Abstract
A mathematical model is obtained for the process of cooling with formation of a planar film. The solution obtained is verified experimentally.
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Abbreviations
- Γ:
-
mean axial velocity gradient
- vx :
-
current axial velocity
- vo :
-
initial polymer velocity
- v1 :
-
sampling velocity
- K:
-
draw ratio
- \(\{ \dot \gamma \} \) :
-
deformation rate tensor
- x, y, z:
-
spatial coordinates
- X, Y:
-
dimensionless coordinates
- L(Θ):
-
differential operator
- T:
-
temperature
- To :
-
initial temperature
- Tc :
-
temperature of surrounding medium
- Θ:
-
dimensionless temperature
- \(\bar \Theta \) :
-
dimensionless temperature averaged over film thickness
- α :
-
thermal-diffusivity coefficient
- 2δo :
-
initial film thickness
- λ:
-
thermal conductivity
- α:
-
heat-transfer coefficient
- f(X):
-
distance function
- Bi:
-
Biot criterion, Bio, Biot criterion calculated for initial film thickness
- Gz*:
-
modified Graetz criterion
- V:
-
dimensionless velocity
- α1, α2, α3 :
-
heat-transfer coefficients produced by radiation, free convection, and forced convection
- vc, δc :
-
mean velocity and film half-thickness in formation zone
- T1 :
-
calculated temperature value
- T2 :
-
experimental temperature value
- l :
-
formation zone length
Literature cited
L. A. Polovikhina, Khim. Volokna, No. 4 (1972).
N. V. Tyabin et al., Plast. Massy, No. 4 (1977).
V. G. Litvinov, Mekh. Polim., No. 2 (1967).
L. V. Kantorovich and V. I. Krylov, Approximate Methods in Higher Analysis [in Russian], Fizmatgiz, Moscow (1962).
A. V. Lykov, Izv. Akad. Nauk SSSR, Énerg. Transport, No. 5 (1970).
P. V. Tsoi, Methods for Calculation of Individual Heat- and Mass-Transfer Problems [in Russian], Énergiya, Moscow (1971).
M. A. Mikheev and I. M. Mikheeva, Fundamentals of Heat Transfer [in Russian], Énergiya, Moscow (1977).
A. V. Lykov, Heat and Mass Transfer (Handbook) [in Russian], Energiya, Moscow (1971).
W. Predöhl, Kunststoffe,61, No. 7 (1971).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 854–858, November, 1979.
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Shapovalov, V.M., Tyabin, N.V. & Ivashchenko, S.K. Heat transfer in plane film formation. Journal of Engineering Physics 37, 1322–1325 (1979). https://doi.org/10.1007/BF01102229
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DOI: https://doi.org/10.1007/BF01102229