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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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In the citing paper
“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].”
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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)
In the citing paper
“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)
In the citing paper
“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)
In the citing paper
“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)
In the citing paper
“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
In the citing paper
“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)
In the citing paper
“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)
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“the saturation model over predicts the data approximately 50%”
From New model for frost growth rate (2004) · cites this paper as [8]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“The Jones and Parker [8] model significantly underpredicts their own data.”
From New model for frost growth rate (2004) · cites this paper as [8]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“the supersaturation model provides good agreement with the data.”
From New model for frost growth rate (2004) · cites this paper as [8]
In the citing paper
“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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“…coordinate gives the frost surface temperature as follows: (8) Numerical results were compared to the experimental work of Yonko and Sepsy (1967), Jones and Parker (1975), and Sahin (1995), resulting in satisfactory agreement. dδf dt ------- 1 ρf ---- hm ρv,a ρv ,fs–( ) D– Mv RT ------ ⎝ ⎠ ⎛…”
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Experimental 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 15
“Jones and Parker [3] studied frost formation with varying environmental parameters.”
BackgroundDevelopment 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 15
Effect 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
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
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
“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.”
BackgroundJadav, C. D., & Chowdhury, K. (2020) · Renewable Energy · doi:10.1016/j.renene.2020.08.141 · Cited by 13
An 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
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
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
Study on the Heat Transfer Characteristics of an Ambient Air Vaporizer with Multi-Component Fluids
Wang, J., Li, C., Jia, W., & Wang, K. (2022) · Processes · doi:10.3390/pr10050851 · Cited by 10
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
Juhola, V., Mikkola, V., Inkeri, E., Kabelac, S., & Tynjälä, T. (2025) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2025.127396 · Cited by 9
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 9
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
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 8
Jadav, C. D., & Chowdhury, K. (2021) · Thermal Science and Engineering Progress · doi:10.1016/j.tsep.2021.100864 · Cited by 7
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
Variation of Frost Roughness on a Flat Plate Under Forced Convection
Tongxin, Z., O’Neal, D. L., & McClain, S. T. (2020) · Journal of Thermal Science and Engineering Applications · doi:10.1115/1.4047570 · Cited by 7
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
Metadata
- 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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