Frost formation with varying environmental parameters
Abstract
In practical applications frost formation often takes place with varying environmental parameters (air velocity, temperature, and humidity). Most correlations that have been developed are for constant parameters. Since the frost formation process is dependent on both time and on the history of the frost layer, the correlations for constant environmental parameters will not work when the parameters vary. For this reason, a study was made to develop a method to predict frost formations with varying parameters. A theoretical model of frost growth based on molecular diffusion of water vapor at the frost surface and using energy and mass balances was developed. The model can incorporate varying environmental parameters. The model uses functions relating heat and mass transfer coefficients at the frost surface to the environmental parameters. The model was first tested and calibrated using data taken by previous investigators. A facility was then built to test the validity of the model for varying environmental parameters. Tests were made for changes in humidity and air velocity. The model showed good agreement with the basic trends observed for varying parameters. The qualitative results were generally within 25 percent of the predicted values for time periods up to 3 hr.
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Most experimental tests have been conducted on horizontally assembled plates or fin-and-tube heat exchangers under horizontal air flow conditions.
“In addition, most experimental tests have been con ducted on horizontally assembled plates [12 -17] or fin-and-tube heat exchangers under horizontal air flow conditions [18 -21].”
During frost formation, frost thickness, frost surface temperature, frost density, and frost thermal conductivity all increase continuously.
“These studies suggest that during frost formation, frost thickness, frost surface temperature, frost density, and frost thermal conductivity all increase continuously.”
From Frost growth and densification in laminar flow over flat surfaces (2011) · cites this paper as Jones and Parker [1]
During frost formation, a portion of the total mass flux of water vapor diffuses through the frost layer and undergoes phase transformation to ice that deposits on existing frost crystals, resulting in frost densification.
“During frost formation, a portion of the total mass flux of water vapor diffuses through the frost layer, and undergoes phase transformation to ice which deposits on the existing frost crystals, resulting in frost densification (Jones and Parker [1]; Na and Webb [2]).”
From Frost growth and densification in laminar flow over flat surfaces (2011) · cites this paper as Jones and Parker [1]
The remainder of the water vapor mass flux freezes at the frost surface and serves to increase frost thickness.
“The remainder of vapor mass flux freezes at the frost surface, and serves to increase the frost thickness.”
From Frost growth and densification in laminar flow over flat surfaces (2011) · cites this paper as Jones and Parker [1]
The initial frost thickness and density can be given sufficiently small values without affecting the solution for frost growth and densification.
“As long as the initial frost thickness and density are given sufficiently small value, they will not affect the solution for the frost growth and densification.”
From Studies of an air cooler under frost condition (2019) · cites this paper as Jones and Parker (1975)
Jones and Parker (1975) concluded that as long as the initial value of the frost density is significantly smaller than the expected frost, it will not affect the solution for the frost growth and densification.
“They concluded that as long as the initial value of the frost density is significantly smaller than the expected frost, it will not affect the solution for the frost growth and densification.”
From Studies of an air cooler under frost condition (2019) · cites this paper as Jones and Parker (1975)
Jones and Parker (1975) found that frost density and thickness converged to the same value when initial frost density was varied from 8 to 48 kg/m3.
“As for the density, they evaluate the effect of the initial value by changing the value from 8 to 48 kg/m 3 .They found that the frost density and thickness converged to the same value.”
From Studies of an air cooler under frost condition (2019) · cites this paper as Jones and Parker (1975)
Jones and Parker (1975) found that initial frost thickness can approach zero (~2 x 10^-5 m) without causing significant problems in predicting the frost growth rate.
“Jones and Parker (1975) tested the initial conditions by changing the values of the initial frost thickness and found that the initial thickness can approach zero (~ 2 x 10 -5 m) without causing significant problems in predicting the frost growth rate.”
From Studies of an air cooler under frost condition (2019) · cites this paper as Jones and Parker (1975)
The main approach in the literature is to develop models based on heat and mass diffusion through the frost layer considered as a porous solid.
“Finally, the main approach is to develop models based on heat and mass diffusion through the frost layer considered as a porous solid (Jones and Parker, 1975; Kondepudi and O'Neal, 1993; Le Gall and Grillot, 1997; Lee et al., 1997; Na and Webb, 2004a).”
From Frosting modeling on a cold flat plate: Comparison of the different assumptions and impacts on frost growth predictions (2016) · cites this paper as Jones and Parker, 1975
Jones and Parker showed that for their model, if initial thickness approaches zero (~1e-5 m) and initial density is significantly lower than frost density during growth (8-48 kg/m3), results are not affected by initial conditions after a few minutes.
“Indeed, Jones and Parker showed that, for their model, if initial thickness approaches zero ( ~1 10 5 ⋅ -m ), and initial density is significantly lower than the frost density during frost growth (between 8 48 3 -⋅ -kg m ), the results are not affected by those initial conditions after a few minutes of simulation.”
From Frosting modeling on a cold flat plate: Comparison of the different assumptions and impacts on frost growth predictions (2016) · cites this paper as Jones and Parker (1975)
For the 'p1D with αw = cst' and '0D' models both with Yonko's correlation, frost thickness results are almost constant for different initial frost densities within the advised range 8-48 kg/m3.
“Regarding the two others presented cases, the ' p1D with α w = cst ' model and the ' 0D ' model both with Yonko's correlation, the results are almost constant for different initial frost densities within the advised range by Jones and Parker (1975) analysis (8-48 kg.m -3 )”
From Frosting modeling on a cold flat plate: Comparison of the different assumptions and impacts on frost growth predictions (2016) · cites this paper as Jones and Parker (1975)
Existing frosting models have focused on predicting heat and mass transfer characteristics at surfaces of basic geometries such as a flat plate or cylindrical surface.
“Existing frosting models have focused on predicting the characteristics of heat and mass transfer at the surfaces of basic geometries, such as a flat plate or cylindrical surface [1-12].”
From Performance prediction of a fin-and-tube heat exchanger considering air-flow reduction due to the frost accumulation (2013) · cites this paper as [1]
Frost formation on flat plate and cylindrical surfaces is relatively well known and can be predicted reliably with existing models and correlations.
“Therefore, frost formation on flat plate and cylindrical surface is relatively well known and can be predicted reliably with existing models and correlations.”
From Modeling for predicting frosting behavior of a fin–tube heat exchanger (2006) · cites this paper as [1]
Early modeling approaches primarily relied on one-dimensional quasi-steady frameworks for computational efficiency, yielding rapid estimates of bulk frost properties via semi-empirical correlations.
“Early modeling approaches primarily relied on one-dimensional (1D) quasi-steady frameworks for computational efficiency, yielding rapid estimates of bulk frost proper ties via semi-empirical correlations [22 -25].”
From A physics-informed quasi-steady frosting model with coupled heat–mass transfer for predicting frost layer growth (2026) · cites this paper as [22]
The Jones and Parker model incorporated environmental dependencies, yet its assumption of frost uniformity led to significant prediction errors.
“For instance, the Jones and Parker model [22] incorporated environmental dependencies, yet its assumption of frost uniformity led to significant prediction errors.”
From A physics-informed quasi-steady frosting model with coupled heat–mass transfer for predicting frost layer growth (2026) · cites this paper as [22]
Frost thickness converged to the same value regardless of the initial value of frost thickness, if it is chosen from 8 to 48 kg/m3.
“Authors evaluated the effect of the initial value of the frost density on the frost growth rate by changing the value from 8 to 48 kg/m 3 . They found that the frost thickness converged to the same value regardless the initial value of frost thickness, if it is chosen from the mentioned range.”
From Transient two-dimensional model of frost formation on a fin-and-tube heat exchanger (2009) · cites this paper as [7]
The saturation model overpredicts the Jones and Parker [8] data by approximately 50%.
“the saturation model over predicts the data approximately 50%”
From New model for frost growth rate (2004) · cites this paper as [8]
Initial frost thickness can approach zero (2 × 10^-5 m) without causing significant problems in predicting the frost growth rate.
“Initial thickness can approach zero ( 2 · 10 5 m) without causing significant problems in predicting the frost growth rate.”
From New model for frost growth rate (2004) · cites this paper as [8]
As long as the initial value of the frost density is significantly smaller than the frost density during growth, it will not affect the solution for the frost growth rate and densification.
“As long as the initial value of the frost density is significantly smaller than the frost density during growth, it will not affect the solution for the frost growth rate and densification.”
From New model for frost growth rate (2004) · cites this paper as [8]
The initial value of the frost density can be taken as any value within 8-48 kg/m3.
“Based on their investigation, the initial value of the frost density can be taken as any value within 8-48 kg/m 3 .”
From New model for frost growth rate (2004) · cites this paper as [8]
When the initial frost density was varied from 8 to 48 kg/m3, the frost density and thickness converged to the same value in a few minutes.
“Jones and Parker [8] evaluated the effect of the initial value of the frost density on the frost growth rate and densification in their model by changing the value from 8 to 48 kg/m 3 . They found that the frost density and thickness converged to the same value in a few minutes.”
From New model for frost growth rate (2004) · cites this paper as [8]
The analytical models of Brian et al. and Jones and Parker assume that the density of fresh frost is the same as the average density of the frost layer, so they did not account for density variation within the frost layer.
“The analytical models of Brian et al. [2,3] and Jones and Parker [8] assume that the density of the fresh frost is same as the average density of the frost layer. Thus, they did not account for the density variation within the frost layer.”
From New model for frost growth rate (2004) · cites this paper as [8]
Jones and Parker state that their model underpredicts their data by 35%.
“Jones and Parker state that their model underpredicts their data by 35%.”
From New model for frost growth rate (2004) · cites this paper as [8]
The Jones and Parker [8] model significantly underpredicts their own data.
“The Jones and Parker [8] model significantly underpredicts their own data.”
From New model for frost growth rate (2004) · cites this paper as [8]
This may be a reason the Jones and Parker model underpredicts their experimental data by approximately 35%.
“This may be a reason the Jones and Parker model underpredicts their experimental data approximately 35%.”
From New model for frost growth rate (2004) · cites this paper as [8]
The density variation within the frost layer clearly affects the frost growth rate, and the uniform frost density Jones and Parker model [8] underpredicts the frost growth rate.
“The density variation within the frost layer clearly affects the frost growth rate, and the uniform frost density Jones and Parker model [8] underpredicts the frost growth rate.”
From New model for frost growth rate (2004) · cites this paper as [8]
The Jones and Parker [8] model assumes no density variation through the frost thickness and saturated water vapor at the frost surface.
“The figure also shows the Jones and Parker model, which assumes no density variation through the frost thickness and saturated water vapor at the frost surface.”
From New model for frost growth rate (2004) · cites this paper as [8]
The supersaturation model provides good agreement with the Jones and Parker [8] data.
“the supersaturation model provides good agreement with the data.”
From New model for frost growth rate (2004) · cites this paper as [8]
The Jones and Parker [8] model has two deficiencies: the assumption of uniform frost density and the assumption of saturated water vapor at the frost surface.
“The Jones and Parker [8] model has two deficiencies: (1) the assumption of uniform frost density, and (2) assumption of saturated water vapor at the frost surface.”
From New model for frost growth rate (2004) · cites this paper as [8]
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“[7], Jones and Parker [8], Sherif et al.”
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Experimental Characterization of Frost Growth on a Horizontal Plate Under Natural Convection
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Wong, J. C. Q., Pareek, V. K., & Sun, B. (2022) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2022.123396 · Cited by 23 · see citing works
Condensation frosting detection and characterization using a capacitance sensing approach
Shen, Y., & Wang, S. (2019) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2019.118968 · Cited by 20 · see citing works
Predictive models on the frost formation for plain surface - a review and comparative study
Li, S.-M., & Wang, C.-C. (2021) · International Communications in Heat and Mass Transfer · doi:10.1016/j.icheatmasstransfer.2021.105670 · Cited by 24 · see citing works
Effects of Evaporator Frosting on the Performance of an Air-to-Air Heat Pump
Martínez-Frías, J., & Aceves, S. (1997) · Advanced Energy Systems · doi:10.1115/1.2795061 · Cited by 21 · see citing works
Modeling of a fan-supplied flat-tube heat exchanger exposed to non-uniform frost growth
Breque, F., & Nemer, M. (2017) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2016.12.012 · Cited by 21 · see citing works
Experimental Study on Energy Efficiency of Heat-source Tower Heat Pump Units in Winter Condition
Li, N., Wenjie, Z., Lijie, W., et al. (2011) · International Conference on Measuring Technology and Mechatronics Automation (ICMTMA) · doi:10.1109/icmtma.2011.321 · Cited by 21 · see citing works
“However, there are two main problems with ASHPs: heating capacity decreases as outdoor air temperature drops and when there is frost formation on the outdoor heat exchanger (evaporator) surfaces in humid climate [5] [6] [7].”
Kwon, J., Yun, S., Lee, S., Cho, W., & Kim, Y. (2021) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2021.122245 · Cited by 19 · see citing works
Farzaneh, M., Zgheib, N., Sherif, S. A., & Balachandar, S. (2022) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2022.123233 · Cited by 15 · see citing works
Ye, H.-Y., Park, J., & Lee, K.-S. (2014) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2014.08.069 · Cited by 17 · see citing works
Modeling the airside dynamic behavior of a heat exchanger under frosting conditions
Gao, T., & Gong, J. (2011) · Journal of Mechanical Science and Technology · doi:10.1007/s12206-011-0615-5 · Cited by 16 · see citing works
“A large number of studies [1-6] are available on the frost properties and heat transfer involved in frosting and the mechanism of frost growth.”
BackgroundEffect of Moisture Transfer Through a Semipermeable Membrane on Condensation/Frosting Limit
Niroomand, S., Fauchoux, M. T., & Simonson, C. J. (2018) · Journal of Heat Transfer · doi:10.1115/1.4041185 · Cited by 14 · see citing works
Thawing of frozen foods in humid air
Mannapperuma, J. D., & Singh, R. P. (1988) · International Journal of Refrigeration · doi:10.1016/0140-7007(88)90032-1 · Cited by 15 · see citing works
Heat transfer—a review of 1975 literature
Eckert, E. R. G., Sparrow, E. M., Goldstein, R. J., et al. (1976) · International Journal of Heat and Mass Transfer · doi:10.1016/0017-9310(76)90075-2 · Cited by 15 · see citing works
Wang, Z., Cui, W., Li, L., Zhan, C., & Zhang, Y. (2024) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2024.125604 · Cited by 14 · see citing works
Jadav, C. D., & Chowdhury, K. (2020) · Renewable Energy · doi:10.1016/j.renene.2020.08.141 · Cited by 13 · see citing works
Free convection frost growth in a narrow vertical channel
Tanda, G., & Fossa, M. (2006) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2005.11.010 · Cited by 14 · see citing works
“Several models for frost growth have been proposed in the literature [9–15]; however, owing to the complexity of the phenomenon, the development of precise predictions of frost growth characteristics as well as of correlations to evaluate frost properties is still a demanding task.”
BackgroundExperimental Study on Frost Height of Round Plate Fin-Tube Heat Exchangers for Mobile Heat Pumps
Lee, M., Kim, Y., & Lee, D.-Y. (2012) · Energies · doi:10.3390/en5093479 · Cited by 14 · see citing works
“Jones and Parker [3] studied frost formation with varying environmental parameters.”
BackgroundAn Eulerian multiphase frost model based on heat transfer measurements
Saygin, A., Başol, A. M., & Arık, M. (2023) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2023.124575 · Cited by 13 · see citing works
Critical operating conditions for prevention of frost formation in fin-tube heat exchangers
Ye, H.-Y., Park, J.-S., & Lee, K.-S. (2014) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2014.04.044 · Cited by 13 · see citing works
Westhaeuser, J., Schulze, C., Albrecht, J.-C., Tegethoff, W., Lemke, N., & Koehler, J. (2023) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2023.120140 · Cited by 12 · see citing works
Development and validation of a numerical model for frost growth based on nucleation theory
Qiu, G., Li, S., Shi, Y., Fang, X., & Cai, W. (2023) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2023.125137 · Cited by 13 · see citing works
Juhola, V., Mikkola, V., Inkeri, E., Kabelac, S., & Tynjälä, T. (2025) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2025.127396 · Cited by 9 · see citing works
Study on the Heat Transfer Characteristics of an Ambient Air Vaporizer with Multi-Component Fluids
Wang, J., Li, C.-J., Jia, W.-L., & Wang, K. (2022) · Processes · doi:10.3390/pr10050851 · Cited by 9 · see citing works
Numerical prediction of frost formation on cooled heat exchangers
Sami, S. M., & Duong, T. (1988) · International Communications in Heat and Mass Transfer · doi:10.1016/0735-1933(88)90009-7 · Cited by 11 · see citing works
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 · see citing works
Hattori, A., Sato, T., Himeno, T., & Watanabe, T. (2024) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2024.126321 · Cited by 10 · see citing works
Jadav, C. D., & Chowdhury, K. (2021) · Thermal Science and Engineering Progress · doi:10.1016/j.tsep.2021.100864 · Cited by 7 · see citing works
Prediction of heat and mass transfer inside 3D frost microstructure
Mao, N., Nishimura, K., Gong, J., Takayashiki, M., Ściążko, A., Komatsu, Y., Tang, J., & Shikazono, N. (2024) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2024.122978 · Cited by 7 · see citing works
Variation of Frost Roughness on a Flat Plate Under Forced Convection
Zhang, T., O'Neal, D., & McClain, S. (2021) · Journal of Thermal Science and Engineering Applications · doi:10.1115/1.4047570 · Cited by 7 · see citing works
Study on heat and mass transfer characteristics of humid air-flow in a fin bundle
Kim, D.-H., Koyama, S., Kuwahara, K., Kwon, J.-T., & Park, B.-D. (2010) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2010.05.013 · Cited by 6 · see citing works
The research of optical fiber frost sensor and intelligent refrigerator defrost system
Zhang, L.-H., Zhang, J., Li, H., & Hu, Q. H. (2012) · International Conference on Signal Processing · doi:10.1109/icosp.2012.6492017 · Cited by 7 · see citing works
- Authors
- Jones, B. W., & Parker, J. D.
- Affiliations
- Oklahoma State University (US)
- Venue
- Journal of Heat Transfer
- Publisher
- Wiley
- Published
- 1975-05-01
- Volume
- 97
- Issue
- 2
- Pages
- 255-259
- ISSN
- 0022-1481 (ISSN-L)
- 1528-8943
- OpenAlex
- W2079897980
- Cited by
- 171
- References
- 0
- Citations by year
- 2026: 9 · 2025: 5 · 2024: 6 · 2023: 6 · 2022: 7 · 2021: 12 · 2020: 4 · 2019: 5 · 2018: 13 · 2017: 6 · 2016: 11 · 2015: 4 · 2014: 6 · 2013: 2 · 2012: 8
- FWCI
- 2.21
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- ASME 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 formation, frost growth, water vapor diffusion, frost layer, heat and mass transfer coefficients, air velocity, humidity, mass and energy balance
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