Heat transfer - A132

Heat transfer
Foundational knowledge article
Document Type	Article
Document Identifier	132
Themes	Thermal management
Relevant Class	Material
Tags	Governing science Heat transfer
Prerequisites	Composites manufacturing

Introduction

Heat transfer is the physics process responsible for the redistribution of thermal heat energy between systems. For composites, this includes the redistribution of heat both within the laminate itself, and between the laminate body and its surrounding environment. The heat transfer process has important roles in both the composite manufacturing process and the operational service of the composite material.

Scope

This page introduces the fundamental topic of heat transfer and its application to composites processing. It describes the three main mechanisms of heat transfer, i.e. thermal conduction, thermal convection and thermal radiation, outlines the energy equation, measurement techniques, and the modelling of heat transfer in process simulation.

Significance

Heat transfer is a fundamental component of the composite manufacturing process. In many cases, sufficient amounts of heat must be imposed on the laminate during the manufacturing process for its physical, and in certain cases chemical transformation into the final composite part.

Precise control of the temperature imposed on the laminate during manufacturing plays an important role in the following aspects:

• Thermoset matrix: ensuring a suitable level of cure is achieved for the intended mechanical properties. At the same time, tight control of temperature is critical during processing to control the evolution of cure and mitigate the development of defects due too little or too much resin flow
• Thermoplastic matrix: ensuring sufficient heating for melting and flow, and cooling for recrystallization
• All matrix types: influencing the microstructure distribution of the reinforcement fibres and matrix tougheners, morphology of matrix tougheners, final matrix porosity

Prerequisites

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

• Composites Manufacturing

Overview

Heat Transfer Mechanisms

Illustration of classic candle heating rod heat transfer example.

Fundamentally, heat transfer is organized into three main mechanisms:

• Conduction
• Convection
• Radiation (considered negligible in a majority of composites processing scenarios)

For a system, heat transport can involve multiple mechanisms. Using the classic example of a metal rod being heated over a flame; the heat being transferred from the flame to the rod is considered to be by convection, while the heat transferred along the rod itself is by conduction . Applying this analogy to the composites processing scenario for a laminate curing in an oven or autoclave environment; the hot air transfers heat by convection, while the heat transfer between the tool and laminate part, and within the laminate itself is then by conduction.

Conduction

Link to main Conduction page

Example of conductive heat transfer. The temperature within the tool is redistributed by conduction mechanisms.

Conduction is a heat transfer mode associated with the microscopic collisions between high energy particles and adjacent lower energy particles causing a redistribution of the kinetic energy within a material or medium. The heat flow is proportional to the temperature gradient imposed and the intrinsic properties of the material. Conduction is considered the primary heat transfer mechanism in solid materials.

Convection

Link to main Convection page

Example of convective heat transfer. Heat is transferred to the part by hot air moving over the surface.

Convection is a heat transfer mode driven by the bulk motion of a fluid. Energy transport by convection (e.g. heat) results from the combination of two heat transfer mechanisms: conduction and the fluid flow process of advection. Convection takes place in the presence of fluid motion and can occur by forced fluid motion (forced convection) or by natural fluid motion (natural convection). In composites processing, convection is an important heat transfer mechanism occurring in oven and autoclave processing methods.

There are two types of convection transport: forced convection and free convection. These two modes of convection differ by the driving force leading the fluid flow:

Forced Convection

In forced convection, the motion of the fluid is governed by external mechanical forces and typically controlled in production by a pump or a fan.  For heating equipment like autoclaves or ovens, flowing gas driven by a fan is used to heat the part-tool assembly.

Natural Convection

In free convection, also known as natural convection, the motion of the fluid is driven by the temperature gradients in the fluid without external input. This occurs for open-air processes without a fan, where air movement may develop due to temperature-induced buoyant forces acting on the air. Similarly, a hot part naturally cooling in an open air environment is an example of natural convection heat transfer taking place.

Radiation

In composites processing, conduction and convection are the dominant heat transfer mechanisms and thermal radiation is generally negligible .

Heat Transfer Interactions During Composites Processing

Link to main System Interactions page

Heat plays a critical role in the composites manufacturing process, controlling resin flow, cure and crystallization kinetics, and even the physical distribution and morphology of the various laminate constituents. During processing, heat is transferred between the laminate, tooling and manufacturing equipment. Heat transfer in composites processing is a systems problem, where the laminate part, tool, and heating equipment all interact together. During heated manufacturing processes, thermal heat is transferred from the manufacturing equipment to the laminate to form the final part. For thermoset matrix composites (e.g. polyester, epoxy) the heat is required for the curing of the thermoset resin, while for thermoplastic matrix composites the heat is required for melting (flow) and recrystallization (solidification) of the matrix.

Example of Thermal Process Interactions

Two typical processing examples illustrating the role of heat transfer in the composite manufacturing process are given below (for further details of the interactions outlined, please see the Systems Interactions page):

Manufacturing Process		Heat Transfers Involved
Hot Press	Schematic of heat transfer in a hot press process.	Press platen –> part [conduction] Internal laminate heat redistribution [conduction]
Autoclave and Convection Oven	Schematic of heat transfer in an autoclave or similarly convective oven process.	Gaseous environment –> part (via consumables) [convection] Gaseous environment –> tool [convection] Tool –> part [conduction] Internal laminate heat redistribution [conduction]

System Heat Sources and Heat Sinks

Like water flowing downstream, thermal heat flows from regions of high thermal energy (warmer temperature) to regions of lower thermal energy (cooler temperature). Whether a laminate heats up or cools down depends on the temperature gradient present between the laminate and the surrounding system. The thermal heat energy flowing into or out of the laminate can be described by considering the potential heat sources (heat input) and heat sinks (heat removal) in the system.

Heat Sources (adds heat)

• Equipment with a heat source
• Tool when hot
• Material when generating heat (i.e. exothermic curing reaction of a thermoset resin)

Heat Sinks (removes heat)

• Equipment with a cooling system
• Tool when cold
• Material when absorbing heat (i.e. melting of a thermoplastic resin)

All system objects can act as either a heat source or a heat sink. Whether an object is a source or a sink is dependent upon the object's temperature in comparison to other surrounding objects in its environment.

Modelling

Heat transfer can be modelled to various levels of complexity, from 0-D (no part thickness or dimensional considerations) up through 3-D.

Examples of thermal modelling possible with varying levels of complexity (increasing spatial dimensions). Images produced from simulations using commercial software RAVEN and COMPRO by Convergent Manufacturing Technologies.

The necessary number of dimensions to obtain sufficient accuracy is dependent on the geometry of the part, and the analysis being performed. For some cases, 1-D modelling is sufficient, while in other cases 2-D and 3-D modelling may be required.

In many cases, the typical laminate part aspect ratio (thickness is order of magnitudes less in comparison to length and depth dimensions) and part geometry generally allows for simple 1-D modelling of the through-thickness thermal distribution to often be sufficient.

The Energy Equation

The heating of a laminate can be simplified and described as a heat energy balance, where\[Rate\ of\ heat\ increase = Rate\ of\ heat\ addition\ by\ conduction\]

Illustration of heat balance distribution. Heat transferred to laminate (heat energy increase) = laminate heat conduction contributions.

Modelled, this can be presented as the following general heat balance equation\[\frac{\partial}{\partial t}(\rho c_pT)= \frac{\partial}{\partial x}\Bigl(k_{xx}\frac{\partial T}{\partial x}\Bigr)+\frac{\partial}{\partial y}\Bigl(k_{yy}\frac{\partial T}{\partial y}\Bigr)+\frac{\partial}{\partial z}\Bigl(k_{zz}\frac{\partial T}{\partial z}\Bigr)\]

Breaking down the general heat balance equation by the individual heat components,

\(\frac{\partial}{\partial t}(\rho c_pT)=\) Heat accumulation in the laminate

\(\frac{\partial}{\partial x}\Bigl(k_{xx}\frac{\partial T}{\partial x}\Bigr)+ ... =\) Conduction heat transfer contributions

Where,

\(t =\) Time [s]

\(\rho =\) Density [kg/m³]

\(c_p =\) Specific heat capacity [J/kg·K]

\(T =\) Temperature [K]

\(k =\) Thermal conductivity (in principle direction x, y, or z) [W/m·K]

\(x,\, y,\, z =\) Respective principle direction x, y, or z

The rate of heat transferred into the system is provided by the heating equipment or environment (room temperature cure). If this heat transfer boundary condition is convective in nature (moving air), the heating rate can be described by\[\dot Q = hA\Delta T\]

Where,

\( h =\) Convective heat transfer coefficient [W/m²·K]

\(A = \) Surface area [m²]

\(\Delta T = \) Change in temperature [K]

During the curing cycle for thermosets, internal heat is generated by the exothermic cross-linking reaction. In this scenario, the heat balance equation gains an additional \(\dot Q_r\) term (reaction heating rate)\[\frac{\partial}{\partial t}(\rho c_pT)= \frac{\partial}{\partial x}\Bigl(k_{xx}\frac{\partial T}{\partial x}\Bigr)+\frac{\partial}{\partial y}\Bigl(k_{yy}\frac{\partial T}{\partial y}\Bigr)+\frac{\partial}{\partial z}\Bigl(k_{zz}\frac{\partial T}{\partial z}\Bigr)+\dot Q_r\]

The internal heat generation modelled as\[\dot Q_r = \frac{d\ x}{dt}(1-V_f)\rho_r H_R\]

Where,
\(\frac{d\ x}{dt} = \) Rate change of degree of cure [1/s]

\(V_f = \) Volume fraction fibre

\(\rho_r = \) Density of resin [kg/m³]

\(H_R = \) Total heat of reaction [J/kg]

1-D Thermal Modelling Example

For many cases, 1-D modelling of the through-thickness thermal distribution is sufficient. Provided here is an example for the curing of a thermoset matrix laminate modelled 1-D in the through-thickness direction. Shown are the heat transfer interactions, temperature profile, and heat equation involved for the lay-up stack for the heating stage, and after the thermoset exothermic reaction has kicked off with internal generated heat being released. If a substantial amount of heat is generated, the heat may leave the laminate and transfer into its surrounding environment.

Example: Autoclave cured carbon fibre/epoxy prepreg laminate

• Scenario Setup:

Laminate	1-D (through-thickness) Lay-up Stack	Temperature History
Thick carbon fibre/epoxy prepreg laminate.	1-D schematic of typical lay-up stack for an autoclave cured laminate.	Example of a typical temperature history of a laminate following a manufacturer's recommended cure cycle (MRCC). Note the hump in laminate temperature due to the thermoset resin exothermic reaction.

• 1-D Thermal Modelling Representation:

	Temperature Profile	Heat Transfer System Interactions	Heat Equations
Laminate Heat Up	1-D temperature profile during laminate heating.	1-D system heat transfer interactions during heating stage.	Heat Transfer Balance: Air/Part Interface Rate of heat transfer by convection\[\dot Q = hA\Delta T\] Laminate and Tool Heat Balance Laminate and tool energy balance\[\frac{\partial}{\partial t}(\rho c_pT)= \frac{\partial}{\partial z}\Bigl(k_{zz}\frac{\partial T}{\partial z}\Bigr)\] Air/Tool Interface Rate of heat transfer by convection\[\dot Q = hA\Delta T\]
Laminate Exotherm	1-D temperature profile during laminate exothermic reaction.	1-D system heat transfer interactions during laminate exothermic reaction.	Heat Transfer Balance: Air/Part Interface Rate of heat transfer by convection\[\dot Q = hA\Delta T\] Laminate and Tool Heat Balance Laminate energy balance\[\frac{\partial}{\partial t}(\rho c_pT)= \frac{\partial}{\partial z}\Bigl(k_{zz}\frac{\partial T}{\partial z}\Bigr)+\dot Q_r\] Internal heat generation (laminate exotherm)\[\dot Q_r = \frac{d\ x}{dt}(1-V_f)\rho_r H_R\] Tool energy balance\[\frac{\partial}{\partial t}(\rho c_pT)= \frac{\partial}{\partial z}\Bigl(k_{zz}\frac{\partial T}{\partial z}\Bigr)\] Air/Tool Interface Rate of heat transfer by convection\[\dot Q = hA\Delta T\]

Measurement

The heat transfer process can be measured by proxy in two ways:

1. Temperature measurement: tracking temperature evolution (with time and position) to develop an understanding of the thermal management system and when available to validate a thermal model
2. Heat transfer coefficients: measuring the heat transfer coefficients, conduction \(k\) and convection \(h\) to use them for thermal modelling as inputs

Listed below are the different techniques to measure temperature and heat transfer coefficients.

Temperature Measurement

• Thermocouple
• Infrared Camera
• Fibre Optic

Heat Transfer Coefficients

Thermal Conductivity

• Link to Thermal Conductivity page - Measurement

Convective Heat Transfer Coefficient

• The following table from Slesinger et al. , provides a list of the possible methods available to measure airflow and convective heat transfer coefficients (HTC).

Airflow and heat transfer measurement methods. Source:

	Advantages	Disadvantages
Anemometers	• Measures actual velocity values	• Non-directional • Noisy results (turbulence) • Expensive, difficult to position • Local – need to know where
Calorimeters	• Inexpensive • Provides representative HTC values	• Time consuming data reduction • Non-directional • Length scale dependency (real HTC may be different) • Local - need to know where
CFD	• Shows velocity magnitude and direction • All areas can be evaluated • Parametric evaluation	• Model may lack realistic detail • Time consuming, expensive • Requires skilled personnel • Must be validated experimentally
Instrumented Part	• Provides actual HTC	• Accuracy limited by number of thermocouples • Time consuming data reduction •Autoclave load or part geometry changes require new test • Non-directional • Local - need to know where
Video	• Inexpensive • Intuitive to analyze • Large areas can easily be monitored	• Qualitative • Limited to ambient temperature and pressure

Explore this area further

• Heat transfer - A132
  • Conduction - A118
  • Convection - A106

Related pages

Page type	Links
Introduction to Composites Articles
Foundational Knowledge Articles	Conduction - A118 Convection - A106 Heat transfer - A132 Materials science - A235 Processing science - A151 Thermal behaviour - A232
Foundational Knowledge Method Documents
Foundational Knowledge Worked Examples
Systems Knowledge Articles
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	Composite materials engineering webinar session 4 - Thermal management and resin cure - A123 Composites Process Simulation: A Review of the State of the Art for Product Development - A283 Dr. Anoush Poursartip's cdmHUB global composites expert webinar - A136 Heat Transfer in Composites Processing - A321

References

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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.

The use of multiphysics models to predict the outcome of real-world scenarios. May be analytical (closed form, "hand calculations") or computational (implementation on computers is required due to the large number of calculations involved. e.g. finite element method, finite difference method)

Most often in composite materials engineering, modelling refers to either:

• Process modelling (predicting manufacturing outcomes, or the inverse problem of predicting manufacturing parameters to achieve a desired outcome), or
• Performance modelling (predicting the stiffness/strength/suitability of a structure, or the inverse problem of the material properties and dimensional requirements to achieve a desired stiffness/strength/suitability of a structure)

(same as "Simulation")

The use of multiphysics models to predict the outcome of real-world scenarios. May be analytical (closed form, "hand calculations") or computational (implementation on computers is required due to the large number of calculations involved. e.g. finite element method, finite difference method)

Most often in composite materials engineering, simulation refers to either:

• Process simulation (predicting manufacturing outcomes, or the inverse problem of predicting manufacturing parameters to achieve a desired outcome), or
• Performance simulation (predicting the stiffness/strength/suitability of a structure, or the inverse problem of the material properties and dimensional requirements to achieve a desired stiffness/strength/suitability of a structure)

(same as "Modelling")

The continuous material phase that binds the reinforcement together, maintains shape, transfers load, protects the reinforcement from environment and damage, and provides the composite support in compression.

Desirable characteristics:

• Moisture/chemical resistance
• Low density
• Processability

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.

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.

A class of polymer, some common examples include polypropylene and polyethylene.

They soften and melt upon heating (i.e. potentially recyclable), high viscosity when melted, therefore difficult to saturate fibres. Usually needs a lot of pressure and heat to process.

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.

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.

Carbon fibres are composed of large aromatic sheets similar to those in graphite. These graphitic layers form the basic structural units in the shape of ribbons. The structure of carbon fibre ribbon is believed to be a columnar arrangement of disoriented graphite crystallites parallel to the ribbon length. The idealized tetragonal crystallites are stacked above one another, with slight disorientation between the crystals in the direction of fibre axis, trapping sharp needle like voids, where the boundaries between the stacks represent the disordered regions.

Pre-impregnated (prepreg) material refers to fibre that is already combined with resin. It is the most common material form used in aerospace.

During prepreg production, (e.g. fibres are run through a resin bath), prepreg is heated and partially cured to B Stage (< 5 % degree of cure). Thermoset prepregs (e.g. epoxy prepreg) have to be kept in a freezer at around -20 °C. At room temperature, the epoxy starts to cure.

Manufacturer's Recommended Cure Cycle (MRCC).

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.