ANALYSIS OF HEAT TRANSFER COEFFICIENTS AND NO-FLOW

TEMPERATURE IN SIMULATION OF INJECTION MOLDING.

Alberto Naranjo, Juan F. Campuzano, and Iván López ICIPC®, Medellín, Colombia

Abstract

Material properties and boundary conditions are

important inputs for any simulation. For the injection

molding process, there are still many challenges to measure

the polymer properties under processing conditions and

there is not consensus about the thermal boundary

conditions between the polymeric material and mold walls.

This work is oriented to analyze the effect in the simulation

results of the heat transfer coefficient (HTC), which is

related to the boundary conditions, and the no-flow

temperature (NFT), which is related to the material

rheological behavior.

The results for cavity pressure and temperature

evolution from three well-known commercial software

packages (CadMould®, MoldFlow® and Moldex 3D®)

were analyzed and compared with experimental

measurements. A semicrystalline material, PP 505P, from

Sabic was used. In particular, the variation effect of heat

transfer coefficients (HTC) and no-flow temperatures

(NFT) were analyzed through a 32 factorial design of

experiments (DoE).

Based on the results, the most recommendable criteria

to determinate NFT and HTC values for a semicrystalline

material is proposed. The physical meanings of the

obtained values are discussed.

Introduction

The material flow within the mold cavity is a critical

aspect in the injection molding analysis, since the optimal

mold design strongly depends on the analysis of filling

pattern, temperature and pressure during flowing. Design

optimization through simulations allows designers and

developers to significantly reduce mold fabrication and

operation cost. Simulation result reliability strongly

depends on the material properties and boundary

conditions values.

The present study aims to analyze and discuss the use

of some assumptions that are normally made in simulation

software, particularly, for No-flow temperature (NFT) and

Heat Transfer Coefficient (HTC) values. Usually, in

software packages, those values are pre-defined in the data

base or they can be arbitrarily changed by the user, without

standard procedures for their determination.

The no-flow temperature is a concept developed for

simulation software packages to simplify the rheological

behavior of the polymer. This concept assumes that the

polymer material stops flowing under processing condition

below certain temperature. Therefore, the melt flows until

this temperature is achieved during filling and packing.

This temperature determines the evolution of the frozen

layer which influences the pressure evolution, the final

properties of the injected part and it determines the sealing

time, defining the amount of material that enters into the

cavity.

Since cooling in injection molding represents an

important part of the cycle time, estimation of the required

cooling times for the part ejection becomes particularly

critical. Heat Transfer Coefficient (HTC) values strongly

affect the material temperature evolution and therefore the

cooling time. Cooling in an injection molding cycle can be

divided in three main phases: filling, packing and

“detached” or “after packing”. Depending on the phase,

some packages use different HTC values [1], [2].

Injection molding simulation results are usually

experimentally validated by measuring variables such as

injection molding pressure, cavity pressure (when a

pressure sensor is available), average expulsion

temperature and final part dimensions. These variables do

not give direct information about the thermal evolution

during the process. With a device developed by ICIPC [3],

[4], the temperature evolution across the part thickness can

be measured. This information is used to compare the

simulated results with the experimental values.

This research is not intended to qualify the

performance of software packages. Therefore, the specific

relation between the results was avoided. This research is

intended to define how NFT and HTC values can be

defined in order to have a good agreement between

measurements and simulation results. Additionally, the

physical meaning of these values is discussed.

Background

Heat Transfer Coefficients

Many authors have worked on the study and

determination of heat transfer between plastic and metal

surfaces in the cavity of a mold during the injection

molding cycle. In the early 90s, the first studies in that field

were reported by Yu et. al [5]. The authors stated that it is

not possible to achieve a perfect contact between the metal

and the plastic, even under high pressures and high

temperatures inside the cavity, in which gases are housed

SPE ANTEC® Anaheim 2017 / 1394

in the middle of the surfaces decreasing the heat transfer

area, which translates in temperature differences between

the metal and the polymer interface (Figure 1). In order to

simulate this behavior, Robin boundary conditions were

proposed, requiring the definition of heat transfer

coefficients (HTC). HTC is used to adjust the thermal

differences between the mold and the polymer surfaces.

Figure 1. Temperature difference between polymer and

mold surfaces related to non-perfect contact and gasses

allocated between them.

The heat transfer coefficient (HTC) is the inverse of

the thermal contact resistance (TCR) and it is defined as the

heat flow density per unit of area (ϕ ) over the temperature

difference between the mold wall (Tms) and the injected

part (Tps) (1) [6].

𝐻𝑇𝐶 =ϕ

Tps−Tms , [

𝑊

𝑚2∗𝐾] (1)

In the injection molding process, the contact condition

between polymer and mold walls are changing. Because of

that, simulation software packages use at least three

different HTC values for the filling, packing and detached

phases. The packing phase follows the filling phase until

the cavity seals and the pressure reaches a zero value; at

this point, the piece shrinks and detaches from the cavity

(at least from one side depending on part geometry),

changing the boundary conditions and producing a

temperature increase in the polymer surface and therefore

a slower cooling, as shown in Figure 2[7].

Given these conditions, the simulation software must

consider the suitable HTC value for every phase. Reported

HTC values present great differences (See Table 1) because

different methods, sensor types and locations are used to

measure temperature at the mold wall and at the part

surface [3], [8], [9]. Other aspects that can affect the

measurements are surface finishes, materials and

processing parameters [2], [10], [11]. Furthermore, some of

the software packages does not used a measured value and

instead, predefined values or models for the automatic

calculation of the HTC value are used.

Figure 2 Measured temperature and pressure curves for

Sabic PP 505P at process conditions. Sprue pressure (blue),

Cavity pressure (yellow), polymer temperature at the center

of thickness (green), Polymer temperature at 0.5mm from

the surface (orange), Mold surface temperature (gray).

Table 1 Literature reported HTC values. Ref Material Detail Valor HTC

(W/m2-K)

Cadmould 9 ® Any Filling

Packing

After packing

2000

1000

1000

Moldflow Insight

2016 ®

Any Filling

Packing

Detached

5000

2500

1250

Moldex R14 ®

Any Filling

Packing

Detached

5000

25000

2500

Delaunay et. al [2] PP Fix mold side

mobile mold side

Min. 1000

Min. 280

Bluhm et. al [12] - - 500-3000

Bendada et. al [13] PP - 1250-2500

Dawson et. al [14] PMMA - 7000

S. Some et. al [10] PP and

ABS

- 500-5000

Yao Liu et. al [11] PE - 20000-30000

ICIPC developed a model for the prediction of the

temperature of semicrystalline polymers based on thermal

diffusivity that has shown a good approximation to the

experimental measurements [15]. This method assumes a

perfect contact between the plastic and the metal where its

temperature is known and measured on the surface of the

cavity, as a boundary condition, to avoid the use of HTC.

This has been verified experimentally and analytically by

Naranjo et al. [3], [16].

In some of the previously mentioned analysis, HTC

values were calculated with steady state configurations

[14], [17] because this condition eases the sensor

positioning and the stability of the readings. These values

may differ from reality because the injection molding

process is transient and the HTC values depend on different

factors. Thereby, recent studies are oriented to achieve

measurements under process conditions, with molds

equipped with the pertinent measurement systems.

However, difficulties with the thermal interference

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SPE ANTEC® Anaheim 2017 / 1395

generated by the measurement instruments in the region of

interest still remains [2], [8], [10].

Thermal Properties and No Flow Temperature

(Freezing Temperature)

Simulations require to numerically solve continuity,

momentum and energy equations. Energy and momentum

equations change when the material stops flowing. The

three analyzed software packages use the No-flow

Temperature value to determine the moment when the

“solidification” happens. At temperatures higher than NFT,

the full momentum and energy equations (2) are solved.

Once the temperature of a node is below NFT, zero velocity

values are assumed (4) and the energy equation is

simplified (3) [18].

𝑣(𝑥, 𝑦, 𝑧) = {𝑣, 𝑇 > 𝑁𝐹𝑇0, 𝑇 ≤ 𝑁𝐹𝑇

(4)

The NFT concept was initial incorporated by

Moldflow and then by other software packages. However,

there is not a generally accepted model or standard

technique to estimate these values under processing

conditions [20], [21]. The NFT value has been tried to

relate to some concepts like gelation effect, crystallization

temperature (for semicrystalline polymers), glass transition

temperature (for amorphous materials [19]) or the melt-

solid transition region in the pvT diagram. These values are

usually measured at low cooling rates, which can lead to

significant errors in the results.

Other approach that does not require the NFT

definition is the extrapolation of the Cross-WLF model for

viscosity to low temperatures. However, because the

material characterization is usually made under high

temperatures and high shear rates, the deviation of the

results can be higher than using the NFT concept [19].

Materials

The material used was a PP from SABIC (PP505P)

fully characterized at the ICIPC and IKV labs (RWTH

Aachen University, Germany). The resin has a MFI of 6.2

cm3/10min at 230°C under a 2.16Kg load, melt density of

0.753 Kg/m3 at 240°C. The pvT and Cp of the material is

presented in the Figure 3.

Figure 3 a) Cp measured by DSC at 20°C/min cooling rate,

b) pvT measured at 5°C/min cooling rate

Experimental setup

The mold used for the experimentation was designed

by the ICIPC along with the IKV institute, based on patent

US 2004/0213321 A1 [3]. In this mold, two rectangular

plates with a thickness of 3mm are injection molded

through a gate that was specially designed to ensure a

parallel flow distribution along the plates, regardless of the

material and processing conditions (See Figure 4). The

mold can also be adjusted to thicknesses of 3, 4 or 5 mm.

Figure 4. Schematic temperature and pressure positions for

the mold designed by the ICIPC along with the IKV.

The mold cavities are made of duralumin with a

thermal conductivity of 180 W/m.K and an average

roughness of 1μm.

115

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Cp

(J/

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vo

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0Mpa

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b)

𝜌 ∙ 𝑐_𝑝 (𝜕𝑇/𝜕𝑡 + 𝑣 ⃗ ∙ 𝛻𝑇) = 𝛻 ∙ ( 𝐾𝛻𝑇) + 𝑝𝛻 ∙ 𝑣 ⃗ +

𝛽𝑇(𝑑𝑝/𝑑𝑡 + 𝑣 ⃗ ∙ 𝛻𝑝) + 𝜎 ̅: 𝛻𝑣 ⃗ + 𝑄 ̇ (2)

𝜌 ∙ 𝑐𝑝

𝜕𝑇

𝜕𝑡= 𝛻 ∙ (𝐾𝛻𝑇) + 𝛽𝑇

𝑑𝑝

𝑑𝑡+ �̇� (3)

SPE ANTEC® Anaheim 2017 / 1396

The mold has three Kistler piezoelectric sensors, one

for each cavity (type 6158A) and the other one for the

nozzle (type 6157BA). Ten non-insulated thermocouples

(type K) with a diameter of 0.25 mm were placed across

the part thickness. Additionally, thermocouples at the mold

surface and at 0,14 mm from the wall were used, as shown

in Figure 4. Sensors were previously calibrated and the

temperature readings were corrected using ICIPC’s

Diffutherm1 software.

The processing parameters used for the injection of the

plates are described in Table 2.

Table 2 processing parameters Parameter Value Unit

Injection time 1.4 s

Melt temperature (Tm) 260 °C

Mold Wall temperature (Tw) 21.5 °C

Packing pressure (Pp) 20 MPa

A factorial Design of Experiments (32) was performed

to analyze the simulations (Table 3). Three different values

of NFT and HTC were used. The HTC values were selected

based on literature reported values (Table 1), taking into

account, that according to previous studies, the use of HTC

values higher than 10,000 W/m2-K does not have a

significant impact in the results. The medium point is

defined at 2,000 W/m2-K, which is close to the default

value used by software packages.

Regarding the NFT, the minimum value used in the

DoE correspond to the crystallization peak (115°C). The

maximum value corresponds to the beginning of the melt

phase in the pvT (175°C). The medium point was set at

140°C, which corresponds to the beginning of the solid

phase in the pvT diagram.

A single HTC value was defined for packaging and

cooling phases. For the filling phase, the software´s

predefined HTC values were preserved, because, according

to previous simulations, the effect of heat transfer during

filling is not significant for the dimensions of this mold.

Table 3 Entries for DoE 3^2 with HTC and NFT factors for

each software.

DoE 3^2

NFT (°C)

HTC (W/m2-K)

LNFT 115 LHTC 500

MNFT 140 MHTC 2000

HNFT 175 HHTC 10000

A constant mold wall temperature of 21.5°C was

defined for the simulations. This value was measured and

verified during the injection molding process, as can be

seen in Figure 2. The measured wall temperature variation

1 Software developed by the ICIPC for the determination and modelling of

thermal diffusivity for thermoplastic materials under process conditions based on

data obtained from the device disclosed in the patent US20040213321 A1.

during the cycle was less than 3°C, therefore, the

assumption of constant temperature is reasonable.

Every software has its own approach to calculate the

wall temperature. By using a constant wall temperature,

these differences are avoided.

Meshes were generated for every software package

looking for similar discretization. However, every software

has its own meshing method. Mesh independence studies

were conducted to guarantee the accuracy of the results.

As output for the DoE, the differences between the

experimentally measured value and the simulated value of

the following parameters were used:

Time to reach the null pressure value (null press),

defined as the time that takes the cavity to reach

the atmospheric pressure (see Figure 5 a).

Time to reach the end of the crystallization

(Tcryst) at the center of the part (see Figure 5 b).

This value was estimated as the time when the

curvature (second derivative) of the graph Time

vs Temperature reaches a zero value.

An optimal combination of NFT and HTC is achieved

when the differences of these values for the simulations

and the measurements are minimum.

Figure 5 Definition of the indices for the outputs of the DoE

a) NullPress, b) Tcryst.

In the Figure 6, the results of the experimental

measurements and the design of experiments are presented.

Pressure and temperature at the center of the rectangular

plate as a function of time are compared. As expected, the

simulations show that the NFT values have an important

effect on the pressure results but not on the temperature

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SPE ANTEC® Anaheim 2017 / 1397

evolution inside the part; and the HTC values have

significant effects on both temperature and pressure

evolutions.

Figure 6 Effect of DoE factors HTC and NFT on cavity

pressure and temperature at the center of the plate a) Effect

of HTC on cavity pressure, b) Effect of NFT on cavity

pressure, c) Effect of HTC on temperature, d) Effect of

NFT on temperature.

Results and analysis

To analyze the results of DoE, a quadratic type model

(5) for the prediction of optimal values of each index in

each program was used. The a, b, c and d factors are listed

in Table 4.

𝐸𝑟𝑟𝑜𝑟 = 𝑎 + 𝑏 ∗ 𝐻𝑇𝐶 + 𝑐 ∗ 𝑁𝐹𝑇 + 𝑑 ∗ 𝐻𝑇𝐶 ∗ 𝑁𝐹𝑇 (5)

Table 4 DoE output model´s factors Indicator a b c d

Software 1 Null press -22.789 1.6.E-03 0.186 -7.0.E-06

Tcryst 0.043 9.7.E-04 0.003 -2.3.E-06

Software 2 Null press -21.206 1.2.E-03 0.182 -5.6.E-06

Tcryst -1.305 5.2.E-04 5.E-05 4.9.E-08

Software 3 Null press -20.620 1.4.E-03 0.183 -6.3.E-06

Tcryst -2.081 5.3.E-04 -0.002 8.1.E-07

The values of the HTC and NFT that minimize the

difference for both indices for each software are presented

in Table 5.

Table 5 Optimum HTC and NFT calculated values for each

software

Parameter Software 1 Software 2 Software 3

HTC (W/m2-K) 1381 2234 1895

NFT (°C) 117 109 105

For any software, the NFT that minimizes the

difference with respect the measurements is around 110°C.

This value is slightly lower than the crystallization peak of

the material measured at a cooling rate of 20 °C/min. In the

case of the HTC, the generalization of a value for the three

software packages was not possible. That means that the

models and assumptions of the three packages in this

boundary condition are different.

With the parameters of Table 5, simulations were

carried out for each software. The results are presented in

Figure 7. A good agreement between the simulated and

experimental results for the times to reach the null pressure

value and the end of crystallization was observed.

However, pressure and temperature evolutions present

different patterns between simulations and experiments.

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SPE ANTEC® Anaheim 2017 / 1398

Figure 7 Cavity pressure and internal temperature curves

from simulations with the adjusted values for each software

compared with experimental measures. a) software 1, b)

software 2, c) Software 3

The HTC values found in Table 5 are too low

compared to the theoretical values of the heat transfer

phenomenon. The HTC concept is used assuming that there

is an air gap between the polymer surface and the mold wall

(Figure 1). If the air is at 15 MPa and 35°C, it has a

conductivity (K) of 0.035 W/m.K. For a value of HTC of

2,000 W/m2-K (similar to the ones found in Table 5 ), the

theoretical air gap thickness is 17μm (See Figure 8), which

is too large taking into account that the surface roughness

of the mold is 1 μm. In order to have a 1 μm gap thickness,

the HTC value should be close to 50,000 W/m2-K. From

this result, it can be concluded that HTC values are selected

based on numerical criteria and not physical criteria.

Figure 8 Air gap thickness related to HTC values under

process conditions.

High values of HTC approximate the solution to the

Dirichlet boundary condition (the wall temperature is equal

to the plastic surface temperature), maximizing the heat

transfer, and therefore, accelerating part cooling. If the

theoretical HTC values (around 50000 W/m2-K) are used,

the cooling simulation is much faster than the actual

phenomenon. Low HTC values are used to correct cooling

rates in order to get closer to the real injection molding

process conditions.

The reason why the measured cooling rate of the part

is lower than the calculated by simulation when the

theoretical HTC values is used can be related to changes in

the material properties under processing conditions. The

difference between the thermal diffusivity measured by the

ICPC method [15] under process conditions against the

calculated from the material database from the software

packages is shown in Figure 9. The thermal diffusivity

calculated with the software databases is always higher

than the measured values, leading to a faster cooling of the

part. Therefore, low values of HTC may amend this effect

in the simulations.

Figure 9 Comparison between measured and calculated

thermal diffusivity.

Conclusions

Evaluations of the impact of HTC and NFT values on

simulation results for a semicrystalline polymer were

presented. HTC and NFT values to better reproduce the

experimentally measured temperatures and pressures were

proposed and validated.

Experimental and simulated results had good

agreement when the NFT value is related to the

crystallization effect. Due to the importance of the

temperature of crystallization, this value should be

measured at high cooling rates, in order to approximate the

processing conditions.

The HTC value that better reproduce the measured

temperature evolution is different for every software

package, in a range between 1,500 and 2,500 W/m2-K.

These differences mean that every software uses its own

models and assumptions for the boundary conditions. The

obtained HTC values are much lower than the theoretical

values.

Material thermal properties are usually measured

under conditions that are far from the actual processing

conditions, which can lead to overestimate the cooling rate

in the plastic materials. Artificial low HTC values help to

compensate the cooling rate overestimation.

Further research works looking for a HTC model that

describes the actual heat transfer during the injection

molding phases and its impact on shrinkage and warpage

prediction are required. New characterizations techniques

and models that describe material thermal properties under

processing conditions are necessary.

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17 μm ; 2000 W/m2-K

1 μm ; 50000 W/m2-K

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Measured surface

Measured intemediate

Measured interior

Calculated 150Bar

𝛿 =𝐾

𝐻𝑇𝐶

SPE ANTEC® Anaheim 2017 / 1399

Acknowledgments

The authors gratefully acknowledged the technical and

financial support of the following organizations and

companies in the region: ICIPC- (Instituto de

Capacitacitación e Investigación del Plástico y del

Caucho), IKV at RWTH-Aachen (Institut für

Kunststoffverarbeitung), SOFASA (Sociedad de

Fabricación de Automotores S.A.), Colciencias

(Administrative Department of Science, Technology, and

Innovation of Colombia) and Universidad EAFIT.

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