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An analytical study of frost nucleation and growth during the crystal growth period

Eine analytische Untersuchung der Reifbildung während der Phase des Kristallwachstums

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Abstract

An analytical study was made to clarify the fundamental nature of the early stage of crystal growth period of frost formation phenomena. A suitable model was developed by using the principles of crystallization and nucleation theory. The effect of four dominant parameters of frost formation; plate temperature, air temperature, air humidity ratio and Reynolds number, was studied. Ice crystal density variation with temperature reported by cloud physicists is used in the model to predict the density variation of frost during the crystal growth period. The temperature variation in the frost layer is formulated and vapor diffusion through the frost layer is taken in the consideration.

Zusammenfassung

Die analytische Untersuchung hat das Ziel, den Grundmechanismus zu klären, der die Frühphase des Kristallwachstums bei der Reifbildung regiert. Die entwickelte Modellvorstellung gründet sich auf die Gesetzmäßigkeiten der Kristallisations- und Keimbildungstheorie. Der Einfluß von vier, bezüglich der Reifbildung dominanten Parametern wurde untersucht: Wand- und Lufttemperatur, relative Feuchte der Luft und Reynolds-Zahl. Die aus der Metereologie bekannte Temperaturabhängigkeit der Kristalldichte wird im Modell für die Dichteänderung des Reifes während der Kristallbildungsphase übernommen. Die Temperaturverteilung in der Reifschicht wird unter Berücksichtigung der überlagerten Dampfdiffusion berechnet.

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Abbreviations

A c :

area of frost columns per unit area of frost layer

A v :

area of the void parts per unit area of the frost layer

D :

diffusivity of water vapor in air (m2/s)

h c :

heat transfer coefficient (W/m2K)

h g :

enthalpy of saturated water vapor (J/kg)

h ig :

latent heat of sublimation (J/kg)

k a :

thermal conductivity of moist air (W/mK)

k f :

frost layer thermal conductivity (W/mK)

k fc :

frost column thermal conductivity (W/mK)

l f :

frost layer thickness (m)

m f :

total frost mass per unit area (kg/m2)

\(\dot m\) :

total mass flux per unit area (kg/m2s)

\(\dot m_d \) :

mass diffusion rate of water vapor into the frost layer per unit area of frost layer (kg/m2s)

\(\dot m_s \) :

sublimation rate of water vapor inside the frost layer per unit volume of frost layer (kg/m3s)

P g :

partial pressure of water vapor (kPa)

P 0 :

partial pressure of water vapor atT 0=273.15 K (kPa)

Pr :

Prandtl number

q a :

conduction heat flux through the voids of frost layer (W/m2)

q c :

conduction heat flux through the frost columns (W/m2)

\(\dot q_{surface} \) :

heat flux through frost layer surface per unit of time (W/m2)

Re :

Reynolds number

Sc :

Schmidt number

T a :

air temperature (K)

T c :

crystal temperature (K)

T p :

plate temperature (K)

T s :

frost surface temperature (K)

u i :

internal energy of ice (J/kg)

y :

distance from the plate surface (m)

β:

volumetric ratio of frost columns

β0 :

initial volumetric ratio of frost columns

ρ a :

density of air (kg/m3)

ρ c :

sublimation density of ice crystal (kg/m3)

ρ f :

frost density (kg/m3)

ρ fc :

density of frost column (kg/m3)

ω a :

humidity ratio of moist air

ω s :

humidity ratio of air at frost surface

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Authors and Affiliations

  1. Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, 31261, Dhahran, Saudi Arabia

    A. Z. Şahin (Assistant Professor)

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  1. A. Z. Şahin
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Şahin, A.Z. An analytical study of frost nucleation and growth during the crystal growth period. Heat and Mass Transfer 30, 321–330 (1995). https://doi.org/10.1007/BF01463923

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  • DOI: https://doi.org/10.1007/BF01463923

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