# Thermal Conductivity Measurement

## What is Thermal Conductivity?

Thermal conductivity refers to the ability of a given material to conduct or transfer heat. There are many techniques of Thermal conductivity measurement, in this article two main techniques are explained.

Thermal conductivity is generally denoted by the symbol ‘k’ but can also be denoted by ‘λ’ and ‘κ’. The SI unit of this quantity is watts per meter-Kelvin or Wm -1K-1.

The reciprocal of thermal conductivity is known as thermal resistivity. Materials with high thermal conductivity are used in heat sinks whereas materials with low values are used as thermal insulators.

Thermal conductivity is expressed in terms of the following dimensions:

Temperature, Length, Mass, and Time.

There are a number of methods to measure thermal conductivity. In general, there are three classes for measuring thermal conductivity

3. Frequency domain methods

The steady‐state technique records a measurement when a tested material’s thermal state reaches complete equilibrium that is its temperature does not change with respect to time. A steady‐state condition is attained when the temperature at each point of the specimen is constant and the temperature does not change with time.

Thermal Conductivity in Steady State is determined as follows

Thermal conductivity in steady state is given by formula:

where,

q is quantity of heat passing through a unit area of the sample in unit time [W/m2]

d distance between two sides of the sample [m]

T1 temperature on warmer side of the sample [K]

T2 temperature on the colder side of the sample [K]

The quantity of transferred heat q is given by:

where,

Q is quantity of heat passing through a base area of the sample [W]

A base area of the sample [m2]

Temperature in the laboratory during the measuring should not vary more than ± 2° C and relative.

humidity should not exceed 65 %.

A disadvantage of this method is that it generally takes a long time to reach the required equilibrium. Also, the method involves expensive method apparatus since a well‐designed experimental installation system is usually needed.

Nevertheless, it is the primary and most accurate measurement method.

### Guarded hot plate (GHP) of Thermal Conductivity Measurement

The guarded hot plate, also known as the Poensgen apparatus, is the most commonly used and most effective method for measuring the thermal conductivity of insulation materials.

The configuration is arranged symmetrically, with guarded hot plates located on the sides while the heater unit is sandwiched between two specimens or a single specimen and an auxiliary layer.

As shown in figure, in single‐sided system state, the heat flow passes through one specimen, while the top of the main heater acts as an insulating guard, thus ensuring an adiabatic environment.

These heat measurements are recorded by differential thermocouples, which are instruments that control a flat electrically heated metering area that is surrounded on all adjacent sides by a guard heater section.

In the two-specimen apparatus heat loss from the hot plate can be controlled more effectively due to the symmetrical arrangement of the specimen on each side of the heater as shown in following figure.

Unlike the single‐specimen method, the symmetrical setup can be used for investigating solid materials. For measuring the conductivity of non-solid materials, it is necessary to heat the specimen from the top in order to avoid convection.

Its operation is based on the establishment of a stationary temperature gradient over a known thickness of a sample and on controlling the flow of heat from one side to the other. It is very important to control the heat flow so that it is unidirectional and perpendicular to the sample.

• Establishing a steady‐state temperature gradient through a specimen is time‐consuming when using the GHP and other steady‐state techniques.
• The temperature gradient must be relatively large, the specimen width must be large, and also that the contact resistance between the thermocouple and the specimen surface poses a major source of error.

### Guarded Heat Flow Meter Method of Thermal Conductivity Measurement

This method is similar to the hot plate, except that instead of measuring temperature differences, the heat flux through the sample is measured. This is attained by means of one or two heat flow sensors permanently installed in the appliance.

In many cases, heat flow sensors consist of a series connection of thermocouples across a thermal resistor, for example a thin ceramic or plastic plate.

In that case the signal is a thermal voltage proportional to the temperature drop across the board. In more modern designs, thermoelectric or Peltier effect modules are used as heat flow sensors, which generate an electric current proportional to the flow of heat that passes through them.

## Transient Methods

The advantages of transient methods are mainly distinguished by the short amount time needed, so that various thermal values can be determined in the measurement process. Therefore, this method is based on a signal measurement and an acceptably small temperature differential.

The transient technique is measured by evaluating the feedback response after a signal is transmitted to the specimen for heat generation in the specimen. Therefore, test time is obtained in a few minutes or a sub second time intervals for transient methods.

Among transient methods, the hot‐wire and the laser flash methods are commonly used for measuring the thermal conductivity of different materials.

A modification of the hot‐wire method is the hot‐strip or disk technique, which can be applied to solid non electrically conducting materials in order to measure the thermal diffusivity and conductivity.

### Hot‐Wire Method (THW) of Thermal Conductivity Measurement

The hot wire technique consists of keeping a conductive wire immersed (eg platinum (Pt) or tantalum) in the material under study and pass a constant electric current through it, so that it is heated by the Joule effect.

A schematic representation of the hot wire model is shown in the Figure.

The speed with which the temperature of the conductive wire increases depends on the heat dissipated by conduction towards the surrounding material.

Therefore, by measuring said speed, the thermal conductivity of the material can be obtained. In fact, in the case of liquids, it has become the standard reference. Some authors use mercury capillaries to measure refrigerant mixtures.

### Laser Flash Method of Thermal Conductivity Measurement

The laser flash method is the most commonly used method for ascertaining the thermal properties of solids. The method can investigate to properties of glasses, metals, and ceramics without significant limitations due to uncertainties of the achievable measurement.

In the method, a laser pulse is sent to the front side of a specimen, and the temperature change on the back side is measured. The method is conducted through heating a specimen with a short laser pulse of 1 ms width on the front side of the specimen. The temperature increase at its rear side is measured and determined.

Laser Flash apparatus has testing temperatures that can range from -125°C to a reported 2800°C in the range of 0.1 to 2000 W/mK.