Analysis of Thermal Conductivity of Frost on Cryogenic Finned-tube Vaporizer Using Fractal Method


Thermal conductivity of frost is not only related to density, but also affected by its microstructure and environmental conditions, and it will continuously change with the formation and growth of frost. Images of frost formation and growth on the cryogenic surface in various shapes at different stages were obtained by experimental measurements, and a numerical simulation of frost formation and growth was carried out based on Diffusion Limited Aggregation (DLA) model of fractal theory in this paper. Based on the frost structure obtained by experiment, the fractal dimension of pore area distribution and porosity of frost layer on the cryogenic finned-tube vaporizer were calculated by using fractal method, and combined with heat conduction model of frost layer obtained by thermal resistance method, the thermal conductivity of frost on the cryogenic surface was calculated. The result shows that the thermal conductivity calculated by the fractal model coincides with the range of the experimental data. Additionally, comparison with other heat conduction models indicated that it is feasible to introduce the fractal dimension of pore area distribution into heat conduction model to deduce the thermal conductivity of frost.

Share and Cite:

S. Chen, S. Yao and F. Xie, "Analysis of Thermal Conductivity of Frost on Cryogenic Finned-tube Vaporizer Using Fractal Method," Energy and Power Engineering, Vol. 5 No. 4B, 2013, pp. 109-115. doi: 10.4236/epe.2013.54B021.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] H. W. Schneider, “Equation of the Growth Rate of Frost Forming on Cooled Surface,” International Journal of Heat and Mass Transfer, Vol. 21, No. 8, 1978, pp. 1019-1024. doi:10.1016/0017-9310(78)90098-4
[2] D. L. O 'Neal and D. R. Tree, “Measurement of Frost Growth and Density in a Parallel Plate Geometry,” ASHRAE Transactions, Vol. 26, No. 5, 1984, p. 56.
[3] S. M. Sami and T. Duong, “Mass and Heat Transfer during Frost Growth,” ASHRAE Transactions, Vol. 95, No. 1, 1989, pp. 158-165.
[4] D. K. Yang and K. S. Lee, “Dimensionless Correlations of Frost Properties on a Cold Plate,” International Journal of Refrigeration, Vol. 27, No. 1, 2004, pp. 89-96. doi:10.1016/S0140-7007(03)00118-X
[5] G. Biguria and L. A. Wenzel, “Measurement and Correlation of Water Frost Thermal Conductivity and Density,” Industrial and Engineering Chemistry Fundamentals, Vol. 9, No. 1, 1970, pp. 129-138. doi:10.1021/i160033a021
[6] A. Z. ahin, “Effective Thermal Conductivity of Frost During the Crystal Growth Period,” International Journal of Heat and Mass Transfer, Vol. 43, No. 4, 2000, pp. 539-553. doi:10.1016/S0017-9310(99)00162-3
[7] C. H. Cheng and C. H. Shiu, “Frost Formation and Frost Crystal Growth on a Cold Plate in Atmospheric Air Flow,” International Journal of Heat and Mass Transfer, Vol. 45, No. 21, 2002, pp. 4289-4303.
[8] P. L. T. Brian, R. C. Reid and Y. T. Shah, “Frost Deposition on Cold Surfaces,” Industrial and Engineering Chemistry Fundamentals, Vol. 9, No. 3, 1970, pp. 375-380. doi:10.1021/i160035a013
[9] Y. Hayashi, A. Aoki, S. Adachi and K. Hori, “Study of Frost Properties Correlating with Frost Formation Types,” Journal of Heat Transfer, Vol. 99, No. 2, 1977, pp. 239-245. doi:10.1115/1.3450675
[10] Y.-X. Tao, R. W. Besant and K. S. Rezkallah, “A Mathematical Model for Predicting the Densification and Growth of Frost on a Flat Plate,” International Journal of Heat and Mass Transfer, Vol. 36, No. 2, 1993, pp. 353-363. doi:10.1016/0017-9310(93)80011-I
[11] R. Le gall, J. M. Grillot and C. Jallut, “Modeling of Frost Growth and Densification,” International Journal of Heat and Mass Transfer, Vol. 40, No. 13, 1997, pp. 3177-3187. doi:10.1016/S0017-9310(96)00359-6
[12] H. Chen, R. W. Besant and Y. X. Tao, “Frost Characteristics and Heat Transfer on a Flat Plate under Freezer Operating Conditions, Part II: Numerical Modeling and Comparison with Data,” ASHRAE Transactions, Vol. 105, No. 1, 1999, pp. 252-259.
[13] L. Cai, R. H. Wang, P. X. Hou and X. S. Zhang, “Computer Simulation of Frost Growth and Computation of Its Thermal Conductivity,” Chinese Journal of Chemical Engineering, Vol. 60, No. 5, 2009, pp. 1111-1115.
[14] Y. L. Hao, I. Jose and X. T. Yong, “Experimental Study of Initial State of Frost Formation on Flat Surface,” Journal of Southeast University, Vol. 35, No. 1, 2005, pp. 149-153.
[15] P. X. Hou, L. Cai and W. P. Yu, “Experimental Study and Fractal Analysis of Ice Crystal Structure at Initial Period of Frost Formation,” Journal of Applied Sciences, Vol. 25, No. 2, 2007, pp.193-197.
[16] S. P. Chen, S. T. Yao, F. S. Xie, Z. X. Chang and H. Y. Han, “Frost Model and Numerical Simulation of Air-heating Fin-tube Vaporizer,” Cryogenics & Superconductivity, Vol. 39, No. 11, 2011, pp. 64-67.
[17] K. Falconer, “Fractal Geometry Mathematical Foundations and Applications,” W.Q. Zeng, Transactions, Second edition, Posts &Telecom Press, Beijing, 2007, pp. 270-275.
[18] B. Na, “Analysis of Frost Formation in an Evaporator,” ph.D. Thesis, Pennsylvania State University, 2003.
[19] J. D. Yonko and C. F. Sepsy, “An Investigation of the Thermal Conductivity of Frost while Forming on a Flat Horizontal Plate,” ASHRAE Transactions, Vol. 73, No. 2, 1967, pp. 1.1-1.11.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.