Abstract
The differential equations describing heat and mass transfer during each stage of defrost are solved, and results are compared to measurement. Numerical solutions for defrost Stages I and II are obtained, while an analytical solution for Stage III is possible. For Stage I, the duration of the stage is predicted and validated by experiment. For Stage II, melt front and duration of the stage are predicted and in good agreement with measurement. For Stage III, the solution under predicts defrost time but generally simulating the general trends for duration seen in the experiments. We conclude with a graphical summary that indicates that further research is needed for measurements with greater super saturation and subcooling.
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Abbreviations
- Bi:
-
Biot number, hδ/kf
- C1, C2 :
-
Constants (6.6)
- h:
-
Heat transfer coefficient (W/m2Â K)
- k:
-
Thermal conductivity (W/m K)
- Le3 :
-
Lewis number for Stage III
- Q:
-
Heat transfer (W)
- S:
-
Water content (–)
- St3 :
-
Stephan number for Stage III (3.73)
- t:
-
Time (s)
- u:
-
Convective velocity of the melt stream (3.16)
- U:
-
Dimensionless velocity of frost thickness in Stage II (–)
- δ:
-
Frost thickness (m)
- ε:
-
Porosity (–)
- Γ1 :
-
Inverse of Lewis and Stephan number product for Stage I, 1/LeSt (3.39)
- Γ3 :
-
Inverse of Lewis and Stephan number product for State III (3.73)
- η:
-
Dimensionless thickness, y/δ0
- ηd :
-
Efficiency (6.1)
- ηi :
-
Dimensionless frost thickness in Stage II (6.3)
- λif :
-
Latent heat of fusion (J/kg)
- θ:
-
Dimensionless temperature (T − Ts)/(Tm − Ts)
- Ï„:
-
Dimensionless time, αft/δ 20
- 0:
-
Initial time
- 1,2,3:
-
Denoting the defrost stage
- a:
-
Ambient
- c:
-
Critical value
- f:
-
Frost
- fs:
-
Frost surface
- s:
-
Surface
- w:
-
Water
- m:
-
Integration step
Reference
Mohs WF (2013) Heat and mass transfer during the melting process of a porous frost layer on a vertical surface. Doctoral dissertation, Universality of Minnesota, Minneapolis
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Mohs, W.F., Kulacki, F.A. (2015). Solution of Defrost Model. In: Heat and Mass Transfer in the Melting of Frost. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-20508-3_6
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DOI: https://doi.org/10.1007/978-3-319-20508-3_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-20507-6
Online ISBN: 978-3-319-20508-3
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