Heriot-Watt University

Thermodynamics Thermal Conductivity Measurement

Summary
An unknown material was heated on one end by an electric heater and cooled on the other
by a water flow. 4 thermocouples where attached evenly spaced along the sample material.
Once it reached a steady state, and the temperature gradient showed a straight line on the
VI (virtual instrument). Values calculated by the VI were then put in the equation stated in
theory to calculate a value for conductivity. The thermal conductivity calculated of 17.97
W/mK was close to the researched theoretical values for stainless steel.
Introduction
The thermal conductivity of a material is a property which defines the rate of heat travel
through the material. The thermal conductivity of a material is measured in Watts per meter
Kelvin (W/mK). A material with a very high conductivity allows heat to conduct through it
easily and is termed a conductor, whereas as a material with a low conductivity makes it
hard for heat to conduct and is termed an insulator.
When engineers are deciding on the materials to be used for an application, where theres
thermal conduction involved, such as brakes in a car where the material needs to handle
high temperatures due to the friction without deforming, there needs to be a balance
between the thermal conductivity of the material and the cost.
An example of the use of a highly thermally conductive material is in the cooling system of a
computer, where a heat sink made from a material with a high conductivity will allow heat
produced by a computer to conduct through the heat sink, and dissipate from the many fins
into the surrounding air, maintaining an acceptable temperature of the electronic
components.
A practical use for a low thermal conductive (insulating) material would be used in the
manufacture of thermo flasks. Where the material within the thickness of the flask wall will
have low thermal conductivity, and therefore will stop the heat of the liquid inside from
conducting out and causing the liquid to lose heat.
Objective
The objective of this laboratory experiment is to determine the thermal conductivity of an
unknown material, and then decide on what material it is from researched values. The
results for the thermal conductivity of the material will also be compared to theory.

Theory
To calculate the thermal conductivity of the material, a sample is heated on one end by an
electrical heating element and the other end is cooled by water. The sample is surrounded
by an insulator to make sure as little heat as possible is lost to the atnosphere. Once the flow
of heat has reached a steady state, a linear temperature gradient will occur along the length
of the material.

List of symbols
P - Power
V - Voltage
I - current
Q - Power transmitted by
heat

Cp

K Thermal
conductivity
A Cross section area
of sample.

dT
dx

Temperature

gradient
Flow rate of water
Specific heat

capacity
The power of the electric heater used to heat one end of the sample material is calculated as
shown in equation 1:

P=IV

(1)

This power will equate to the heat transferred to the cooling fluid, which can be calculated
from equation 2:

water
T water out T
p
Q= mC

(2)

Heat transfer through the sample is by conduction and is described by equation 3, it is

Q=kA

dT
dx

(3)

Rearranging equation 3 and an equation for k, the thermal conductivity constant can be
calculated:

k=

Q/ A
dT /dx

(4)

The input electrical power in is calculated using equation 1 as shown below;

Q=IV

Q=0.25

240
2

Q=30 W
The heat out into the fluid is calculated below using equation 2;

water
T water out T
p
Q= mC
3

4.476 10 4179 0.504

Researched theoretical values for thermal conductivity values for two materials;
Aluminium 172W/mK
Stainless steel 15W/mK
Apparatus

Cooling
water

Electrical
heating
source

Self clamping
specimen

Dewar

Current
reading
The apparatus in this experiment is purposely designed to calculate the thermal conductivity
of a range of materials. It contains a self-clamping specimen stack assembly which has an
electrically heated source at one end of the specimen, a calorimeter base, a Dewar vessel
enclosure to minimise the heat lost, and a constant head cooling water supply tank at the
other end of the specimen. Two thermocouples are provided to measure the temperature of
the water before and after its been heated. The samples used are 25mm in diameter and
100mm in length and have four evenly spaced holes to allow T-Type thermocouples to be
attached. These then digitally measure the temperature of the sample at each interval of
25mm along the length of the material.
Procedure
1. The length and diameter of the sample material is recorded. Then the locations of the
thermocouples are noted and then entered into the VI (Virtual Instrument).
2. The thermal interface material is then applied to each end of the sample and it is then
clamped. This is used to improve the conductivity, since it fills in gaps which would
otherwise be filled with air; which is a very poor conductor.
3. Each thermocouple is then evenly placed along the length of the specimen at
intervals of 25mm; a Dewar vessel is then placed over the specimen to cut down on
heat loss of the experiment.
4. Begin the water flow and make sure all air bubbles have been evacuated from the
water tubes to reduce the error in the water flow rate. Measure the flow rate using a
stop watch and a measuring cylinder. Enter this value and the fluid density into the
VI.
5. The electrical heating element is turned on and the voltage is applied. A note of the
magnitude of both the applied voltage and the current drawn is taken and then
entered into the VI.

6. Using the LabVIEW VI the temperatures along the sample are observed. When
steady state is achieved, the four temperatures of the samples will form a straight
line. The temperature gradient (gradient of the line) is recorded.
7. The VI records the inlet and outlet water temperature and then calculates the heat
transfer (the difference) automatically. This should equal the electrical input power
used to heat the sample. One of these values can then be used to calculate the
thermal conductivity of the sample

Results and discussion

Results graph
450
400
350
300
Temperature of sample (K)

250

gradient

200

Linear (gradient )

150
100
50
0
0

0.05

0.1

Distance of Sample Temperature Measuring Points (m)

The graph shows a linear trend as the temperature is proportional to the distance along the
sample. This was expected since the further away you move from the heated end of a
material the cooler it gets. The gradient of the line of best fit from the results graph is 1071

dT
which is the temperature gradient ( dx

). The heat out to the fluid calculated in the theory

section (Q) is 9.43w. Using equation 4 a value for the conductivity can be calculated as
shown below;

k=

Q/ A
dT /dx

9.43 0.00049
1071

17.97 W /mK
Since we know the material is either aluminium or stainless steel, the thermal conductivity
value of 17.97W/mK is very close to that of stainless steel, so it can be deduced that the
material used in the experiment was stainless steel.
The experimental result did not exactly correlate with the theoretical value, but this is due to
the many errors introduced by the experimental method such as heat loss in the material
and in the electric heater itself. The material used may also be a particular grade of stainless
steel having a slightly different thermal conductivity.. To improve the accuracy of the results a
more efficient heating source and a better insulator could be used to cut down on the heat
loss. A higher grade pure stainless steel could also be used to improve the accuracy of the
result.
The input electrical power, which was calculated to be 30W from the theory, is a larger value
than the heat out to the fluid calculated to be 9.43W. This 20.57W difference is due to the
heat loss stated in the above paragraph. If the experiment was done in an ideal situation the
electrical power in should in theory be equal to the heat output dissipated by the water.
The result shows that the thermal conductivity of stainless steel is 17.97W/mK. This
indicates a fairly poor conductor because of its a low value. This type of information is useful
for engineers as it can assist them to choose the correct material for an application, for
example, a heating element, where a material with greater conductance is necessary
compared to an insulating material where low conductance is required. This experiment is
also very useful for engineers as it can help identify what type of material is being
experimented on.
Conclusion
The result calculated by the experimental procedure was relatively close to the theoretical
value, however not exactly. This discrepancy is due to the experimental errors noted in the
results and discussion section. The results do give a relatively close estimate of the thermal
conductivity, which is close enough to estimate the type of material in the experiment from
researched theoretical values.
Reference

Cussons technology Thermal conductivity lab

Bibliography

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thercond.html
Engineering Thermodynamics and Heat Transfer- Rogers and Mayhew