Experiment No # 2

Objectives:
To determine the thermal conductivity k (the constant of proportionality) of a metal specimen
(good conductor).

Theory:
Thermal Conductivity:

Thermal conductivity is simply how well a material can transfer heat. It tells us how much heat
moves through a material over time when there's a temperature difference. Think of it as a
measure of how easily heat can travel from one side to the other. Metals and ceramics, with high
thermal conductivity, transfer heat quickly, while materials like insulators or plastics resist heat
flow. This property is crucial in designing things like insulation, electronics, or heat exchangers,
where managing heat is key to their performance.

Modes of Heat Transfer:

Heat transfer happens in three ways: conduction, convection, and radiation.

• Conduction is when heat moves through a solid material or between objects that are
touching. If you hold a metal spoon in a hot cup of tea, the heat travels up the spoon to
your hand—that’s conduction at work.
• Convection happens in fluids like air or water. It can be natural, like when warm air rises
and cooler air takes its place, or forced, like when a fan blows hot air around a room.
• Radiation doesn’t need any material to travel through. It’s how the Sun warms the
Earth—heat energy moves in the form of electromagnetic waves, even through the
vacuum of space.

Each of these modes plays a role in how we experience temperature changes in everyday life.

Apparatus:
• Heat Transfer Base Unit (TD1002)
• Computer Compatible Linear Heat Conduction Accessory TD1002a.

Provided that the heated, intermediate and cooled sections are clamped tightly together, so that the
end faces are in good thermal contact, and create a composite wall by clamping the metal specimen
of unknown thermal conductivity in the intermediate section between two Brass sections (heated
and cooled sections).
From Fourier’s Law:

𝛥𝑇𝑖𝑛𝑡
𝑄 = 𝑘𝑖𝑛𝑡𝐴𝑖𝑛𝑡
𝛥𝑋𝑖𝑛𝑡
Where,

∆T int = T hot face – T cold face , ∆X int = 30 mm = 0.03 m Therefore,

𝑄. 𝛥𝑋𝑖𝑛𝑡
𝑘𝑖𝑛𝑡 =
𝐴𝑖𝑛𝑡𝛥𝑇𝑖𝑛𝑡

Thermocouple T2 and T6 are located 7.5 mm from the end faces compared with a distance of 15
mm between adjacent thermocouples (half the distance), therefore:

In the case of heated section, the temperature of the end face (hot face) will be lower than T2 and
can be calculated as follows:

𝑇ℎ𝑜𝑡 𝑓𝑎𝑐𝑒 = 𝑇2 −
In the case of cooled section, the temperature of the end face (cold face) will be higher than T6 and
can be calculated as follows:

𝑇𝑐𝑜𝑙𝑑 𝑓𝑎𝑐𝑒 = 𝑇6 +

Apparatus Setup:
The Apparatus is setup as shown in the following figure. Attach the TD1002a Linear Heat
Conduction Experiment module with the TD1002 Heat transfer experiment Base unit. To make
the Uniform wall, clamp the brass intermediate section with uniform Cross section.
Procedure:
1. Connect the specimen according to the connection of the sensor and switch on the system.
2. Set the value of power according to the Table.
3. Wait for some time so that readings get stable.
4. Note the value of temperature from T1 to T7.
5. Calculate the value of K using formula mentioned in the table.
6. Plot a graph of temperature against distance.

Readings and Calculations:

Distance between each thermocouple = 15 mm = 0.015 m Temperature

of hot face = 𝑇ℎ𝑜𝑡 𝑓𝑎𝑐𝑒 = 𝑇2 −

Temperature of cold face = 𝑇𝑐𝑜𝑙𝑑 𝑓𝑎𝑐𝑒 = 𝑇6 +

Heat flow (power to heater) = Q (Watts)

For ______________:
Thermal
Heater
T1 T2 T3 T4 T5 T6 T7 conductivity
Sr No. Power
(K) (K) (K) (K) (K) (K) (K) Kint
(Watt)
(W/mK)
1.
2.
3.
4.
5.
6.
7.
Mean Measured Thermal Conductivity of Specimen = ___________ W/mK

For ____________:
Thermal
Heater
T1 T2 T3 T4 T5 T6 T7 conductivity
Sr No. Power
(K) (K) (K) (K) (K) (K) (K) Kint
(Watt)
(W/mK)
1.
2.
3.
4.
5.
6.
7.

Mean Measured Thermal Conductivity of Specimen = ___________ W/mK Results

analysis and Discussion:

The thermal conductivity of the metal sample was determined using the thermal conductivity
measuring apparatus. The apparatus contained the metal block upon which the heating element
and two temperature sensors were placed on either side of the sample. The steady-state heat flow
through the sample was generated with the application of the heating element while the
temperature sensors measured the temperature difference across the sample.
According to Fourier's law of heat conduction, the thermal conductivity of the metal sample was
calculated as the heat flux divided by the temperature gradient across the sample.
Measurement of thermal conductivity is of prime importance in the calculation of the thermal
transfer properties of the material and is utilized in the designing and optimization of the heat
transfer system. The experimental methodology used in this study provides a convenient and
reproducible method of measuring the thermal conductivity of metal materials that is useful in
many engineering and scientific applications.
Graph:
Plot a graph of temperature against distance along the bar and draw the best straight line through
the points.