Modeling spatial and temporal frost formation with distributed properties on a flat plate using the orthogonal collocation method
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The absolute deviation of Benítez and Sherif's model was in the order of 3.0% or less, provided that the supersaturation degree at the frost-air interface was properly adjusted.
“As reported, the absolute deviation was in the order of 3.0% or less, provided that the supersaturation degree at the frost-air interface was properly adjusted.”
From Review on the measurement and calculation of frost characteristics (2018) · cites this paper as [65]
The most recent reported density relation was reported by Benítez and Sherif in 2017, who modeled spatial and temporal frost formation with distributed properties on a flat plate using the orthogonal collocation method.
“The most recent reported density relation was reported by Benítez and Sherif in 2017 [65], who modeled spatial and temporal frost formation with distributed properties on a flat plate using the orthogonal collocation method.”
From Review on the measurement and calculation of frost characteristics (2018) · cites this paper as [65]
After solving the initial-value equations using Matlab's ode15s, the model results were compared with existing experimental data.
“After the resulting set of initialvalue equations had been approximately solved using the ode15s program of Matlab, the results from the model were compared with existing experimental data.”
From Review on the measurement and calculation of frost characteristics (2018) · cites this paper as [65]
The frost density gradient inside the frost layer near the plate surface and frost surface were both significantly smaller than other regions within the frost layer.
“The frost density profile indicated that the frost density gradient inside the frost layer near the plate surface and frost surface were both significantly smaller than other regions within the frost layer [86,88].”
From Frosting mechanism and behaviors on surfaces with simple geometries: A state-of-the-art literature review (2022) · cites this paper as [88]
Hermes et al., Benitez and Sherif, and You et al. all presented a linear temperature distribution characteristic inside the frost layer on a flat plate with a fixed surface temperature.
“Hermes et al. [50], Benitez and Sherif [88], and You et al. [93] all presented a linear temperature distribution charac teristic.”
From Frosting mechanism and behaviors on surfaces with simple geometries: A state-of-the-art literature review (2022) · cites this paper as [88]
The water vapor density gradient inside the frost layer near the plate surface was significantly smaller than that near the frost surface.
“For water vapor density, its gradient inside the frost layer near the plate surface was significantly smaller than that near the frost surface [50,80,86,88,90,91].”
From Frosting mechanism and behaviors on surfaces with simple geometries: A state-of-the-art literature review (2022) · cites this paper as [88]
Cites
Kraus, A. D., Welty, J. R., & Aziz, A. (2011) · CRC Press eBooks · doi:10.1201/b12301-22 · Cited by 4,223 · see citing works
ASHRAE Handbook—1981 Fundamentals
(1981) · Building Services Engineering Research and Technology · doi:10.1177/014362448100200409 · Cited by 3,398 · see citing works
Adsorption Analysis: Equilibria and Kinetics
Do, D. D. (1998) · Series on chemical engineering · doi:10.1142/9781860943829 · Cited by 2,983 · see citing works
Free and Moving Boundary Problems.
Cryer, C. C., & Crank, J. (1986) · Mathematics of Computation · doi:10.2307/2008018 · Cited by 2,170 · see citing works
Adsorption Analysis: Equilibria and Kinetics
Do, D. D. (1998) · Series on chemical engineering · doi:10.1142/p111 · Cited by 1,928 · see citing works
Solution of differential equation models by polynomial approximation
Villadsen, J., & Michelsen, M. L. (1978) · Prentice Hall eBooks · Cited by 1,286 · see citing works
Simultaneous Heat, Mass, and Momentum Transfer in Porous Media: A Theory of Drying
Whitaker, S. (1977) · Advances in heat transfer · doi:10.1016/s0065-2717(08)70223-5 · Cited by 1,156 · see citing works
Solution of boundary-value problems by orthogonal collocation
Villadsen, J. V., & Stewart, W. E. (1967) · Chemical Engineering Science · doi:10.1016/0009-2509(67)80074-5 · Cited by 673 · see citing works
An introduction to heat transfer
(2002) · CRC Press eBooks · doi:10.1201/9781482267693-12 · Cited by 563 · see citing works
Free and Moving Boundary Problems
(2006) · Computational fluid and solid mechanics · doi:10.1007/1-84628-205-5_10 · Cited by 398 · see citing works
The role of diffusion in catalysis
Satterfield, C. N., & SHERWOOD, T. K. (1963) · Cited by 396 · see citing works
Applied mathematics and modeling for chemical engineers
(1995) · Choice Reviews Online · doi:10.5860/choice.32-5708 · Cited by 389 · see citing works
Solution of boundary-value problems by orthogonal collocation
Villadsen, J. V., & Stewart, W. E. (1995) · Chemical Engineering Science · doi:10.1016/0009-2509(96)81831-8 · Cited by 376 · see citing works
A one-dimensional model for frost formation on a cold flat surface
Lee, K.-S., Kim, W.-S., & Lee, T.-H. (1997) · International Journal of Heat and Mass Transfer · doi:10.1016/s0017-9310(97)00074-4 · Cited by 296 · see citing works
A mathematical model for predicting the densification and growth of frost on a flat plate
Tao, Y.-X., Besant, R. W., & Rezkallah, K. S. (1993) · International Journal of Heat and Mass Transfer · doi:10.1016/0017-9310(93)80011-i · Cited by 183 · see citing works
Frost formation with varying environmental parameters
Jones, B. W., & Parker, J. D. (1975) · Journal of Heat Transfer · doi:10.1115/1.3450350 · Cited by 171 · see citing works
Modelling of frost growth and densification
Le Gall, R., Grillot, J. M., & Jallut, C. (1997) · International Journal of Heat and Mass Transfer · doi:10.1016/s0017-9310(96)00359-6 · Cited by 153 · see citing works
Frost growth and densification in laminar flow over flat surfaces
Kandula, M. (2011) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2011.02.056 · Cited by 141 · see citing works
Mass transfer on and within a frost layer
Na, B., & Webb, R. L. (2004) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2003.08.023 · Cited by 129 · see citing works
(1967) · ASHRAE winter conference papers · Cited by 128 · see citing works
Frosting 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 · see citing works
An experimental study of frost formation on a horizontal cylinder under cross flow
Lee, Y. B., & Ro, S. T. (2001) · International Journal of Refrigeration · doi:10.1016/s0140-7007(00)00073-6 · Cited by 95 · see citing works
Principles and Modern Applications of Mass Transfer Operations
Benítez, J. (2002) · Cited by 95 · see citing works
Transient two-dimensional model of frost formation on a fin-and-tube heat exchanger
Lenic, K., Trp, A., & Frankovic, B. (2009) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2008.06.005 · Cited by 92 · see citing works
Drainage of frost melt water from vertical brass surfaces with parallel microgrooves
Rahman, M. A., & Jacobi, A. M. (2011) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2011.11.015 · Cited by 77 · see citing works
Measurement and Correlation of Water Frost Thermal Conductivity and Density
Biguria, G., & Wenzel, L. A. (1970) · Industrial & Engineering Chemistry Fundamentals · doi:10.1021/i160033a021 · Cited by 75 · see citing works
Effect of frost growth on the performance of louvered finned tube heat exchangers
Kondepudi, S. N., & O'Neal, D. L. (1989) · International Journal of Refrigeration · doi:10.1016/0140-7007(89)90030-3 · Cited by 67 · see citing works
Observations of early-stage frost formation on a cold plate in atmospheric air flow
Cheng, C.-H., & Wu, K.-H. (2003) · Journal of Heat Transfer · doi:10.1115/1.1513576 · Cited by 66 · see citing works
Experimental study on frosting/defrosting characteristics of microgrooved metal surfaces
Rahman, M. A., & Jacobi, A. M. (2014) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2014.11.002 · Cited by 62 · see citing works
Dimensionless correlations of frost properties on a cold cylinder surface
Kim, J.-S., Yang, D.-K., & Lee, K.-S. (2008) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2008.01.007 · Cited by 57 · see citing works
Generalized correlation of the water frost thermal conductivity
Dietenberger, M. A. (1983) · International Journal of Heat and Mass Transfer · doi:10.1016/0017-9310(83)90011-x · Cited by 52 · see citing works
The use of the orthogonal collocation method on the study of the drying kinetics of soybean seeds
Barrozo, M. A. S., Henrique, H. M., Sartori, D. J. M., & Freire, J. T. (2005) · Journal of Stored Products Research · doi:10.1016/j.jspr.2005.06.002 · Cited by 47 · see citing works
Effects of microgroove geometry on the early stages of frost formation and frost properties
Rahman, M. A., & Jacobi, A. M. (2013) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2013.02.037 · Cited by 43 · see citing works
Tahavvor, A., & Yaghoubi, M. (2010) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2010.06.004 · Cited by 35 · see citing works
Frost formation and heat transfer on a cold surface in ice fog
Mago, P. J., & Sherif, S. A. (2004) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2004.10.004 · Cited by 32 · see citing works
Self-citationHeat and mass transfer on a cylinder surface in cross flow under supersaturated frosting conditions
Mago, P. J., & Sherif, S. A. (2003) · International Journal of Refrigeration · doi:10.1016/s0140-7007(03)00076-8 · Cited by 31 · see citing works
Self-citationFrost formation and heat transfer on circular cylinders in cross-flow
Raju, S. P., & Sherif, S. A. (1993) · International Journal of Refrigeration · doi:10.1016/0140-7007(93)90056-e · Cited by 30 · see citing works
Self-citationHeat and mass transfer under frosting conditions
Marinyuk, B. T. (1980) · International Journal of Refrigeration · doi:10.1016/0140-7007(80)90128-0 · Cited by 25 · see citing works
Local frost behaviors of a scaled-up louvered fin heat exchanger
Park, J.-S., Kim, D. R., & Lee, K.-S. (2015) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2015.06.025 · Cited by 24 · see citing works
Xia, Y., Hrnjak, P., & Jacobi, A. M. (2005) · ASHRAE winter conference papers · Cited by 13 · see citing works
Determination of the enzyme reaction rate in a differential fixed-bed reactor: a case study
Filho, E. A. B., Baruque, M. D. G. A., & Junior, G. L. S. (2001) · Brazilian Journal of Chemical Engineering · doi:10.1590/s0104-66322001000100001 · Cited by 11 · see citing works
Junior, E. C. B., Mansur, M. B., Salum, A., & de Castro, R. M. Z. (2001) · Brazilian Journal of Chemical Engineering · doi:10.1590/s0104-66322001000200004 · Cited by 10 · see citing works
Heat and mass transfer in frost and ice, packed beds, and environmental discharges
Arimilli, R. V., Beasley, D. E., Sengupta, S., Sherif, S. A., & Watts, R. G. (1990) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · Cited by 8 · see citing works
Self-citationXia, Y., Hrnjak, P., & Jacobi, A. M. (2006) · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign) · Cited by 3 · see citing works
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Review on the measurement and calculation of frost characteristics
Song, M., & Dang, C. (2018) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2018.03.094 · Cited by 212 · see citing works
Zhang, L., Song, M., Deng, S., Shen, J., & Dang, C. (2022) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2022.118984 · Cited by 83 · see citing works
Zhang, L., Song, M., Shen, J. J., Zhang, X., Xu, Y., & Yanxin, H. U. (2023) · International Communications in Heat and Mass Transfer · doi:10.1016/j.icheatmasstransfer.2023.106654 · Cited by 43 · see citing works
Chen, G., Deng, X., Zhang, G., & Yan, X. (2019) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2018.12.133 · Cited by 31 · see citing works
Yoo, J., Chung, Y., Kim, G. T., Song, C.-W., Yoon, P., Sa, Y., & Kim, M. S. (2018) · International journal of refrigeration · doi:10.1016/j.ijrefrig.2018.08.014 · Cited by 22 · see citing works
Chen, W., Sun, Q., Bai, Y., & Zhang, B. (2018) · Energy Conversion and Management · doi:10.1016/j.enconman.2018.04.060 · Cited by 25 · see citing works
Liang, X.-Y., & Wu, L. (2022) · Energy and Buildings · doi:10.1016/j.enbuild.2022.112366 · Cited by 18 · 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
Self-citationHuang, L., Tian, Y., Song, M., Zhang, L., & Chao, C. Y. H. (2023) · Applied Thermal Engineering · doi:10.1016/j.applthermaleng.2023.121537 · Cited by 17 · see citing works
Yang, X., Liu, X., Dong, X.-J., Meng, Y., Hou, Y., & Lai, T.-W. (2022) · Energy Storage and Saving · doi:10.1016/j.enss.2022.05.001 · Cited by 16 · see citing works
A physics-based model for frost buildup under turbulent flow using direct numerical simulations
Zgheib, N., Farzaneh, M., Balachandar, S., & Sherif, S. (2022) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2021.121915 · Cited by 14 · see citing works
Self-citationFrost layer thickness measurement and calculation: A short review
Song, M., Dang, C., Liu, S.-C., Sun, Z.-L., & Mao, N. (2017) · Energy Procedia · doi:10.1016/j.egypro.2017.12.281 · Cited by 13 · see citing works
An analytical model for predicting frosting limit in membranes
Navid, P., Niroomand, S., & Simonson, C. J. (2018) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2018.11.035 · Cited by 15 · see citing works
Harrington, L., Aye, L., & Fuller, B. (2017) · International Journal of Refrigeration · doi:10.1016/j.ijrefrig.2017.12.002 · Cited by 12 · see citing works
Experimental investigation on thermal conductivity of cryogenic frost under forced convection
Jeong, H., Son, H., Byun, S., Hyeon, S., Lee, K.-S., & Kim, D. R. (2023) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2023.124504 · Cited by 9 · see citing works
Benítez, T., Sherif, S., & Benitez, J. (2019) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2019.02.005 · Cited by 8 · see citing works
Self-citationLobato, F. S., Lima, W. J., Borges, R. A., Cavalini, A. A., & Steffen, V. (2019) · Soft Computing · doi:10.1007/s00500-019-04541-y · Cited by 7 · see citing works
“Benı́tez and Sherif (2017) used OC to solve a model used to describe the frost formation process when a cold flat plate is exposed to a humid air stream.”
InfluentialIranagh, S. A., Tahavvor, A., Yaghoubi, M., & Tavakol, M. (2022) · Heat Transfer Engineering · doi:10.1080/01457632.2022.2059218 · Cited by 7 · see citing works
Lisowski, F., & Lisowski, E. (2024) · Energies · doi:10.3390/en17143579 · Cited by 4 · see citing works
A Unified Review of Physical Modeling of Heat and Mass Transfer Processes in Frosting and Icing
Balachandar, S., & Sherif, S. A. (2026) · ASME Journal of Heat and Mass Transfer · doi:10.1115/1.4070930 · Cited by 1 · see citing works
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Liu, B., Shi, S., Liu, Y., Bennacer, R., Chen, A.-Q., & Theodorakis, P. (2021) · E3S Web of Conferences · doi:10.1051/e3sconf/202132104019
Effect of Different Plenum-Chamber Coefficients on the Frosting of Air-Cooler
Liu, B., Shi, S., Liu, Y., Bennacer, R., Chen, A., & Theodorakis, P. E. (2022) · Energies · doi:10.3390/en15020422
Song, M., & Zhang, L. (2024) · Elsevier eBooks · doi:10.1016/b978-0-323-95457-0.00009-5
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Song, M., & Zhang, L. (2024) · Elsevier eBooks · doi:10.1016/b978-0-323-95457-0.00006-x
Patrício, P. C. P., Hazlett, M. J., & Visscher, A. D. (2025) · Process Safety and Environmental Protection · doi:10.1016/j.cherd.2025.01.030
Research on mechanism and measurement technology of frost formation of micro water frosting
Zhi, X., Qi, Y., Shu, W., & Qiu, L. (2025) · Elsevier eBooks · doi:10.1016/b978-0-443-15495-9.00009-5
- Authors
- Benítez, T., & Sherif, S. A.
- Affiliations
- University of Florida (US)
- Corresponding author
- Benítez, Teresa
- ORCID
- Sherif, S.A.
- Venue
- International Journal of Refrigeration
- Publisher
- Elsevier BV
- Published
- 2017-04
- Volume
- 76
- Pages
- 193-205
- ISSN
- 0140-7007 (ISSN-L)
- OpenAlex
- W2581255880
- Cited by
- 27
- References
- 45
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 3 · 2023: 3 · 2022: 6 · 2021: 2 · 2019: 3 · 2018: 5 · 2017: 2
- FWCI
- 2.13
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- International Journal of Refrigeration (publishedVersion)
- Topics
- Physical Sciences › Engineering › Mechanical Engineering › Refrigeration and Air Conditioning Technologies
- Physical Sciences › Engineering › Aerospace Engineering › Icing and De-icing Technologies
- Physical Sciences › Engineering › Computational Mechanics › Heat Transfer and Numerical Methods
- Keywords
- frost formation, frost layer, flat plate, moving boundary problem, frost density, frost thickness, heat flux
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