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For drag flow the velocity gradient is given by
Equation 3.49 can now be written as
If the temperature of the upper plate is T1 and that of lower plate is T0, the temperature
profile of the melt is obtained by integrating Equation 3.51. The resulting expression is
(3.52)
As shown in Section 4.2.3, this equation can be used to calculate the temperature of the
melt film in an extruder.
3.4 Dimensionless Groups
Dimensionless groups can be used to describe complicated processes that are influenced
by a large number of variables with the advantage that the entire process can be analyzed
on a sound basis by means of a few dimensionless parameters. Their use in correlating
experimental data and in scaling-up of equipment is well known.
Table 3.2 shows some of the dimensionless groups often used in plastics engineering.
Table 3.2 Dimensionless Groups
Symbol
Bi
Br
Deb
F0
Gr
Gz
Le
Na
Nu
Pe
Pr
Re
Sh
Sc
Sk
Name
Biot number
Brinkman number
Deborah number
Fourier number
Grashof number
Graetz number
Lewis number
Nahme number
Nusselt number
Peclet number
Prandtl number
Reynolds number
Sherwood number
Schmidt number
Stokes number
Definition
a Xl Xx
7]w 2 1 (AAT)
at It
g/3-ATflv
l 2 l(a-tv)
aid
/3T W 2 T] IX
all X
wll a
v I a
pwll T]
PJIS
vlS
P-II(T]-W)
(3.50)
(3.51)