# Direct and Indirect Measurement of Thermal Conductivity and its Limitations

## Topics Covered

Introduction
Direct Thermal Conductivity Measurement
Transient Mode Testers
Indirect Thermal Conductivity Measurement – The Flash Method
Deviations in Indirect Thermal Conductivity Measurement
Conclusions
Anter Thermal Analysis Equipment

## Introduction

A single instrument that can determine the thermal conductivity of a spectrum of incongruous materials such as glass, metal and various composites does not exist. These materials usually have entirely different parametric requirements for thermal conductivity testing and an instrument which can satisfy one requirement will not satisfy all the others, thus making it almost impossible to have a universal device. The principles that prevent the realization of a single machine for thermal conductivity measurement are detailed below.

## Direct Thermal Conductivity Measurement

Thermal conductivity can be given as I = (Q/A)/(DT/DL)

where

• Q/A is the heat flux
• Q is the quantity of heat passing through a cross section A of the sample
• DT is the difference in temperature across a length DL along the heat flow
• and DT/DL is the resulting thermal gradient

The above equation holds true for unidirectional heat flow. Hence some other means should be employed to minimize heat dissemination in other directions. However, all such methods are necessarily quantitative, since the amount of heat that gives rise to the measured difference in temperature should be known. The process is independent of the properties of the sample material as long as the constituents of this quantitative relationship are evaluated.

## Steady State Thermal Conductivity Testers

By using insulators like the flat disk sample, which has a low conductivity, a good thermal gradient can be achieved easily even across a thin sample. In comparison, the gradient would be significantly less for a metallic sample. In order to increase the gradient and make it measurable, one would need to increase the power or a thicker sample can be used. When the sample is a good conductor, it will should have a thickness-diameter ratio of 2 or more. Hence, simply escalating power will result in more losses and shunting paths. This holds true for any steady state thermal conductivity tester using any method. Just increasing the thickness is also not recommended as it will affect the geometry and the machine will function well with only a specific material. So a combination of the above two should be used.

Anter’s cut-bar instruments are used for the 0.5 to 60 W/(mK) range. They can operate in the thickness-diameter ratio range of 1/2–1 or 1–2.

## Transient Mode Testers

The transient mode testers usually operate in the steady state part of transient phenomena and cannot withstand conductivities of more than 4-5 W/(mK). They work well with insulators and porous samples and samples containing large aggregates. Currently, Anter limits the operation of transient mode testers to 1400°C.

## Indirect Thermal Conductivity Measurement – The Flash Method

The Flash Method is the most widely used method for indirect measurement of thermal conductivity. This method evaluates thermal diffusivity and the corresponding thermal conductivity can be calculated using the following equation which shows the relationship between thermal conductivity and thermal diffusivity:

I = áCpñ

where

• á is the thermal diffusivity
• Cp is the specific heat capacity and
• ñ is the density

The above equation will hold good only for pure, homogenous and anisotropic materials. Also, the values of Cp and ñ should be precisely known to get an accurate value for I.

## Deviations in Indirect Thermal Conductivity Measurement

The Flash Method measures the increase in temperature at the back surface of the sample when the front side of the sample is irradiated by a high energy pulse from a laser or a flash lamp. The rise in temperature is in line with the pattern of propagation of the pulse, thus giving a qualitative and not a quantitative measurement of heat transfer. Composite materials usually furnish erroneous results, more so when translated into conductivity values. Also, testing of highly porous insulators by this method is not recommended.

Ideally, the sample should have a diameter of 12.5 mm and a thickness of 1-2 mm, though very high conductors can have thicknesses of up to 5mm. Larger samples are occasionally used in exceptional cases. This small size of the sample in this method makes it beneficial for a variety of applications, but at the same time makes it not suitable for samples having a large fraction of pores or particles.

## Conclusions

The Flash Method, despite being the most widely used method for testing thermophysical properties, does not provide a solution for all the problems encountered during measurement of thermal conductivity. Also, it cannot be applied to all materials. This review is aimed at warning investigators of the potential traps in trying to choose a universal thermal conductivity/diffusivity testing machine that covers an unrealistically wide range of materials and temperatures. It also aims at alerting potential users to factors that influence the applicability of a device for a specific purpose.

## Anter Thermal Analysis Equipment

Anter Corporation manufactures thermal properties analyzers to measure:

This information has been sourced, reviewed and adapted from materials provided by Anter Corporation.