Effect of shape in a thermal management system - A154

Effect of shape in a thermal management system
Systems knowledge article
Document Type	Article
Document Identifier	154
Themes	Thermal management
Relevant Classes	Shape
Tags	System control Thermal properties Thermal transformation Shape Shape parameters Thermal management interaction
Prerequisites	Degree of cure Heat of reaction Heat transfer System interactions Thermal and cure/crystallization management (TM)

Introduction

Aside from thermal conditions imposed on the part by the equipment and tooling, features of the part itself may influence its thermal response. This includes heat transfer into and out of the part. It is not just the part material(s) that influences its thermal behaviour, but its geometry as well. From a thermal management perspective, thin laminates behave different than thick laminates. In order to capture this behaviour using a system-level approach, the effect of shape on the thermal response of the part is discussed.

Scope

This article discusses the impact of shape parameters on the part thermal response. The page links out to foundational knowledge content and brings in physics-based simulation to demonstrate the impact of part shape in a thermal system. While the content presented here is applicable to all thermal management factory cells, the focus of this page is on the thermal transformation cell as that is the predominant cell associated with thermal management.

Significance

The part represents the product that is being manufactured. As such, manufacturing specifications are typically based on outcomes of the part, including thermal requirements. While material-specific thermal requirements often exist, they may not account for size or other geometric complexities associated with the part. Such parameters may have a significant effect on the part's thermal response and, as a result, the as-designed mechanical properties. Understanding such parameters from a thermal management perspective allows for the system to be tailored appropriately to the part(s) being manufactured.

Prerequisites

Recommended documents to review before, or in parallel with this document:

• Degree of cure
• Heat of reaction
• Heat transfer
• Thermal management
• System interactions
• Shape (system class)

Overview

The shape of the part is representative of its geometry, including internal, external, local, and global features. The part geometry plays a key role in influencing heat transfer into and out of the part. Moreover, the dimensions and local features of the tool-part assembly can redirect and even block airflow in a convective heating system.

The shape can be thought of as one aspect of the part. The other being the material. Together, the material and shape dictate how heat will flow through the part. Since the outcomes of concern are to do with the part, the material and shape thereby define the outcome sensitivity of the system. That is, how the outcomes will be influenced by the imposed boundary conditions.

In most cases, the system can be analyzed accurately by assuming 1D heat transfer through the thickness of tool-part assembly. This is because the in-plane dimensions are typically much larger than the thickness. As a result, the part exhibits much smaller thermal gradients in-plane versus through its thickness. Therefore, part thickness is one of the most important shape parameters to consider as it directly affects the part temperature profile. There may be cases, however, where 2D or 3D thermal analysis is warranted.

Heat transfer into and out of the part occurs by conduction through the tool-part assembly. If the temperature across the part surfaces (or tooling surfaces) is known, then the temperature within the part can be approximated using the 1D form of the heat balance equation, as shown below.

\(\frac{\partial}{\partial t}(\rho C_pT)=\frac{\partial}{\partial z}\Bigl(k_{zz}\frac{\partial T}{\partial z}\Bigr)+\dot{Q}_{r}\) 1D form of the heat transfer equation, where:<br />\(t\) = time,<br />\(\rho\) = density,<br />\(C_p\) = specific heat capacity,<br />\(T\) = temperature,<br />\(z\) = through-thickness distance (z direction),<br />\(k_{zz}\) = thermal conductivity in z direction, and<br />\(\dot{Q}_{r}\) = rate of energy given off by material during exotherm.

Where,

\(\dot Q_r = \frac{d\alpha}{dt}(1-V_f)\rho_r H_R\) Internal heat generation during polymerization (exotherm), where:<br />\(\dot{Q}_{r}\) = rate of energy given off by material,<br />\(\alpha\) = degree of cure,<br />\(t\) = time,<br />\(V_f\) = fibre volume fraction,<br />\(\rho_r\) = resin density, and<br />\(H_R\) = heat of reaction of resin

To understand how to perform a thermal profile of a tool/part, refer to the following documents.

• How to perform an experimental thermal profile
• How to perform a numerical thermal profile

Geometry

Part thickness

The energy required to raise the temperature of a material can be represented by the following equation:

\(Q=mC_p\Delta{T}\) Energy required to raise an object's temperature, where:<br />\(Q\) = energy,<br />\(m\) = object mass,<br />\(C_p\) = specific heat capacity,<br />\(\Delta{T}\) = change in temperature from applied energy. Note that \(mC_p\) is the thermal mass of the object.

The thicker an object is, the greater mass it has and therefore the more energy required to raise its temperature. In practical terms, this means higher temperatures or longer hold times are required for the internal temperature of a thick part to reach its intended temperature as compared with a thin part. That is, the thermal lag (difference in temperature between the center of the part and its surface) is greater for a thick part than for a thin part. This is important for outcomes such as degree of cure (DOC). If the center of a thick part does not reach the specified temperature range for the allotted period of time, it may be undercured and demonstrate poor mechanical properties. Similarly, if a thin part remains at elevated temperatures for too long it may overcure or thermally degrade, and also exhibit poor mechanical properties. The problem is compounded if the part varies in thickness along its length. This is analogous to cooking meat of uneven thickness. Often the thick portion may be undercooked, while the thin portion is overcooked or burnt.

However, unlike in cooking, thermoset parts actually give off their own heat. The thicker the part, the more material the heat must dissipate through and the longer it takes for heat to escape from within the part. This can cause a buildup of heat at the centre of the part which acts to further the cure reaction and release even more heat. This can result in an "inside-out" cure. If not managed properly, this may cause a runaway exotherm leading to thermal degradation and residual stress deformation of thick parts. This is especially true during high temperature processing. Thin parts, in contrast, allow for heat to escape much easier and do not experience as significant of an exotherm as a result. For low temperature processing, the trapped heat given off by thick parts can actually be beneficial in advancing the cure reaction. In fact, for room temperature cure materials (such as polyester resins), a thicker part can reach the same degree of cure at a lower ambient air temperature as compared with a thinner part. This phenomenon is shown in the figures below. In particular, the right hand figure shows that at an ambient temperature of 20°C, an 8mm part reaches a DOC of 85%, whereas a 3mm part only reaches a final DOC of 76%. This difference becomes more stark the higher the ambient temperature. In contrast, at very low ambient temperatures, the thermal energy is not sufficient to significantly increase either the 3 or 8mm part to a high DOC. The green line represents the theoretical degree of cure of pure resin ignoring its mass and looking strictly at the specific (per mass) material properties. In other words, thickness of the resin layer is not taken into account. Hence why both the 3 and 8mm laminates display a higher final degree of cure as ambient air temperature increases.

For low temperature processing materials, thicker parts generally result in a higher degree of cure due to an increase of heat released during cure.

Part temperature	Degree of cure

The right hand figure shown above can be expanded to demonstrate the general cure behaviour of room temperature cure materials based on laminate thickness. As noted above, for a given ambient temperature, a thicker part results in a higher final DOC than a thinner part. Perhaps more notable is that, once the part is thick enough, an increase in ambient temperature does not significantly increase the final DOC. For example, a 20mm part processed at 10°C results in the same final DOC as a 20mm part processed at 30°C. Conversely, the thinner the part, the more pronounced an effect the ambient temperature has on the final DOC. In fact, up to a critical thickness, an increase in thickness will not significantly impact the final DOC. In such a case, ambient air temperature must be increased.

These phenomena can be explained by the amount of heat given off by the laminate and the nature of the cure reaction. In order for the cure reaction to advance, enough thermal energy must be provided. Initially the thermal energy is provided by the ambient air temperature. Therefore, at higher ambient air temperatures the cure reaction will kick off sooner. However, once the reaction starts, the part itself will begin to add heat to the system due to the exothermic nature of the polymerization reaction. The more massive (thick) the part is, the more heat will be trapped within the part and the further the cure reaction will be advanced. If the part is large enough, the heat added by the part will dominate the cure reaction more so than the ambient air temperature.

In the case of high temperature processing, typically the applied temperature rather than the part exotherm plays a more significant role in controlling the cure reaction. That said, the exotherm may still have a significant effect on the overall part temperature, especially for thick parts. If managed properly, this can be beneficial in bringing the part to temperature. However, it can also be detrimental as it may result in the part going above its temperature specifications. In the examples provided below, the exothermic heat from a 50mm part results in a part temperature increase more than 30°C above the applied temperature for both a conductive and convective heating scenarios. In contrast, a 10mm part results in a much less severe exotherm. Although, even in this case, the part temperature is raised more than 10°C above the applied temperature for the convective heating scenario.

Another important aspect of high temperature processing in relation to part thickness is thermal lag. In this case, that is the difference in temperature between the part surface and its midplane. Because there is a "heat-up" or "ramp" phase involved, there will, inevitably, be a thermal gradient existing through the thickness of the part. This gradient becomes more drastic, the larger the part. This is true for convective and conductive heating environments. As shown below, a 50mm part in a convective heating environment such as an oven may experience a thermal lag greater than 30°C between its surface and midplane during heat-up. For a conductive heating environment, such as a hot press where the equipment or tooling is already at the set temperature, the initial thermal lag through a 50mm part can be upwards of 150°C depending on the initial part temperature and the tooling temperature. Such a temperature difference may even last for a couple minutes. For thin parts, in contrast, the thermal lag existing through the part is significantly smaller, especially in conductive heating. This is seen in the 10mm sample.

For high temperature processing, a larger part thickness results in a greater thermal lag between between the part surface and its midplane. It also results in a larger exotherm which may bring the part above its temperature specifications. This is true for convective and conductive heating environments.

10mm part	50mm part
Convective heating - heating rate of 3°C/min	Convective heating - heating rate of 3°C/min
Conductive heating - part surface temperature and applied temperature are practically equivalent	Conductive heating - part surface temperature and applied temperature are practically equivalent

In order to obtain the as-designed mechanical properties, the entire part (surface to midplane) needs to reach the appropriate DOC. This means fulfilling the temperature requirements. In doing so, it is pertinent that both the surface and the midplane of the part reach the set temperature for the required amount of time. In doing so, however, it is also pertinent that the exotherm does not bring the part (surface or midplane) above the temperature requirements, as this may degrade the part. The thermal management strategies used must consider that a thin part will behave different than a thick part. That is, a thin part will experience less thermal lag and a smaller exotherm, while a thick part will experience greater thermal lag and a larger exotherm. For both cases, all locations of the part must be brought to the required temperature for an appropriate amount amount of time, consistent with the material requirements.

In order to achieve this, different strategies may include introducing intermediate holds in the cycle, reducing the temperature ramp rate, changing the heating equipment, increasing the tooling thickness, or changing the part or tooling material. To learn more about how these changes may affect the system visit the following pages:

• Effect of equipment in a thermal management system
• Effect of tooling in a thermal management system
• Effect of material in a thermal management system

Part configuration

In forced convection heating (such as in an oven or autoclave), the size of the tool-part assembly must be considered in relation to the airflow. This is especially true if multiple parts are loaded in the same piece of equipment. Impinging airflow may be redirected or blocked by a given part. For example, if a large part is placed in the air stream in front of a smaller part, then the heat transfer coefficient (HTC) on the smaller part will be significantly reduced, thus negatively affecting its thermal history. The same may even occur from local features on the same part. That is, obtrusions on the front of a part may create dead zones or redirect airflow away from the back of the part. Additionally, large cavities or holes may not see as high an airflow velocity as the rest of the part. In such situations, the HTC will vary over the part surface. This will result in a spatially-dependent thermal response across the part, which in turn may cause the part to cure unevenly.

The image above demonstrates how the tool-part assembly may influence airflow in an autoclave. The same principle is true for an oven or any other forced convection equipment.

To learn how to measure or model airflow, refer to the following links:

• How to measure airflow in a thermal system
• How to simulate airflow in a thermal system

Scenarios

1. A small composite shop is manufacturing flat laminates for use in the construction industry. They are using a glass fibre, polyester-based material system. The design allowables give them flexibility to make laminates as thin as 5mm or as thick as 15mm. However, to reduce cost and weight, they would like the panels to be as thin as possible. In order to meet the mechanical requirements, the parts should be cured to at least 90% DOC. Their manufacturing method involves a room temperature cure where the panels are left in a shed with minimal temperature control. In the summer, the temperature can reach 30°C, whereas in the winter it can drop to 15°C.

In order to obtain the optimum part thickness, experiments or simulation software can be used to obtain the degree of cure of the material system as a function of mass (corresponding to the part thickness). This can then be repeated at different hold temperatures indicative of the ambient air temperature. Results of such tests for a glass-polyester system are presented below.

Figure description

Obtaining DOC curve for summer and winter temperatures	Determining necessary laminate thickness to achieve a DOC of 0.9

From these curves, one can select the intended DOC and determine the necessary part thickness according to the ambient temperature. In this scenario, curing in the summer (30°C) allows for a minimum part thickness of ~4.6mm. However, because the design allowables don't allow for a thickness less than 5mm, this would have to be increased to 5mm. In the winter (15°C), the minimum part thickness to achieve a DOC of 0.9 is ~10.4mm. Therefore, the minimum part thickness required to achieve a DOC of 90% year-round is 10.4mm. In the summer this will result in a DOC close 1, whereas in the winter this will result in a DOC equal to 0.9. In both cases, the condition of having a DOC greater than 90% is satisfied. Increasing the thickness will further satisfy the requirements, however then the solution is no longer optimized. That said, since the design allowables allow for a thickness up to 15mm, slightly increasing the part thickness to 11 or 12mm may allow for a more robust solution in the event of temperature fluctuations. As it stands, using a part thickness of 10.4mm puts the manufacturer at risk of not achieving specifications if the temperature drops slightly below 15°C on the day of curing.

Complicating factors/edge cases

It should be noted that while this page demonstrates the general effects the part shape has in a thermal system, the figures generated are material specific. Results will differ between materials, even for seemingly similar material systems (i.e. one polyester resin based system versus another). Similarly, changes in other processing parameters such as tooling thickness/material, HTC values, and others will influence the outcomes. Finally, in the generated curves, consumables were not considered for simplicity. Depending on the consumables used and their thickness, they may have a notable effect on the part response. The results shown here are intended only to highlight the importance of the part shape from a thermal management perspective.

Related pages

Page type	Links
Introduction to Composites Articles
Foundational Knowledge Articles
Foundational Knowledge Method Documents
Foundational Knowledge Worked Examples
Systems Knowledge Articles	Effect of equipment in a thermal management system - A110 Effect of material in a thermal management system - A155 Effect of shape in a thermal management system - A154 Effect of tooling in a thermal management system - A142
Systems Knowledge Method Documents
Systems Knowledge Worked Examples
Systems Catalogue Articles
Systems Catalogue Objects – Material
Systems Catalogue Objects – Shape
Systems Catalogue Objects – Tooling and consumables
Systems Catalogue Objects – Equipment
Practice Documents
Case Studies
Perspectives Articles	Introduction to Tooling for Composite Materials Processing - A340

References

References

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A central processing theme in the manufacturing cycle. This theme is concerned with managing the thermal response of materials during storage and handling or parts/tools when they are subsequently heated.

Degree of cure (DOC) is an indication of how far the chemical curing reaction (crosslinking process) has advanced in a thermoset resin.

DOC is defined with a number between 0 and 1 (or 0% and 100%) where 100% is a fully cured resin. It does not have to fully reach 100% for the resin to become solid or the part to be used. In some aerospace applications, resins are only cured to about 90%. Higher the degree of cure, higher the mechanical properties.

Volume fraction of either matrix or fibres with respect to total composite volume (matrix + fibre).

For polymer matrix composites (PMCs), resin refers to the matrix; the continuous material phase that binds the reinforcement together, maintains shape, and transfers load. Resins are divided into two main groups: thermosets and thermoplastics.

Polymerization of thermoset resins is an exothermic reaction and heat is generated during the curing process. A thermosetting resin has the potential to release a certain amount of energy while curing. This is called the total heat of reaction, H_R, with a unit of J/g (SI units).

The heat of reaction during polymerization is measured using a Differential Scanning Calorimeter (DSC) equipment measuring much energy/heat comes out of the reaction for a small resin sample.

Thermosets are a class of polymer that undergo polymerization and crosslinking during curing with the aid of a hardening agent and heating or promoter. Initially they behave like a viscous fluid. During curing, they change from viscous fluid to rubbery gel (viscoelastic material) and finally glassy solid.

If heated after curing, initially they become soft and rubbery at high temperatures. If further heated, they do not melt but decompose (burn)

Comes in two parts: part A (resin) and B (hardener). When mixed, curing reaction starts and is not reversible.

Examples include epoxy or polyester.

Engineered materials (designed to have specific properties) made from two or more constituent materials with different physical or chemical properties. The constituents remain separate and distinct on a macroscopic level within the finished structure.

With regards to manufacturing, risk is the combination of the probability and consequences of undesirable manufacturing outcomes. Manufacturing risk can lead to technical issues, program/schedule delays, and cost overruns.