Abstract
When polymer melts flow through narrow channel or small-orifice dies, highly unsteady or irregular flow have sometimes been observed even when the imposed boundary conditions are steady and uniform (Pearson, 1969).
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Abbreviations
- b :
-
rheological parameter of the fluid defined by eq.[4]
- B :
-
dimensionless viscosity-temperature parameter defined by eq. [11]
- C :
-
rheological parameter defined by eq. [4]
- h :
-
distance between the two parallel plates, ft.
- H :
-
a thermal transfer coefficient (1/h)
- l :
-
length of the plates, ft.
- p :
-
pressure
- P :
-
inlet pressure
- Gz :
-
Graetz number defined by eq. [11]
- t :
-
time, h
- T :
-
mean temperature as defined by eq. [2]
- T 1 :
-
inlet temperature
- u :
-
velocity vector with u x, u y, u z as component velocities
- v :
-
mean velocity vector as defined by eq. [1]
- V :
-
mean steady state axial velocity
- x y, z :
-
Cartesian coordinate system
- w :
-
refers to wall condition
- α:
-
thermal diffusivity, ft2/h
- A:
-
effective thermal diffusivity tensor
- ξ:
-
dimensionless x coordinate
- λ:
-
wave number in y direction
- Λ :
-
dimensionless wave number in y direction
- μ0 :
-
viscosity of fluid
- ϱ:
-
density of fluid
- Ψ:
-
dimensionless velocity in x direction
- ω:
-
growth rate of disturbances
- Ω:
-
dimensionless growth rate
- \(\mathop K\limits^ - \) :
-
proportionality constant for heat generation in eq.[5]
References
Pearson, J. R. A., Plastics and Polymers 37, 285 (1969).
Pearson, J. R. A. and Y. T. Shah, Stability of Non-Isothermal Flow in Channels (Paper aceepted by Chem. Eng. Sci.).-Pearson, J.R. A., Mechanical Principles of Polymer Melt Processing, p. 60 (Oxford, England, 1966).
Martin, B., Intl. J. Non-Linear Mech. 2, 285 (1967).
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© 1975 Springer-Verlag Berlin Heidelberg
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Pearson, J.R.A., Shah, Y.T. (1975). On the stability of non-isothermal flow in channels. In: Vallet, G., Meskat, W. (eds) Rheological Theories · Measuring Techniques in Rheology Test Methods in Rheology · Fractures Rheological Properties of Materials · Rheo-Optics · Biorheology. Steinkopff, Heidelberg. https://doi.org/10.1007/978-3-662-41458-3_28
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DOI: https://doi.org/10.1007/978-3-662-41458-3_28
Publisher Name: Steinkopff, Heidelberg
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