S. P. CHEN ET AL.

114

between each model shown in Figure 13. Therefore, it

shows that the thermal conductivity of frost is not only

depended on density, but also on the microstructure and

frosting environmental conditions. Curve No.1is obtained

from the maximum parallel model and Curve No.5 from

the minimum series model. These two curves represent

the limits of thermal conductivity of frost, and the curve

of thermal conductivity of actual frost should lie between

these two curves. Curve No.2 is the random mixture

model, which applies to the mixture of air and ice mixed

at certain proportion. But it has big deviation from prac-

tical case due to the soaring of thermal conductivity un-

der small porosity. The cubic lattice model Curve No.3

consists of open cubic lattice structure, with ice deposit-

ing on the edge of the lattice, where the moist air exists

between lattices. It can be seen from the Figure 13 that

the thermal conductivity of this model is going up rapidly

in the low density, not in accordance with the real situa-

tion. Yonko-Sepsy model Curve No.4 considers frost as a

mixture of ice and air. The calculation result is more

practical, but this model is only valid to a certain range

of porosity [19]. Curve No.6 is obtained from the model

in the present paper. The modeling result lies in between

the minimum series model and Yonko-Sepsy model. The

model can be applied to the density of frost greater than

500 kg·m-3, that is, the frost turning into the scale of full

growth and not restricted by the porosity. Therefore, the

thermal conductivity calculated by the above fractal

model coincides with the real situation better than other

models, and the thermal conductivity of frost has a wider

applicable scale.

5. Conclusions

The fractal dimension of pore area distribution and frac-

tal porosity of frost profile were determined based on the

observed structure of frost growth. Then, the heat con-

duction model in frost layer is proposed by using fractal

method, and the thermal conductivity is also expressed

by a function of the fractal dimension of pore area dis-

tribution and porosity of frost. The calculated result

shows that thermal conductivity of frost obtained by the

fractal model agrees well with the testing data of the ef-

fective thermal conductivity. In addition, this fractal

model of heat conduction is not restricted by the porosity,

and will have broader application area compared to other

models. It also verifies the feasibility of adopting the

fractal dimension of pore area distribution into the model

of heat conduction to determine thermal conductivity.

The research shows that frost physical properties is of

great importance in evaluating the heat transfer perform-

ance of air-heating vaporizer under frosting conditions,

which will help optimizing the structure of vaporizer and

the defrosting time.

6. Acknowledgements

This study was supported by the National Natural Sci-

ence Foundation of China No. 51076061.

REFERENCES

[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,” ASH-

RAE Transactions, Vol. 26, No. 5, 1984, p. 56.

[3] S. M. Sami and T. Duong, “Mass and Heat Transfer dur-

ing 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 Jour-

nal 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 Correla-

tion 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 Deposi-

tion 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 Mathe-

matical 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 Character-

istics and Heat Transfer on a Flat Plate under Freezer Op-

erating Conditions, Part II: Numerical Modeling and

Comparison with Data,” ASHRAE Transactions, Vol. 105,

No. 1, 1999, pp. 252-259.

Copyright © 2013 SciRes. EPE