Kutz M. Handbook of materials selection
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1016 PLASTIC PARTS PROCESSING II
Operating conditions to be specified include initial flow rate, melt tempera-
ture, reactor yield, pressures, screw speed, vent/additive/rework flowrates, and
zone temperatures. Physical property data required are density, viscosity, heat
capacity, heat of vaporization, and monomer vapor pressure and temperature.
The program calculates the volumetric flowrate, temperature distributions, and
power consumption. Prior work on this modeling effort was done by Hudson
44
;
Richardson
45
had previously modeled a similar partially intermeshing twin-screw
extruder.
5 WIRE COATING
Constants and Definitions
A
⫽
PR/
1/2
1
–
2
a
1
⫽
c(

2
⫺ 1 ⫺ ln

2
)
1
–
2
a
2
⫽
c(

2
⫺ 1 ⫺

2
ln

2
)
1
–
2
B ⫽ R
0
1/2
b ⫽
c ln

2
⫹ c
␣
(

␣
⫺
1
⫺ 1)/(
␣
⫺ 1)
1
–
2
C ⫽ [A(1 ⫺ k
2
) ⫺ v /B]/ln k
2
c ⫽ [b ⫺ c
␣
(

␣
⫺
1
⫺ 1)/(
␣
⫺ 1)]/ln

, which is implicit in c
c
ED
⫽
{a
1
c ⫹ [2c
␣
/(
␣
⫺ 1)][(

2
⫺

␣
⫺
1
)/(3 ⫺
␣
) ⫺ (

2
⫺ 1)]}(
m
/
s
)
1
–
2
c
E3D
⫽ [(a
1
c ⫺ c
3
a
2
)/b](
m
/
s
)
c
ND
⫽ [(

2
⫺1)/ln(

2
)](
m
/
s
)
c
PLD
⫽ {(

2
⫺ 1)/(1 ⫺

(1
⫺
n)/n
) ⫹ [2n/(3n ⫺ 1)](1 ⫺

(3n
⫺
1) / n
)}(
m
/
s
)
D
⫽ Diameter of the die
d
⫽ Diameter of the wire
k
⫽ (d/D) ⬍ 1
P
⫽ Pressure in the melt, upstream of the die
R
⫽
Radius of the die ⫽ D
1
–
2
v ⫽ Velocity of the wire

⫽ (1/k) ⫽ (D/d) ⬎ 1
␦
⫽ Thickness of the coating
0
⫽ Zero-shear-rate-limit viscosity of the melt
⫽
22
兹(1 ⫺ k )/ln (

)
m
⫽ Density of the polymer melt
s
⫽ Density of the solidified coating
1/2
⫽ Ellis model parameter
In the usual wire coating operation, a metal wire is drawn through a polymer
melt and the combined product passes through a die; the polymer is subsequently
solidified around the wire to provide a suitable electrical insulation. An extruder
upstream provides a sufficient quantity of polymer melt.
As mentioned earlier, this process is an example of drag flow; the momentum
of the moving wire is transferred to the polymer, causing it flow through the
die. The first normal stress function of the melt keeps the wire centered within
the surrounding polymer. Convective heat transfer from the ambient air removes
the latent heat of fusion of the polymer, and the solidified product is wound on
spindles for distribution.
5 WIRE COATING 1017
5.1 Drag Flow Only
For drag flow only, the melt pool must come from a reservoir that is uninfluenced
by the upstream extruder. When one solves this problem for drag flow of a
Newtonian melt, a very limiting solution is obtained: the thickness of the coating
is a function of the die and wire dimensions only!
兹1 ⫹ c
␦
ND
⫽⫺1 (5.1)
d 2
In one sense, this solution is appealing: The thickness is predicted to be inde-
pendent of wire speed, polymer melt properties, temperature, etc. However,
knowing that process upsets will occur, this result gives no indication of how to
control the coating thickness. And, only one product can be made for a given
die and wire; there is no process flexibility.
For a power law fluid (see Section 2.2),
兹1 ⫹ c
␦
PLD
⫽⫺1 (5.2)
d 2
Boese
46
has solved these problems for an Ellis fluid (see Section 2.2), using
the assumption that
s
⬇
m
; the equations given here do not make that as-
sumption. Three cases exist:
␣ ⫽ 1 is the Newtonian solution, Eq. (5.1);
␣
⫽ 1
or 3 is the general Ellis case; finally,
␣
⫽ 3 is a special Ellis case. For
␣
⫽ 1
or 3,
兹1 ⫹ c ⫺ 1
␦
ED
⫽ (5.3)
d 2
For
␣
⫽ 3, (5.4)
兹1 ⫹ c ⫺ 1
␦
E3D
⫽
d 2
5.2 Drag and Pressure Flow
To overcome the limitations of drag flow only, pressure flow is added by causing
the pressure in the melt pool to be that developed by the extruder. Now, the
coating thickness is a function of variables that provide a means of process
control and a variety of products from a given wire and die.
There are two possible situations. If the maximum velocity of the melt around
the wire is that of the wire, then drag flow is controlling, even though pressure
flow is present. If, however, the maximum velocity in the melt occurs between
the wire and the die, then pressure flow is controlling, even though drag flow is
present.
For drag flow controlling,
1018 PLASTIC PARTS PROCESSING II
␦
BA
24 222 2
⫽ (1⫺ 2k ⫹ k ) ⫹ C(1 ⫹ k ln k ⫺ k ) ⫹ k ⫺ k (5.5a)
冋冉 冊 册
冪
R v 2
For pressure flow controlling,
2224
␦
AB 1 ⫺ 4
⫹ 4
k ⫺ k
42 2
⫽⫹
ln k ⫹
⫺ k (5.5b)
冉冊
冪
R v 2
These equations are expressed in terms of the Boese
46
parameters to facilitate
the use of his graphical results.
6 CALENDERING
Constants and Definitions
F
⫽ Force trying to separate the second and third rolls of a three-roll stack
H
⫽ Thickness of the calendered sheet
H
ƒ
⫽ Thickness of the melt fed between the second and third rolls
H
0
⫽ Closest approach distance between the second and third rolls, the nip
P
⫽ Pressure within the melt
Q
⫽ Volumetric flowrate of the calendered sheet
R
⫽ Radius of the rolls
T
⫽ Temperature within the melt
V
⫽ Tangential velocity of the second and third roll surfaces
W
⫽ Width of the calendered sheet
x
⫽ Distance from the nip, in the direction in which the sheetis being calen-
dered
X
⫽ Dimensionless ‘‘distance’’ measured from the nip, x /兹(Rh )
0
⫽ Dimensionless ‘‘distance’’ where the calendered sheet leaves the rolls
In calendering, an extruder supplies a sheet of polymer melt of width W that
is placed on top of a heated clockwise-rotating cylinder, a roll. Below this is a
second roll, rotating counterclockwise; if it rotates slightly faster than the first,
the melt will leave the first and follow the second. Finally, there is a clockwise-
rotating third roll. The sheet passes between the latter two, whose line of closest
approach is called the nip.
Within the region where the sheet contacts both the second and third rolls,
the pressure within the melt rises and falls; this must be the case, since the
upstream and downstream pressures are ultimately ambient. Although calender-
ing contains drag and pressure flow, the former dominates; the melt receives its
momentum primarily from the metal rolls.
To produce a uniform thickness across the width of the sheet, the axes of the
rolls need to be skewed; the gap between the rolls needs to be smaller in the
middle of the sheet and larger at the sides. This, again, is a requirement due to
the normal stress functions of the polymer.
Ewing
47
derived the equations that relate the thickness of a calendered sheet
to the processing variables for the isothermal processing of a Newtonian melt,
7 FIBER SPINNING: MELT 1019
a power law fluid, a Bingham plastic, and special case (n ⫽ 0.5) of the Cross
model (see the generalized Yasuda model in Section 2.2). For a Newtonian melt,
2
H ⫽ (1 ⫹
)H (6.1)
0
If the feed to the last pair of rolls is unlimited in thickness, then
⫽ 0.47513;
hence,
H
⫽ 1.2257H (6.2)
0
If, however, the feed to the last pair of rolls is finite, and not much different
than the nip, then
is a function of that thickness. The results show that
decreases significantly for H
ƒ
/H
0
⬍ 10.
Although simple, these results are disturbing because they predict that the
thickness of the calendered sheet is independent of everything but the gap be-
tween the last two ‘‘finishing’’ rolls. If true, then the only way to control the
thickness of the product to be sold is to control the position of these large fast-
rotating rolls of metal.
Since ‘‘real’’ melts are non-Newtonian and possess normal stress functions
(see Section 2.2), these forces try to separate the rolls; hence, control of the
thickness of the calendered sheet is best accomplished by adjusting the ‘‘roll
separating force’’ rather than the size of the nip.
For a shear-thinning power law fluid, 0.47513
⬍
⬍ 0.522 and 1.2257 ⬍
H/H
0
⬍ 1.295 as 1 ⬎ n ⬎ 0.2, respectively.
For the Cross model, the equations were ‘‘unsolvable’’ except for the special
case of n
⫽ 0.5. For the Bingham plastic, a solid plug exists in the feed, between
the rolls, and (of course) as the calendered sheet. The last region exists not
because the sheet has solidified but because the shear stress is less than
0
.An
example shows that disjoint regions of the shear-thinned melt may exist between
the feed and the nip; these are separated by a solid plug.
PART II. Continuous Processes: Extension Dominated
7 FIBER SPINNING: MELT
Fiber spinning processes include melt, dry, and wet. In melt spinning, a polymer
melt is extruded through a spinneret and the strands are cooled and solidified in
air; heat transfer is the only transport phenomenon. In dry spinning, a polymer
solution is extruded and the solvent is evaporated to produce solid strands; here,
both heat and mass transfer are involved. In wet spinning, a solution is extruded
and the solidification involves mass transfer of the solvent from the strands in
a coagulation process; hence, mass transfer to and from the fiber occurs.
McMackin
48
developed and compared empirical models for melt spinning,
using experimental data from an industrial laboratory. She developed 12 models
for poly(ethylene-terephthalate), which describe how stick point, tension, and
denier per filament (dpf) vary with melt temperature, winder speed, and pump
speed. The parametric variables were spinneret hole size and intrinsic viscosity
(which was used to characterize the polymer, even though this was melt, not dry
or wet, spinning).
1020 PLASTIC PARTS PROCESSING II
McMackin
48
concluded that (1) stick point depended primarily on pump
speed, (2) tension depended primarily on winder speed, and (3) dpf was influ-
enced by pump speed, winder speed, their interaction, and melt temperature.
8 FILM BLOWING
Constants and Definitions
A
n
⫽ Multiplicative constant of I
1
in the infinite series
B
n
⫽ Multiplicative constant of K
1
in the infinite series
c
⫽ (Q
ann
/
V
F
)(
m
/
s
)
I
1
⫽ Modified first-order Bessel function of the first kind
K
1
⫽ Modified first-order Bessel function of the second kind
P
⫽ Pressure of the air inside the bubble
r
⫽ Radial position within the film
R
⫽ Outside radius of the film at z
R
D
⫽ Outside radius of the die
R
F
⫽ Outside radius of the film at the frost line
V
D
⫽ Average velocity of the melt at the exit of the die
V
F
⫽ Constant velocity of the solid film at the frost line
z
⫽ Axial position; z ⫽ 0 at the die
Z
F
⫽ Axial position of the frost line
␦
⫽ Thickness of the film
␦
F
⫽ Thickness of the film at the frost line
⫽ Inside radius of the annular die/R
D
m
⫽ Density of the polymer melt
s
⫽ Density of the solidified film
⫽ Stream function
Film blowing is the process whereby a relatively thick-walled small-radius
annulus is converted into a relatively thin-walled large-radius annulus. The poly-
mer melt is extruded from an annular die containing a center hole through which
air pressure provides the source of momentum to expand the polymer film.
Outside air-cooling causes the molten film to solidify; this occurs at the frost
line. The solid film is collapsed and drawn through nip rollers, which maintain
the pressure (with little-to-no air leakage).
A material balance between the die and the frost line leads to the relationship
2
1 RV
DD
2
␦
⫽ (1 ⫺
) (8.1)
冋册
F
2 RV
FF
Hence, to make a bag with a given circumference (or a flat sheet with a given
width), 2
R
F
, and a specified thickness,
␦
F
, from a given die (with dimensions
R
D
and
R
D
), the extruder output must be
22
Q ⫽ (1 ⫺
)RV (8.2)
die DD
the same relationship as for the extrusion of a pipe.
Alternatively,
8 FILM BLOWING 1021
␦
⫽ 1 ⫺ 兹1 ⫺ c (8.3)
R
F
similar to the relations seen for drag-flow wire coating.
Although these results are useful, from them we learn nothing about the shape
of the film nor how its size is related to the rheological properties of the melt
and the pressure inside the bubble.
It is easy to see that a single cosine function,
1
z
R ⫽ (R ⫹ R ) ⫺ (R ⫺ R ) cos (8.4)
冋冉冊册
FD FD
2 Z
F
satisfies the boundary conditions at the die and the frost line. However, it is not
a solution to the equations of motion. This is a two-dimensional flow problem,
which may be expressed in either cylindrical or spherical coordinates:
v
⫽ (v ,0,v ) ⫽ C(r,0,z) (8.5a)
rz
or
v
⫽ (v ,v ,0) ⫽ S(r,
,0) (8.5b)
r
Sukadia
49
modeled the film blowing process using the stream function in
cylindrical coordinates approach (see Section 4.2 of Bird, Stewart, and Light-
foot
1
). In steady-state flow, a constant value of the stream function traces out
the path that an element of the fluid follows—the ‘‘particle path’’; hence,
(r,
z) describes the shape of the film.
⬁
n
rn
rn
z
(r,z) ⫽ rAI ⫹ BK cos (8.6)
冘
冋冉冊 冉冊册冉冊
n 1 n 1
ZZZ
n
⫽
1
FFF
where the A
n
and B
n
are determined from the orthogonality relationships, eval-
uated at the die:
RD
冕
(r,0)I (n
r/Z ) dr
1 F
RD
A ⫽ (8.7)
n
RD
2
冕 r[I (n
r/Z )] dr
1 F
RD
and
RD
冕
(r,0)K (n
r/Z ) dr
1 F
RD
B ⫽ (8.8)
n
RD
2
冕 r[K (n
r/Z )] dr
1 F
RD
provided
1022 PLASTIC PARTS PROCESSING II
RD
n
rn
r
冕 rI K dr⫽ 0 (8.9)
冋 冉 冊册冋 冉 冊册
11
RD
ZZ
FF
for each n. One can see that
(R ,0) ⫽
(R ,Z )
(
R ,0) ⫽
(R ⫺
␦
,Z ) (8.10)
DFF DFF
PART III. Cyclic Processes: Shear Dominated
9 MELT INJECTION MOLDING
Constants and Definitions: Center-Gated Part with Rotational Symmetry
B
⫽ Bottom and wall half-thickness
L
⫽ Wall length
P
⫽ Injection pressure
R
⫽ Bottom radius
R
g
⫽ Gate radius
t
fill
⫽ Cavity fill time
⫽ Newtonian melt viscosity
Melt injection molding is the cyclic analog to extrusion. It uses a similarly
designed screw in a barrel but uses a nozzle instead of a die; this is called the
‘‘press.’’ The mold, called the ‘‘tool,’’ consists of a sprue bushing, runners, gates,
and cavities through which, and into which, the polymer melt is injected in order
to produce the desired part; it has (at least) two halves that, when separated,
allow one to remove the part.
To produce the polymer melt for the molded parts cyclically, instead of con-
tinuously, the screw reciprocates. That is, the screw rotates and moves backward
from the nozzle, producing a polymer melt pool in front the screw called the
‘‘shot.’’ This pool has more than enough melt to make the next part; the excess
must be sufficient to fill the runners, the sprue, as well as providing a cushion
of polymer to prevent the metal screw from banging into the end of the barrel
upon injection.
If the mold is closed and empty, the screw ‘‘rams’’ forward, injecting the
polymer into the tool; it continues to apply pressure, and a little more material,
as the melt in the cool mold solidifies. As soon as the gate of the cavity freezes,
no melt may come out, and the screw may begin its plasticating step of preparing
the next shot. When the part in the cavity is sufficiently cool, such that upon
removal it retains its shape, the mold halves open and the part is ejected. Then,
the mold halves close, and the cycle is repeated.
Richards
50
used a mold that produced a 2 ⫻ 2 in. plaque for Gardner impact
(ASTM D3029) and two Type L tension-impact specimens (ASTM D1822) of
Lexan 141. This was mounted on a highly instrumented 18g Battenfeld injection
molding machine. The injection controls permitted constant velocity injection,
rather than the usual constant pressure injection. The viscosity of the Lexan 141
was fully characterized via capillary rheometry, using an Arrhenius dependence
(see Section 2.3). The density of each plaque was determined via water displace-
ment.
9 MELT INJECTION MOLDING 1023
A complete analytical solution to the plaque filling step was obtained by
dividing the problem into (i) diverging flow in a cylindrical wedge for the fan
gate and initial entry into the plaque cavity, followed by (ii) rectangular flow
between parallel plates for the remainder of the cavity. The resulting velocity
profiles were necessary to determine the shear rate profiles, from which the
viscosities were specified.
Richard’s
50
primary interest was in comparing destructive and nondestructive
properties of the parts in order that the latter might be used instead of the former.
Plaque volume and weight revealed ‘‘global’’ variations in density, part to part.
Optical birefringence revealed local variations within each part due to process
orientation. The attempt to use dielectric properties was unsuccessful because
the electrodes were the same size as the plaque; hence, no detail ‘‘within a part’’
could be obtained.
In preparation for further experimental studies, Moore
51
and Hudson
52
deter-
mined the rheological properties of a single lot of high-density polyethylene
(HDPE). O’Nan
10
used these data to compare the ability of various shear vis-
cosity models to describe the shear rate and temperature dependencies. Peter-
son
53
contributed additional data and correlations using the Arrhenius equation.
Taghizadegan
54
then carried out an extensive experimental study of the ASTM
plaque and tensile bar mold used in the Richards dissertation with the HDPE
characterized by Moore,
51
Hudson,
52
and Peterson.
53
Utilizing a ‘‘composite de-
sign’’ with 16 treatment combinations—eight corners of a cube plus six star
points and a replicated center point—response surface analysis of the data
yielded equations that related processing conditions to part thickness as well as
tensile and impact strength. Then, computer simulations demonstrated the po-
tential effectiveness of employing statistical process control (SPC) as part of a
feedback loop to decrease part-to-part variations. This was an extension of prior
work by the team of Wright,
55
Ralston et al.,
56
Stoll, and Harper. Lee
57
continued
the application of SPC by using the correlations discovered by Taghizadegan.
Henz
58
simulated the cooling phase of the injection-molding process and ver-
ified the model experimentally. He used a finite-element program called C-
COOL, developed by AC Technology of Ithaca, New York (now dba Mold-Flow,
Louisville, Kentucky), to predict the cooling of a rectangular plaque,
21
⫻ 11 ⫻ 0.1 in. The experimental phase used polystyrene and 20% talc-filled
polypropylene. Henz concluded that the predicted temperature distribution in the
part was within 10% of the measured values. The wall temperatures of the mold
were less accurately predicted; he attributed this to some imperfect assumptions
in the software that ‘‘should be . . . easy to remedy.’’
Barbarito
59
showed that the hold pressure affected the impact strength of
thermally aged polycarbonate plaques. Notched Izod specimens were aged in a
silicone oil bath at 110
⬚C, and slow cooled them before testing. For a lower hold
pressure of 250 psi, the ductile-to-brittle transition ran from 10 to 29 min,
whereas, for a higher hold pressure of 1000 psi, this transition was delayed as
long as 40 min. The average transition times were 15.3 and 16.2 min for the
low and high values, respectively.
In Section 3 the work of Cecil
42
was cited to point out that reprocessing
material, as in the pelletizing and reuse of the sprue and runners, can affect the
properties of the final parts. Experimental studies with total recycling of molded
parts are often used to determine the percentage of acceptable regrind. That is:
1024 PLASTIC PARTS PROCESSING II
(1) Properties of a sample of the first ‘‘virgin’’ parts are measured; (2) all of the
remaining parts are pelletized and remolded for, perhaps, five cycles, and the
properties of a sample of these parts are measured; (3) step 2 is repeated; etc.
Then, these measurements are plotted versus the number of cycles; when the
data fall below those which are acceptable, the corresponding number of cycles
is the percentage of permissible regrind.
Benkert
60
has derived an equation for the fill time of the isothermal injection
molding of a solid-walled center-gated part with rotational symmetry, using a
Newtonian melt under constant pressure:
2
2
2
1 ⫺ (R /R)
3
R (L/R) L 1 R
g
t ⫽⫹⫹ln ⫺ (9.1)
冉冊冋 冉 冊 冉冊 册
fill
PB 2 R 2 R 4
g
The cavity for a 6.5-lb conical waste receptacle, made of plasticized
poly(vinyl chloride), with a maximum diameter of 15.5 in. and a height of 30
in. requires about 10 s to fill.
The selection of a machine to accomplish this task requires one to specify
the following recommended heuristics for the ‘‘press’’:
1. The clamping force (tons) shall exceed two times the projected area of
the part (in.
2
). (Note: The relationship between these two magnitudes
actually depends on the first normal stress function; see Section 2.2.
When sufficient data for
⌿
1
are available for a number of polymers, this
heuristic will be improved.)
2. Shot size and plasticating capacity are always expressed in ounces of
polystyrene (PS); hence, one must calculate these using the ratio of the
densities of PS and that of the material being used.
3. Tie-bar separation must be greater than the size of the part (at least in
one direction, horizontal or vertical).
4. Open daylight must be greater than twice the part depth plus the closed
mold thickness.
A number of commercial injection-molding machines are listed, with these char-
acteristics, in the annual editions of the Modern Plastics World Encyclopedia
(cited in the bibliography under Journals, Modern Plastics). Upon finding sev-
eral that could do the job, a selection would be made on the basis of capital
investment and operating expenses.
Although melt injection molding is used overwhelmingly for thermoplastic
polymers, it is possible to injection mold thermosetting resins. The author
61
used
the same Battenfeld press and ASTM mold as Richards
50
to make solid plaques
and tensile bars out of ethylene-propylene-diene monomer (EPDM) elastomers.
He found that successful manufacture of such parts, avoiding short-shots and
overpacking, was extremely sensitive to injection velocity! In this case, the
molds were heated rather than cooled. (Compare reaction injection molding,
which produces foamed parts.)
The solid objects produced by melt injection molding usually have relatively
thin walls. If the desired object as designed would have thick walls, one can
11 TRANSFER MOLDING 1025
save material costs and produce thin walls by using the new technology of ‘‘gas-
assist’’ injection molding. (Again, compare reaction injection molding.)
10 REACTION INJECTION MOLDING
In reaction injection molding, the polymer melt contains a blowing agent, which
may be (i) a dissolved gas that flashes upon a reduction of pressure, (ii) a volatile
liquid that boils upon an increase of temperature, (iii) a nonvolatile liquid that
thermally decomposes, or (iv) a product from a change in the polymer compo-
sition. The first two classes are physical blowing agents (PBAs); the third is
chemical blowing agents (CBAs). (An extensive list of these agents may be
found in the annual issues of Modern Plastics World Encyclopedia.) An example
of the fourth class is the release of CO
2
from the product of an isocyanate and
an acid, which produces an internally foamed polyamide:
——
—R—N C O
⫹ HO—CO—R⬘— →
——
—[R—NH—CO—O—CO—R
⬘]— →
—[R—NH—CO—R⬘]— ⫹ CO
2
In any case, the injection takes place under much lower pressures than those
of melt injection molding (IM). Then, the use of a heated mold (rather than a
chilled mold, as in IM) causes the volatilization of a physical blowing agent,
the decomposition of a chemical blowing agent, or a reaction (such as that shown
above) to take place. Obviously, every part that utilizes such an agent or reac-
tion has either closed or open voids. This technology facilitated the creation of
foamed plastics that matched the density of wood. Knocking on such objects
created the illusion that the object was made of wood.
11 TRANSFER MOLDING
Transfer molding uses thermosetting resins to make an object of intricate ge-
ometry, such as a household electrical wall socket. (Compare compression mold-
ing, which is used for an object of very simple geometry.) However, to illustrate
the complexity of modeling the process, consider a simple plaque mold.
Shah
62
developed six levels of models for the transfer molding of a rectangular
parallelepiped with a phenolic resin. Using a recipe from Sauers,
63
data from
Mark and Bikales,
64
a software package called FLUENT, as well as the spread-
sheet Excel, the various models were (i) isothermal; (ii) nonisothermal, including
viscous heating but neglecting
(T) and k(T), steady-state heat transfer to con-
stant temperature walls; (iii) as in (ii) but with unsteady-state heat transfer; (iv)
. . . including
(T); (v) using FLUENT: Constant Pressure; and (vi) FLUENT:
Free Surface Model. Velocity and temperature profiles are presented as functions
of gap and flow direction distances; in addition, color presentations reveal the
variations in temperature. Fill-time predictions are given. What remains for the
process engineer is to model the kinetics of cross-linking in the phenolic resin
that occurs after fill; the ‘‘hold time’’ before the mold may be opened and the
part removed depends upon this analysis, which is a function of the temperature
profiles.