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Numerical Modelling of Frost Formation of Flat Surface

  • Tapan Rohitbhai Dave
  • Mitesh Ishvarlal Shah
  • Vishal N. Singh
Original Contribution
  • 135 Downloads

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.

Keywords

Frost growth Frost densification Heat and mass transfer Numerical modelling 

Notations

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

Subscripts

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

Superscripts

g

Guessed value

j

Time coordinate

Notes

Acknowledgements

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

References

  1. 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)CrossRefGoogle Scholar
  2. 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. 3.
    B.W. Jones, J.D. Parker, Frost formation with varying environmental parameters. J. Heat Transf. 97, 255–259 (1975)CrossRefGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. 5.
    R. Le Gall, M. Grillot, C. Jallut, Modeling of frost growth and densification. Int. J. Heat Mass Transf. 40, 3177–3187 (1997)CrossRefGoogle Scholar
  6. 6.
    M. Fossa, G. Tanda, Study of free convection frost formation on a vertical plate. Exp. Therm. Fluid Sci. 26, 661–668 (2002)CrossRefGoogle Scholar
  7. 7.
    B. Na, R.L. Webb, New model for frost growth rate. Int. J. Heat Mass Transf. 47(5), 925–936 (2004)CrossRefGoogle Scholar
  8. 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)CrossRefGoogle Scholar
  9. 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)CrossRefGoogle Scholar
  10. 10.
    M. Kandula, Frost growth and densification in laminar flow over flat surfaces. Int. J. Heat Mass Transf. 54, 3719–3731 (2011)CrossRefGoogle Scholar
  11. 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)CrossRefGoogle Scholar
  12. 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)CrossRefGoogle Scholar
  13. 13.
    R. Ostin, S. Anderson, Frost growth parameters in a forced air stream. Int. J. Heat Mass Transf. 34(4/5), 1009–1017 (1991)CrossRefGoogle Scholar
  14. 14.
    Q. Kaiyang, S. Komori, Y. Jiang, Local variation of frost layer thickness and morphology. Int. J. Therm. Sci. 45, 116–123 (2006)CrossRefGoogle Scholar
  15. 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)CrossRefGoogle Scholar
  16. 16.
    H.W. Schneider, Equation of the growth rate of frost forming on cooled surfaces. Int. J. Heat Mass Transf. 21, 1019–1024 (1978)CrossRefGoogle Scholar
  17. 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. 18.
    H Auracher, Effective thermal conductivity of frost, in International Symposium of Heat and Mass Transfer in Refrigeration Cryogenics, Dubrovnik, pp. 285–302 (1986)Google Scholar
  19. 19.
    ASHRAE Handbook Fundamentals 2005, (ASHRAE, Atlanta, 2005) 5.2Google Scholar
  20. 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)CrossRefGoogle Scholar
  21. 21.
    B. Na, R.L. Webb, A fundamental understanding of factors affecting frost nucleation. Int. J. Heat Mass Transf. 46, 3797–3808 (2003)CrossRefGoogle Scholar

Copyright information

© The Institution of Engineers (India) 2017

Authors and Affiliations

  • Tapan Rohitbhai Dave
    • 1
  • Mitesh Ishvarlal Shah
    • 1
  • Vishal N. Singh
    • 1
  1. 1.Department of Mechanical EngineeringA D Patel Institute of TechnologyAnandIndia

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