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Thermal Conductivity In Physical Engineering Engineering Essay


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Thermal Conductivity is an essential physical property for designing engineering process and measuring the capacity of temperature exchange between heat and cold passing through a material mass. Techniques were developed to measure thermal conductivity in a various materials, Hence the objective of this work was to evaluate the feasibility of utilizing different methods for measuring thermal conductivity as well as construction of the experimental assemble to measure thermal conductivity of numerous materials with the aim of analysis of the experimental data. This paper illustrates the methods of the measurements of thermal conductivity and the process by which it will be brought to a successful culmination.

The study of thermal conductivity is important for engineers to know the nature of thermal energy, temperature and how materials store thermal energy as well as to predict the performance of any given material over its lifetime in a specific application. Also to identify the thermal properties of material so as to assess the performance of certain material and develop efficient heat transfer materials for engines and spacecrafts. This project has been taken on board, due to a lack of information and research available on thermal conductivity measurements.

Heat is transferred by three procedures which include Conduction, Convection and Radiation. It engages transfer of thermal energy from one place to another. Thermal conductivity is a significant parameter for the analysis of heat transfer through conduction. Conduction takes place due to the particle collision which results in the transfer of thermal energy. Thermal conductivity (k) is an essential property of a material and defined as amount of heat transferred in a unit thickness of materials in a direction because of change in temperature in constant boundary state in a direction perpendicular to the area of transfer. It is measured in watts per Kelvin per meter (WK-1m-1) and determines the rate of energy loss through a material.

The project is titled as study of methods for measurement of thermal conductivity. The project will present the literature review about the methods as well as conducting an experiment to measure the thermal conductivity of different materials. In addition, a thorough analysis of the experimental data is to be obtained while performing the experiment. The aims and objectives of this report pursue as: -

Understanding of theoretical and experimental methods to measure thermal conductivity of solids, liquids and gases.

Construction of experimental rig.

A thorough analysis of the experimental data.



Based on the module guide, the following are the generic deliverables for the academic year 2010-2011;



Start Date

Submission Date

Semester 1

Preliminary start

Monday 27th September

Submit Project Planning Report + Log Book

Friday 26th November

Semester 2

Dissertation start

Monday 31st January

Project seminars and poster

Week commencing 11th April

Submission of final report

Thursday 28th April

Table 2 Delivery dates set by Kingston University for entire project


The objectives of the project have been identified and analysed to produce the following deliverables that will have been produced at the end of the project

Construction of an experimental rig to measure thermal conductivity of selected material

Analysis of the experimental Data

Comparison of the results


The tasks that need to be executed in order to achieve the aims of the project, produce the deliverables on schedule and bring the project to a successful end are as follows:

Literature review of conductivity methods





Conductivity methods of solids

Conductivity methods of Liquids

Conductivity methods of gas

Construction of the experimental Rig

Results Comparison

A literature review will give an insight into various methods of conductivity. Journals, books and other forms of resources will be used to get an understanding of current concepts of methods and recent modifications (Advantages, disadvantages and limitation). This will form the base of the construction of the experimental rig. Once the technique is selected to perform, various materials will be used to determine their conductivity and hence, the data obtained will be analysed.


A timeline/Gantt chart should be produced, showing the sequence and duration of the tasks over the project lifetime. A set of key milestones by which the project progress can be monitored may also be produced.

Figure 1 Illustrate an Inital Gantt Chart


As of 26/11/10 the project is at the beginning of the research phase. The literature review has been completed by looking into journals and online resources. The information gathered has been on advantages, disadvantages, limitation, process and setup of the conductivity measurement techniques. I have gathered and read a number of journals relating to conductivity measurements.


In solids, particles are packed close together by chemical bonds. As heat is transferred, the particles gains energy which results in increase in kinetic energy and particles vibrate against theneighbouring particles causing transfer of energy between the particles. Increase in temperature causes increase in thermal conductivity because of the mobility of boundless electrons. Heat energy is transferred in solids by means of lattice waves, electrical carriers and electromagnetic waves. In metals, the heat is largely transferred by electrical carriers whilst in insulators lattice waves carry large amount of heat. The change in magnitude and temperature of thermal conductivity of solids is due to the dislocations, imperfections of lattice forces and interface between lattice waves and carriers. However the change of thermal conductivity varies depending upon materials. A summary of different techniques to measure thermal conductivities is shown on next page.





Figure 2 Summary of Techniques to measure thermal conductivity of solids

Transient Techniques

Methods to measure thermal conductivity of solids

Steady State Techniques

Comparative Method

Pipe Test Method

Cut Bar Method

Guarded Hot Plate Method


It exists in three forms which include single, crossed resistive wires and two parallel wires distant apart. It is utilized to measure thermal conductivity of refractories and takes several assumptions into account which pursue as: -

Isotropic Material with Uniform preliminary Temperature

Figure 3 Setup of Hot-Wire method

(2010, Home, [Internet], Available at: http://www.tpl.fpv.ukf.sk/engl_vers/hot_wire.htm , accessed on 8 October 2010)Hot wire an ideal, infinite thin, and long line heat supply

Thermal Conductivitycan be determined by temperature vs. time response (K) due to production of heat flux (q) in the wire surrounded in the sample.

Equation 2 Measurement of thermal Conductivity using Hot-Wire Method




Extensive Procedure of measuring at specified temperature

Simplistic in Configuration

Not utilized to measure thermal conductivity of anisotropic material

Short Duration in Measurement

Expertise required

Table 3 Advantages and Disadvantages of Hot-wire Method


It is utilized to measure thermal conductivity of materials as well as thermal diffusivity and specific heat. It has the ability for in-situ measurements and effective contact of the sample with a single tiny gap.

When measuring the thermal conductivities of solids, samples are outfitted with hole machined in order to enclose probe diameter whilst measuring liquids, probes are pushed into the samples that are to be tested. This method consists of hollow tube functioning as heat supply element and temperature sensor estrange by means of medium with high thermal conductivity and electrical insulation to ensure minor difference of radial temperature within the probe.


Figure 4 Apparatus of TPS

(2010, Home, [Internet] Available at: http://www.ask.com/wiki/Thermal_conductivity_measurement , 10 October 2010)It is also acknowledged as Hot Disk Method and has several advantages such as accurate, comprehensiveness and ease of application. It consists of a flat sensor along with continuous double spiral of electrically conducting nickel metal etched out of thin foil and clad between two layer of kapton which provides mechanically stability and electrically insulation to the sensor. The rise in temperature is caused when current passes through nickel spiral and heat formed is dispersed by sample. Thermal conductivity is measured by recording temperature vs. time response in the sensor.

In addition, modified traditional transient plane source method imparts maximum flexibility for scrutinizing thermal conductivity of liquids and powder and sustain heating element on a support. It utilizes single surface interfacial heat reflectance sensor that provides constant heat to the sample and functions temporarily.


It is the infinite line source with constant power per unit length and identical in principle to Hot-wire method. In order to determine temperature at a certain distance the following equation was taken into consideration:

Equation 3 Measurement of temperature using C-Therm TCi System

where: Q = Power per unit Length

E = Exponential Integral

t = Time Passed since Heating


Figure 5 Apparatus of Pipe Test Method

(2010, Home, [Internet], Available at: http://www.evitherm.org/default.asp?lan=1&ID=894&Menu1=894 , 13 October 2010)It is identical in concept to the guarded hot plate method. It consists of a central heater which contains a cylinder placed in such a way that the heater achieves a constant temperature by means of alteration in spacing of windings in the heater in permutation with the utilization of concise split guard heaters at the ends.

It can operate horizontally and vertically by situating the apparatus in a stable environment. It employs radial flow to determine thermal conductivity of minerals, plastics etc.


Figure 6 Apparatus of Comparative Technique

(2010, Home, [Internet], Available at: http://www.evitherm.org/default.asp?lan=1&ID=893&Menu1=893 , 15 October 2010)A test specimen is crammed under load flanked by two reference materials; each is bounded by longitudinal guard cylinder. This results in production of temperature gradient along with the stack as well as longitudinal heat flows as consequences of temperature gradient in the guard cylinder to that in specimen stack. Therefore, the thermal conductivity is measured by recording the difference in temperature across the reference and test specimen. It has several advantages which pursue as: -


Simple in implementation


It is also known as the workhorse of the thermal conductivity field and can be utilized to measure homogenous and heterogeneous composite solids.


Figure 7 Apparatus of Guarded Hot Plate Method

(2010, Home; [Internet], Available at: http://www.azom.com/details.asp?ArticleID=2667 , 16 October 2010)The test material is positioned on a flat plate heater with electrically heated inner plate surrounded by guard heater. Its function is to maintain similar temperature at both sides of the gap extricating the main and guard heaters as a result, prevention of lateral heat flow and heat energy flows in the direction of sample.

Calculated direct current is functioned to the hot plate and numerous temperatures across cold plates and heater is controlled in order to give off constant temperature at the sample surfaces. Hence, the accuracy of thermal conductivity measurements is dependent on conservation of constant temperature conditions and is measured by Fourier heat flow equation: -

Equation 4 Measurement of Thermal Conductivity using Guarded Hot plate method

where: W = Electrical Power Input

dT = Difference in temperature across the specimens

d = Sample thickness


Figure 8 Apparatus of Cut-Bar Technique

(2010, Home, [Internet] Available at: http://www.anter.com/TN67.htm , 17 October 2010)It is utilized for axial thermal conductivity measurements. An unknown thermal conductivity disk sample is sandwiched between two known thermal conductivity cylinder metal brass by thermal grease and pliable metal in order to reduce interfacial thermal between the cylinders. In addition, a thermocouple situated along the three material pieces produces information on the rate of heat flow by the two known thermal conductivity. Hence, thermal conductivity is calculated using the following equation: -

Equation 5 Measurement of thermal Conductivity using cut-bar technique

There are some other techniques to measure thermal conductivity of solids which include: -

Steady-State techniques

Transient Techniques

Four-Probe Method

Laser Flash Method

Guarded Heat Flow Method

Angstrom Method

Heat Flow Meter Method

Photo thermal Method

Transient Hot Strip Method

Table 4 Other Techniques to measure thermal conductivity of solids


Liquids particles are situated in a cubic lattice, as energy moves from a single lattice plane to the following at a speed at which sound passes through the liquid of interest. Thermal conductivity can be estimated using Bridgeman's equation: -

Equation 6 Bridgeman's Equation

where: N = Avogadro's Constant = (6.023 x 1023)

K = (Boltzmann's Constant) = (1.3807 x 10-23 J/K)

V= Molar Mass = M/ρ

= Speed of sound through fluid sample

A summary of different techniques to measure thermal conductivities of liquids is shown on next page.











Figure 9 Techniques to measure thermal conductivity of liquids


The apparatus consists of hot-wire cells utilizing electrically insulated hot wires dependent on an electrically conducting fluid. Wires of minute diameter are immersed within the fluid and utilized simultaneously as an electrical resistance as well as resistance thermometers, thus to enable calculation of the increase in temperature due to the resistance heating. Thermal conductivity is determined using the same process as mentioned above. Finite dimensions of the fluid can be improved, however modification to the finite dimension of wire can be reduced by utilizing minute hot-wires.


Its features include a heating frequency (of 10 KHz), direct measurement of thermal conductivity and temperature range of -190 to 500. It comprises of alternating current and lock in amplifier to estimate thermal conductivity of the dielectric materials directly. Advantages of 3-Omega Method are being precise and fast. Thin metal situated on the specimen, an alternating current with frequency ω exceeds via strip causing heating of the material and measurement of voltage v (t) simultaneously. In addition, assumption of the heat flow along the cross plane axis of the film results in determination of the thermal conductivity using the following equation: -

Equation 7 Determination of thermal conductivity using 3 Omega Method

where: - P1 = Power

b = Width of the strip

=Increase in temperature oscillation of the strip


A liquid sample is sandwiched between a minute thin metal disk and a sampler holder. Sample holder minimizes thermal contact with the sample plus suppresses stray light transmitted from the laser to the IR detector. At the time when the laser beam is taken in the front surface of the metal disk, the heat flows downward through liquid sample and temperature rises. Thus, thermal conductivity can be estimated by the disk's foil temperature without measuring the thickness of the sample liquid layer and reference material.


It is a linear heating process that has super imposed sinusoidal oscillation which yields in cyclic heating of the sample. Advantages of the method pursue as: -

Short Analysis time

No instrument modification

Figure 10 Apparatus of DSC

(2010, Home, [Internet], Available at: http://pslc.ws/macrogcss/dsc.html, 1 November 2010)


Small thermal gradient across the sample

Experiment is performed in a non-adiabatic surrounding; numerous unknown specimens with identical length and cross sectional areas are formed. Furthermore, known specimens with their conductivity and a density supplied to the unknown specimen are formed with identical length and cross sectional to the unknown specimen. Each specimen is subjected to an equal amount of rise in heat to estimate the specific heat capacity. Therefore, the thermal conductivity obtained is:

Equation 8 Measurement of thermal conductivity using DSC

where: D = diameter of the specimen

M = Mass of the specimen

= Specific heat capacity


A device designed to overcome the effects of convection that Prevents accurate measurement of liquid's conductivities. Measures organic liquids' conductivity rapidly and has several advantages which follow as: -

Short time measurement


Constant current passes via thermistor which functions as a heating element immersed in the liquid sample. As conductivity varies with liquid, the rate of temperature varies with liquids. Hence, thermal conductivity is inversely proportional to rate of temperature change.


Figure 11 Apparatus of Radia Heat Flow

(2010, Home, [Internet], Available at: http://www.scielo.br/scielo.php?pid=S0104-66321999000400009&script=sci_arttext, 27 October 2010)A steady-state technique which offers variation of conductivity under pressure as well as absolutes values of conductivity. It is fast and requires a small pressure gradient. Liquid sample is situated between two concentric cylinders (brass and Pyrex glass construction), the axis of the inner cylinder acts as a supply of heat which flows out radially crossways the layer of fluid.

Measurements of difference in temperature between inner and an outer surface of the layer of the fluid are taken to obtain thermal conductivity.


Figure 12 TCD to measure thermal Conductivity of Gas

(2010, Home, [Internet], Available at: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-50532004000600009, 2 November 2010)

Thermal conductivity detector (TCD) is utilized to measure thermal conductivity of gas by pulse injection. Heat is transmitted from hot to cold element by way of thermal conduction passing through the carrier gas. However, the difference in temperature between hot and cold element is maintained. Due to the thermal flow energy into the gas medium thermal gradient is generated. The power need to heat the hot element is a direct evaluation of the electrically signal output for the thermal conductivity.


As mentioned above, the project is currently at the beginning of the research phase. Investigation into the areas described above is vital as the information gathered will have implications on the selection of the technique for the experiment. The project objectives should be met on schedule as there are not any limitations restricting the project from completion. Whilst performing the experiment in the near future, there may be some timing conflicts as there will be other students using the same machinery in the workshop but as enough time is allocated for the task in hand there should not be any difficulty in completing the objectives. Although there may be some complications when obtaining results, however with the knowledge and experience available via the lab technicians any problem(s) shall be duly addressed.


In conclusion the project aims and deliverables have been identified and the required tasks needed achieve the aims and produce the deliverables have been identified and discussed. An initial Gantt chart has been drawn up to illustrate the sequences and durations of the tasks to be completed. It can be seen that the performance so far is coincident with the planned set of activities for this time period within the Gantt chart. As a result, it is expected that the project is likely to be completed on time.

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