Skip to main content
SpringerLink
Log in

Numerical Modelling of Frost Formation of Flat Surface

  • Original Contribution
  • Published:
Journal of The Institution of Engineers (India): Series C Aims and scope Submit manuscript

Abstract

Frost formation begins when humid air comes in contact with a cold surface kept below freezing temperature of water. Objective of the present study is to develop a numerical model which can predict frost formation parameters such as rate of frost growth, frost densification and to study effect of ambient conditions on these parameters. The one-dimensional pure implicit finite difference method is adopted for solving differential equations. Numerical code is written in MATLAB 2013. The proposed numerical model is validated against two independent published experimental data with 6.6 and 16.8% deviation. Effect of ambient parameters like wall temperature, ambient temperature, humidity and Reynolds number on frost growth and densification are investigated. Also effect of variable wall temperature and variable ambient temperature on frost growth rate is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Abbreviations

cp :

Specific heat at constant pressure

Co:

Convergence criteria

dh :

Characteristic length

D:

Molecular diffusion coefficient

h:

Heat transfer coefficient

hm :

Mass transfer coefficient

H:

Thickness of frost

k:

Thermal conductivity

L:

Latent heat

Le:

Lewis number

m:

Mass flux

M:

Molecular weight

Nu:

Nusselt number

P:

Pressure

Pr:

Prandtl number

q:

Heat flux

R:

Universal gas constant

Re:

Reynolds number

t:

Time

T:

Temperature

v:

Velocity

x:

Space coordinate

x’:

Distance from leading edge

ε:

Porosity

ρ:

Density

τ:

Tortuosity factor

ω:

Specific humidity

a:

Air

Cond:

Conduction

Conv:

Convective

d:

Diffused

eff:

Effective

fr:

Frost

fs:

Frost surface

i:

Ice

ini:

Initial

lat:

Latent

sat:

Saturated

sub:

Sublimation

svi:

Saturated vapor over ice

t:

Total

th:

Contributed to frost layer growth

v:

Water vapor

w:

Wall

\(\infty\) :

Ambient

g:

Guessed value

j:

Time coordinate

References

  1. Y. Hayashi, A. Aoki, S. Adachi, K. Hori, Study of frost properties correlating with frost formation types. J. Heat Transf. 99, 239–245 (1977)

    Article  Google Scholar 

  2. P.L.T. Brian, R.C. Reid, Y.T. Shah, Frost deposition on cold surfaces. Int. J. Heat Mass Transf. 9(3), 375–380 (1970)

    Google Scholar 

  3. B.W. Jones, J.D. Parker, Frost formation with varying environmental parameters. J. Heat Transf. 97, 255–259 (1975)

    Article  Google Scholar 

  4. Y.X. Tao, R.W. Besant, K.S. Rezkallah, A mathematical model for predicting the densification and growth of frost on a flat plate. Int. J. Heat Mass Transf. 36, 353–363 (1993)

    Article  Google Scholar 

  5. R. Le Gall, M. Grillot, C. Jallut, Modeling of frost growth and densification. Int. J. Heat Mass Transf. 40, 3177–3187 (1997)

    Article  Google Scholar 

  6. M. Fossa, G. Tanda, Study of free convection frost formation on a vertical plate. Exp. Therm. Fluid Sci. 26, 661–668 (2002)

    Article  Google Scholar 

  7. B. Na, R.L. Webb, New model for frost growth rate. Int. J. Heat Mass Transf. 47(5), 925–936 (2004)

    Article  Google Scholar 

  8. Y.B. Lee, S.T. Ro, Analysis of the frost growth on a flat plate by simple models of saturation and supersaturation Exp. Therm. Fluid Sci. 29, 685–696 (2005)

    Article  Google Scholar 

  9. K.-H. Kim, H.-J. Ko, K. Kim, Y.-W. Kim, K.-J. Cho, Analysis of the frost growth on a flat plate by simple models of saturation and supersaturation. Appl. Therm. Eng. 29, 2072–2079 (2009)

    Article  Google Scholar 

  10. M. Kandula, Frost growth and densification in laminar flow over flat surfaces. Int. J. Heat Mass Transf. 54, 3719–3731 (2011)

    Article  Google Scholar 

  11. C. Hermes, An analytical solution to the problem of frost growth and densification on flat surfaces. Int. J. Heat Mass Transf. 55, 7346–7351 (2012)

    Article  Google Scholar 

  12. R.F. Barron, L.S. Han, Heat and mass transfer to a cryosurface in free convection. J. Heat Transf. 87(4), 499–506 (1965)

    Article  Google Scholar 

  13. R. Ostin, S. Anderson, Frost growth parameters in a forced air stream. Int. J. Heat Mass Transf. 34(4/5), 1009–1017 (1991)

    Article  Google Scholar 

  14. Q. Kaiyang, S. Komori, Y. Jiang, Local variation of frost layer thickness and morphology. Int. J. Therm. Sci. 45, 116–123 (2006)

    Article  Google Scholar 

  15. M. Amini, A. Pishevar, M. Yaghoubi, Experimental study of frost formation on a fin-and-tube heat exchanger by natural convection. Int. J. Refrig. 46, 37–49 (2014)

    Article  Google Scholar 

  16. H.W. Schneider, Equation of the growth rate of frost forming on cooled surfaces. Int. J. Heat Mass Transf. 21, 1019–1024 (1978)

    Article  Google Scholar 

  17. M.M. Padki, S.A. Sherif, R.M. Nelsson, A simple method for modeling the frost formation phenomenon in different geometries. ASHRAE Trans. 95(2), 1127–1137 (1992)

    Google Scholar 

  18. H Auracher, Effective thermal conductivity of frost, in International Symposium of Heat and Mass Transfer in Refrigeration Cryogenics, Dubrovnik, pp. 285–302 (1986)

  19. ASHRAE Handbook Fundamentals 2005, (ASHRAE, Atlanta, 2005) 5.2

  20. D.M. Murphy, T. Koop, Review of the vapour pressures of ice and super cooled water for atmospheric applications. Q. J. R. Meteorol. Soc. 131, 1539–1565 (2005)

    Article  Google Scholar 

  21. B. Na, R.L. Webb, A fundamental understanding of factors affecting frost nucleation. Int. J. Heat Mass Transf. 46, 3797–3808 (2003)

    Article  Google Scholar 

Download references

Acknowledgements

The support for this research work from the design department of INOXCVA, Kalol, Gujarat, India is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, A D Patel Institute of Technology, Anand, 388121, Gujarat, India

    Tapan Rohitbhai Dave, Mitesh Ishvarlal Shah & Vishal N. Singh

Authors
  1. Tapan Rohitbhai Dave
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mitesh Ishvarlal Shah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vishal N. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mitesh Ishvarlal Shah.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dave, T.R., Shah, M.I. & Singh, V.N. Numerical Modelling of Frost Formation of Flat Surface. J. Inst. Eng. India Ser. C 99, 531–538 (2018). https://doi.org/10.1007/s40032-017-0364-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40032-017-0364-z

Keywords

Search

Navigation