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# Thermal diffusivity - A143

Thermal diffusivity
Foundational knowledge article
Document Type Article
Document Identifier 143
Themes
Relevant Class

Material

Tags
Prerequisites

## Introduction

Thermal diffusivity, $$\alpha$$, is a quantitative measure of how a material will respond to transient thermal conditions. It is defined as the ratio of thermal conductivity to the volumetric heat capacity of the material (density times the specific heat capacity).

## Scope

This page defines thermal diffusivity, explains its significance in composites processing, and provides some typical values.

## Significance

Materials with large thermal diffusivity have a high thermal conductivity relative to their heat capacity (i.e. their capacity to store thermal energy). As a result, they will rapidly distribute the thermal energy throughout their volume and change temperature quickly during heating or cooling. On the other hand, materials with a low thermal diffusivity have a low thermal conductivity relative to their hear capacity and will have a slow temperature response to a change in thermal conditions and will develop larger temperature gradients.

Thermal diffusivity is a key property in composites processing. For example, the thermal diffusivity of the tooling material dictates the rate at which heat is transferred through the tool between the hot side to the cold side. Tooling materials with a greater thermal diffusivity will react to localized heat change faster compared to a tooling material with low thermal diffusivity, reducing the internal thermal gradient that can form within the tool and subsequently within the part. To learn more about this interaction between tool heating and part curing, please see the effect of tooling in a thermal management system page in the Systems Knowledge volume.

## Prerequisites

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

## Definition

Thermal diffusivity is the measure of the rate of temperature movement through a material. It is used in the heat transfer equation describing the change of temperature for transient (non-steady state) heat flow.

Thermal diffusivity $$\alpha$$ is defined as the ratio of thermal conductivity to the volumetric heat capacity of the material (density times the specific heat capacity) and calculated as$\alpha=\frac{k}{\rho c_p}$

Where,

$$k=$$ Thermal conductivity [W/m·K]

$$\rho=$$ Material density [kg/m3]

$$c_p=$$ Specific heat capacity [J/kg·K]

Together, the bottom terms ($$\rho c_p$$) represent the volumetric heat capacity [J/m3·K].

### Units

The general units of thermal diffusivity can be represented as$\alpha=\frac{Length\, unit^2}{Time\, unit}$

The following are common International System of Units (SI) and US Customary Units found in the literature for thermal diffusivity:

SI Units US Customary Units
Base units m2/s ft2/s
Other common forms m2/h ft2/h
mm2/s

## Typical Values

### Examples of typical thermal diffusivity values seen in a various materials.

Material Typical Value

(SI units)

m2/s

Typical Value

(US Customary Units)

ft2/s

[ref.]
Carbon Fibre (transverse) 1.9 x 10-7 2.0 x 10-6 [1]
Glass Fibre (S2) 8.0 x 10-7 8.6 x 10-6 [2]
Epoxy 1.5 x 10-7 1.6 x 10-6 [3]
PEEK 1.5 x 10-7 1.6 x 10-6 [1]
Cork 2-5 x10-7 2-5 x10-6 [4]
Steel (304 stainless) 4.0 x 10-6 4.3 x 10-5 [4]
Aluminum 9.7 x 10-5 1.0 x 10-3 [4]
Invar 2.6 x 10-6 2.8 x 10-5 [3]

## Measurement

The following methods to measure thermal diffusivity are recommended by the Composites Materials Handbook - 17 (CMH-17) [5]:

## Related pages

Introduction to Composites Articles
Foundational Knowledge Articles
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

## References

1. [Ref] Hoa, S V (2018). Principles of the Manufacturing of Composite Materials. DEStech Publications, Incorporated. ISBN 9781605954219.CS1 maint: uses authors parameter (link) CS1 maint: date and year (link)
2. [Ref] MatWeb LLC. "MatWeb: Online Materials Information Resource". Retrieved 9 September 2020.CS1 maint: uses authors parameter (link)
3. [Ref] Thermtest Inc. "Thermtest Instruments: Materials Thermal Properties Database". Retrieved 14 January 2021.CS1 maint: uses authors parameter (link)
4. [Ref] Gaskell, David R. (1992). An Introduction to Transport Phenomena in Materials Engineering. Macmillan Publishing Company. ISBN 0023407204.CS1 maint: uses authors parameter (link) CS1 maint: date and year (link)
5. [Ref] Composite Materials Handbook 17 - Polymer Matrix Composites; Guidelines for Characterization of Structural Materials. 1. SAE International on behalf of CMH-17, a division of Wichita State University. 2012. ISBN 978-0-7680-7811-4.CS1 maint: date and year (link)

## Welcome

Welcome to the CKN Knowledge in Practice Centre (KPC). The KPC is a resource for learning and applying scientific knowledge to the practice of composites manufacturing. As you navigate around the KPC, refer back to the information on this right-hand pane as a resource for understanding the intricacies of composites processing and why the KPC is laid out in the way that it is. The following video explains the KPC approach:

## Understanding Composites Processing

The Knowledge in Practice Centre (KPC) is centered around a structured method of thinking about composite material manufacturing. From the top down, the heirarchy consists of:

The way that the material, shape, tooling & consumables and equipment (abbreviated as MSTE) interact with each other during a process step is critical to the outcome of the manufacturing step, and ultimately critical to the quality of the finished part. The interactions between MSTE during a process step can be numerous and complex, but the Knowledge in Practice Centre aims to make you aware of these interactions, understand how one parameter affects another, and understand how to analyze the problem using a systems based approach. Using this approach, the factory can then be developed with a complete understanding and control of all interactions.

## Interrelationship of Function, Shape, Material & Process

Design for manufacturing is critical to ensuring the producibility of a part. Trouble arises when it is considered too late or not at all in the design process. Conversely, process design (controlling the interactions between shape, material, tooling & consumables and equipment to achieve a desired outcome) must always consider the shape and material of the part. Ashby has developed and popularized the approach linking design (function) to the choice of material and shape, which influence the process selected and vice versa, as shown below:

Within the Knowledge in Practice Centre the same methodology is applied but the process is more fully defined by also explicitly calling out the equipment and tooling & consumables. Note that in common usage, a process which consists of many steps can be arbitrarily defined by just one step, e.g. "spray-up". Though convenient, this can be misleading.

## Workflows

The KPC's Practice and Case Study volumes consist of three types of workflows:

• Development - Analyzing the interactions between MSTE in the process steps to make decisions on processing parameters and understanding how the process steps and factory cells fit within the factory.
• Troubleshooting - Guiding you to possible causes of processing issues affecting either cost, rate or quality and directing you to the most appropriate development workflow to improve the process
• Optimization - An expansion on the development workflows where a larger number of options are considered to achieve the best mixture of cost, rate & quality for your application.