The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Mass transfer on and within a frost layer
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Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“which is physically impossible as discussed in [15].”
From New model for frost growth rate (2004) · cites this paper as [15]
In the citing paper
“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]
In the citing paper
“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]
Citations
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Self-citationNew model for frost growth rate
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Self-citationA mathematical model for predicting the densification and growth of frost on a flat plate
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New model for frost growth rate
Na, B., & Webb, R. L. (2004) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2003.09.001 · Cited by 212
Self-citationFrosting model for predicting macroscopic and local frost behaviors on a cold plate
Kim, D., Kim, C., & Lee, K.-S. (2015) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2014.11.048 · Cited by 103
An analytical solution to the problem of frost growth and densification on flat surfaces
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Phase change mass transfer model for frost growth and densification
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Transient two-dimensional model of frost formation on a fin-and-tube heat exchanger
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A generalized simple model for predicting frost growth on cold flat plate
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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
ElCheikh, A., & Jacobi, A. M. (2014) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2014.05.054 · Cited by 79
Brèque, F., & Nemer, M. (2016) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2016.06.010 · Cited by 70
Modeling of frosting behavior on a cold plate
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First-principles modeling of frost accumulation on fan-supplied tube-fin evaporators
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Kim, C., Lee, J., & Lee, K.-S. (2017) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2017.07.130 · Cited by 63
Moallem, E., Padhmanabhan, S., Cremaschi, L., & Fisher, D. E. (2012) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2011.08.010 · Cited by 61
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Lee, J., Kim, J., Kim, D. R., & Lee, K.-S. (2018) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2018.05.098 · Cited by 52
Analysis of CO2 frost formation properties in cryogenic capture process
Song, C., Kitamura, Y., Li, S.-H., & Jiang, W.-Z. (2013) · International journal of greenhouse gas control · doi:10.1016/j.ijggc.2012.12.011 · Cited by 58
“In the moisture frost process, the density increases continuously with the total mass of the deposition (Na and Webb, 2004a).”
BackgroundFrost spreading on microscale wettability/morphology patterned surfaces
Zhao, Y., & Yang, C. (2017) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2017.04.063 · Cited by 55
Thermofluid characteristics of frosted finned-tube heat exchangers
Yan, W.-M., Li, H.-Y., & Tsay, Y.-L. (2005) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2005.02.018 · Cited by 52
Numerical simulation of frosting behavior and its effect on a direct-contact ambient air vaporizer
Kuang, Y.-W., Yi, C., & Wang, W. (2015) · Journal of Natural Gas Science and Engineering · doi:10.1016/j.jngse.2015.06.042 · Cited by 45
Transient model of a vertical freezer with door openings and defrost effects
Mastrullo, R., Mauro, A. W., Menna, L., Palma, A., & Vanoli, G. (2014) · Applied Energy · doi:10.1016/j.apenergy.2014.01.069 · Cited by 45
“=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:…”
MethodLiu, S., Jiao, W., Ren, L., & Tian, X. (2019) · Renewable Energy · doi:10.1016/j.renene.2019.10.072 · Cited by 49
Heat transfer—A review of 2004 literature
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Review on frosting, defrosting and frost management techniques in industrial food freezers
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Numerical Simulation of Frosting on Fin-and-Tube Heat Exchanger Surfaces
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Hwang, J., & Cho, K. (2014) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2014.04.026 · Cited by 44
Ma, J., Kim, D., Braun, J. E., & Horton, W. T. (2023) · Energy · doi:10.1016/j.energy.2023.127030 · Cited by 46
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Lenic, K., Trp, A., & Frankovic, B. (2009) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2008.12.030 · Cited by 38
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Frosting in heat pump evaporators part A: experimental investigation
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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).”
Sommers, A., Napora, A., Truster, N., Caraballo, E., & Hermes, C. (2017) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2016.10.025 · Cited by 32
Three dimensional reconstruction of frost structure by replica method
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Evaporator Frosting in Refrigerating Appliances: Fundamentals and Applications
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“According to the vapor crystal growth theory, the crystal growth rate depends on the water vapor supersaturation degree that is defined [14] as:”
BackgroundFrosting in a heat pump evaporator part B: Numerical analysis
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“Na and Webb [ 5 ] investigated fundamental phenomena related to frost deposition and growth.”
BackgroundLiterature Survey of Numerical Heat Transfer (2000–2009): Part II
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Analysis of early-stage frost formation in natural convection over a horizontal cylinder
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Experimental Investigation of Frost Growth on Microchannel Heat Exchangers
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Frost Growth in Regenerative Wheels
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In Situ Observation of Ice Formation from Water Vapor by Environmental SEM
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Literature Survey of Numerical Heat Transfer (2000–2009): Part I
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Tian, C., Li, X., & Yang, X. (2004) · Applied Energy · doi:10.1016/j.apenergy.2004.08.006 · Cited by 11
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Heat Transfer In The Regenerative Heat Exchanger
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Benítez, T., Sherif, S. A., & Benítez, J. (2019) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2019.02.005 · Cited by 9
Matsumoto, K., Honda, M., Ito, Y., & Shirai, D. (2013) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2013.09.004 · Cited by 8
Effects of crystal formation on the initial frost thickness and density on cold surfaces
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Jadav, C. D., & Chowdhury, K. (2021) · Thermal Science and Engineering Progress · doi:10.1016/j.tsep.2021.100864 · Cited by 7
Numerical analysis of the frosting performance of the air-side of a heat pump.
Popovac, M., Seichter, S., Beňovský, P., & al., E. (2015) · Institut International du Froid · doi:10.18462/iir.icr.2015.0028 · Cited by 7
Quick estimation of frost growth on cold fins through thermal network analysis
Kim, S., & Lee, S.-Y. (2014) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2014.07.015 · Cited by 6
Chen, S. P., Xie, F. S., Yao, S. T., Han, H. Y., & Chang, Z. X. (2012) · Advanced materials research · doi:10.4028/www.scientific.net/amr.516-517.24 · Cited by 6
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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
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
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
“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
Benchmarking MELCOR 1.8.2 for ITER Against Recent EVITA Results
Merrill, B. J. (2007) · doi:10.2172/924495 · Cited by 5
A Non-Restrictive Solution to Frost Growth and Densification on Flat Surfaces
Hollon, D., Truster, N., Byrd, L. W., Román, A. J., & Wolff, M. (2023) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2023.124578 · Cited by 4
Bezovsky, M., Stričík, M., & Praščáková, M. (2010) · Applied Energy · doi:10.1016/j.apenergy.2010.02.031 · Cited by 4
“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 2
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
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
“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
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 2
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
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
Study of frost growth on heat exchangers used as outdoor coils in air source heat pump systems
Sankaranarayanan, K. (2011) · Cited by 2
Safikhani, H., & Shabani, H. (2020) · International Journal of Engineering · doi:10.5829/ije.2020.33.12c.17 · Cited by 2
“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
Experimental study of natural frost formation on a horizontal cylinder
Yaghoubi, M., & Khoshnazar, H. (2010) · AIAA/ASME Joint Thermophysics and Heat Transfer Conference · doi:10.2514/6.2010-4659 · Cited by 1
Leoni, A. (2017) · theses.fr (ABES) · doi:10.70675/f052b4afz1f26z4ed9zbeaez6d56015b3f69 · Cited by 2
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
Metadata
- 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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