514/1.c036066 · Cited by 2 · see citing works
Experimental Study of Natural Frost Formation on a Horizontal Cylinder
Yaghoubi, M. A., & Khoshnazar, H. (2010) · AIAA/ASME Joint Thermophysics and Heat Transfer Conference · doi:10.2514/6.2010-4659 · Cited by 2 · see citing works
A real-time frost thickness prediction model via evaporator resistance identification
Liu, S., Li, P., Pu, J., Zhang, H., Jiang, Y. Q., Wang, Y., Wan, Z., Wang, Z., You, S., & Wu, Z. (2026) · Energy and Buildings · doi:10.1016/j.enbuild.2026.116964 · Cited by 1 · see citing works
- Authors
- Na, B., & Webb, R. L.
- Affiliations
- Pennsylvania State University (US)
- Corresponding author
- Webb, Ralph L.
- Venue
- International Journal of Heat and Mass Transfer
- Publisher
- Elsevier BV
- Published
- 2004-02
- Volume
- 47
- Issue
- 5
- Pages
- 899-911
- ISSN
- 0017-9310 (ISSN-L)
- OpenAlex
- W2082230330
- Cited by
- 129
- References
- 15
- Citations by year
- 2026: 12 · 2025: 5 · 2024: 3 · 2023: 6 · 2022: 8 · 2021: 11 · 2020: 2 · 2019: 2 · 2018: 7 · 2017: 9 · 2016: 8 · 2015: 4 · 2014: 11 · 2013: 4 · 2012: 8
- FWCI
- 5.27
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- International Journal of Heat and Mass Transfer (publishedVersion)
- Topics
- Physical Sciences › Engineering › Aerospace Engineering › Icing and De-icing Technologies
- Physical Sciences › Engineering › Mechanical Engineering › Refrigeration and Air Conditioning Technologies
- Physical Sciences › Engineering › Mechanical Engineering › Heat Transfer and Optimization
- Keywords
- frost layer, frost formation, frost growth, surface supersaturation, concentration boundary layer, tortuosity factor, mass diffusion
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