Advertisement

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).

Abbreviations

Notation

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]

T1

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

xy, z

Cartesian coordinate system

Subscript

w

refers to wall condition

Greek symbols

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]

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Pearson, J. R. A., Plastics and Polymers 37, 285 (1969).Google Scholar
  2. 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).Google Scholar
  3. Martin, B., Intl. J. Non-Linear Mech. 2, 285 (1967).ADSCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • J. R. A. Pearson
    • 1
  • Y. T. Shah
    • 2
  1. 1.Department of Chemical EnginneringUniversity of PittsburghPittsburghUSA
  2. 2.Department of Chemical EngineeringChemical Technology Imperial CollegeLondonUK

Personalised recommendations