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Freeze-coating on a continuous moving sheet and on an axially moving cylinder

Erstarrungs-Beschichtung einer kontinuierlich bewegten Platte und eines axial bewegten Zylinders

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Abstract

This paper considers one-dimensional heat transfer model for the freeze-coating of a polymeric substance on a continuously moving sheet and on an axially moving cylinder. Analytical expressions are obtained for the freeze-coat thickness; also presented the solutions for an upper bound on the thickness of the frozenlayer using thermodynamic equilibrium conditions. Effect of Stefan number on freeze-coat thickness is briefly discussed and also the application of the present results with an example.

Zusammenfassung

Diese Arbeit behandelt ein eindimensionales Modell für den Wärmeübergang bei der Erstarrungs-Beschichtung mit einem Polymer an einer kontinuierlich bewegten Platte und an einem axial bewegten Zylinder. Für die Schichtdicke werden analytische Ausdrücke angegeben; auch die Lösung für die obere Grenze der erstarrten Schichtdicke bei thermodynamischem Gleichgewicht wird mitgeteilt. Der Einfluß der Stefan-Zahl auf die Schichtdicke wird kurz diskutiert. Die Anwendungen der Ergebnisse werden an einem Beispiel gezeigt.

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Abbreviations

Cp :

Specific heat of solid layer, J/Kg°C

J0,J1 :

Bessel function of first kind, zero and first order

k:

thermal conductivity of solid-layer, J/sec-m-°C

L:

latent heat of fusion, J/kg

Pr:

Prandtl Number, ν/α

r:

normalized distance within the solidified layer, R/R0

R:

radial coordinate measured from the surface of the cylinder, m

Re:

Reynolds Number, UR0/ν

S:

Interface location, Rf/R0

Ste:

Stefan Number, Cp (Tf-T0)/L

T:

temperature within the frozen-layer, °K

U:

velocity of the object moving through the liquid, m/sec

x:

axial coordinate, m

y:

distance from the object surface, m

Z:

dimensionless axial distance, (x/R0)Re.Pr

α :

thermal diffusivity of solid-layer, m2/sec

δ:

thickness of solid layer, m

η:

similarity variable, y/(U/4νx)1/2

ηs :

value of η at y=σ

ϕ:

dimensionless temperature, (T-Tf)/(T0 -Tf)

ν:

kinematic viscosity of liquid, m2/sec

νm :

positive roots of J0(νm)=0

ρ:

density of solid-layer, kg/m3

0:

object

f:

freezing-front

m:

object material

s:

solid phase

ss:

steady-state

References

  1. Bourne, D.E.; Dixon, H.: The Cooling of fibres in the formation process. Intern. J. Heat and Mass Transfer 14 (1971) 1323

    Google Scholar 

  2. Elmas, M.: On heat transfer with moving boundary. Intern. J. Heat and Mass Transfer 13 (1970) 1625

    Google Scholar 

  3. Gutfinger, C.; Chen, C.H.: Heat transfer with a moving boundary application to fluidized bed coating. Intern. J. Heat and Mass Transfer 12 (1969) 1097

    Google Scholar 

  4. Gutfinger, C.; Chen, C.H.: An approximate theory of fluidized bed coating. Chem. Engng. Prog. Symp. Ser. 101 (1970) 91

    Google Scholar 

  5. Caretaker, R.P.: Dip forming — a continuous casting process. Journal of metals 15 (1963) 774

    Google Scholar 

  6. Carslaw, H.C.; Jaeger, J.C.: Conduction of Heat in Solids, pp. 282–296. Oxford: Clarendon Press 1959

    Google Scholar 

  7. Stammers, E.; Beek, W.J.: Polymer Engng. Sci. 9 (1969) 49

    Google Scholar 

  8. Griftin, O.M.: Heat Transfer to molten polymers. Polymer Engng. Sci. 12 (1972) 2

    Google Scholar 

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Authors and Affiliations

  1. Indian Institute of Technology, 600 036, Madras, Indien

    R. V. Seeniraj (Research Scholar) &  T. K. Bose (Prof. of Aeronautical Engineering)

Authors
  1. R. V. Seeniraj
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  2. T. K. Bose
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Seeniraj, R.V., Bose, T.K. Freeze-coating on a continuous moving sheet and on an axially moving cylinder. Wärme- und Stoffübertragung 15, 239–243 (1981). https://doi.org/10.1007/BF01003644

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  • DOI: https://doi.org/10.1007/BF01003644

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