THERMAL
CONDUCTIVITY
OF METAL ROD
Heat Transfer &
Metrology Lab
Name
: Anil Chejara
Roll No. : 9003022
Group
: 5
BACKGROUND: Thermal conductivity is the physical property of the material denoting the ease
with particular substances can accomplish the transmission of thermal energy by molecular motion.
Thermal conductivity of material is found to depend on the chemical composition of the substances
of which it is composed, the phase (i.e. Gas, Liquid or solid) in which it exists, its crystalline structure
if a solid, the temperature and pressure to which it is subjected, and whether or not it is
homogeneous material.
The atoms in the rod that are exposed to the heat, gain energy in the form of heat and transfer this
energy to their neighbours, which then transfer the heat energy to their neighbouring atoms. In this
manner, the energy is passed along through the length of the rod.
Mechanism of Thermal Conduction in Metals: Thermal energy may be conducted in solids by two
modes.
1. Lattice vibrations.
2. Transport by free electrons.
In good electrical conductors a rather large number of free electrons move about in the lattice
structure of the material. Just as these electrons may transport electric charge, they may also carry
thermal energy from a high temperature region. In fact, these electrons are frequently referred as
the electron gas. Energy may also be transmitted as vibrational energy in the lattice structure of the
material. In general, however, this latter mode of energy transfer is not as large as the electron
transport and it is for this reason that good electrical conductors are almost always good heat
conductors, i.e. Copper, Aluminium & silver. With increase in the temperature, however the
increased lattice vibrations come in the way of the transport by free electrons for most of the pure
metals the thermal conductivity decreases with increase in the temperatures for some metals.
APPARATUS:
The apparatus consists of a metal bar, one end of which is heated by an electric heater while the
other end of the bar projects inside the cooling water jacket. The middle portion of the bar is
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surrounded by a cylindrical shell filled with the asbestos insulating powder. The temperature of the
bar is measured at different section. The heater is provided with a dimmer stat for controlling the
heat input. Water under constant head conditions is circulated through the jacket and its flow rate
and temperature rise are noted by two temperature sensors provided at the inlet and outlet of the
water.
Metal Rod Thermal Conductivity Experiment Setup
ADDITONAL EQUIPIMENTS:
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
Hand Watch
A/C supply
Water supply at constant Rate
Beaker
PROCEDURE:



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
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First of all connect cold water supply at inlet of the Cooling Chamber of setup.
Make sure that drain valve is open.
Start water supply (1 LPM) at constant water supply rate.
Now switch on the supply and make sure the zero position of all digital devices before
switching on it.
Fix the Power Input to the Heater with the help of Variac, Voltmeter and Ammeter
provided.
After 30 Minutes start recording the temperature of various points at each 5
minutes
interval.
If temperatures readings are same for three times, assume that steady state is achieved.
Record the final temperatures.
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
Repeat the above procedure for two different Temperatures.
Closing Procedure: 
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When experiment is over, Switch off heater first.
Adjust Variac at Zero.
Switch off the Panel with the help of Mains On/Off Switch given on the Panel.
Switch off Power Supply to Panel.
Stop cold water supply.
SPECIFICATIONS: -
Length of the Metal Bar
Diameter of the Metal Bar
Test length of the bar
Total no. of temperature sensors in the setup
Number of Temperature Sensors mounted on bar
Number of Temperature Sensors mounted on water jacket
Type of Temperature Sensors
Heater
Cooling Jacket Dia
Length of cooling jacket
Dimmer stat for heater coil
Digital Voltmeter
Digital Ammeter
Temperature indicator
:
450mm
:
25mm
:
235mm
:
8 Nos.
:
6 Nos.
:
2 Nos.
:
RTD PT-100
:
Nichrome heater
:
100mm
:
75mm
:
2Amp, 230VAC
:
0 to 250 Volts
:
0 to 2.5 Amps.
:
Digital Temperature Indicator
0°C to 99.9°C and least count 0.1oC
with multi-channel switch.
FORMULAE USED: 1. Heat gained by water = Q = MCp (T9 – T8)
2. Thermal conductivity of metal rod =
𝒌=
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𝑴𝑪𝒑𝜟𝑻
𝒅𝑻
−𝑨( )
𝒅𝒙
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OBSERVATIONS: Observation table:
Thermocouple
T1
T2
T3
T4
T5
T6
T8
T9
Distance from the
leading edge (mm)
35
75
115
155
195
235
Water inlet
Water outlet
At V=165V
At V=199V
126.4
119.9
105.9
94.8
83.4
70.5
22.8
25.1
162.5
154.1
135.4
120.2
104.6
87
22.5
25.7
Volume flow rate of water at steady state condition= Q = 3.06x10-6 m3/s
Mass flow rate = density x volume flow rate = m = 3.06 x 10-3 m3/s
Cross sectional area of metal rod = 0.000491 m2
Cp of water = 4.18 kJ/kg K
CALCULATIONS: 1. At voltage = 165 V
Heat gained by water = q = mCp (T9 – T8) = 3.06 x 10-3 x 4.18 x 2.3 x 1000 = 29.409 W
dT/dX from graph at 165V = -322.5o C/m
Thermal conductivity of the metal rod:
𝒌=
29.409
−0.000491 x (−322.5)
= 185.724 W/m0C
2. At voltage = 199 V
Heat gained by water = q = MCp (T9 – T8) = 3.06 x 10 -3 x 4.18 x 3.2 x 1000 =40.91 W
dT/dx from the graph for 199 V = -440o C/m
Thermal conductivity of the metal rod:
40.91
𝒌 = −0.000491 x (−440)= 189.363 W/m0C
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GRAPH OBTAINED: T v/s X
180
160
140
120
100
V=199V
80
V=165V
60
40
20
0
0
50
100
150
200
250
CONCLUSION:
The thermal conductivity for copper rod at different voltage obtained.
K at 165 volt = 185.724 W/m0C
K at 199 volt = 189.363 W/m0C
SOURCE OF ERROR: 
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Thermal expansion of rods neglected.
The accuracy limit of thermal sensor display is .1 degree.
Heat transfer from the rod to the water assumed to be by conduction only.
The k of rod assumed same for entire rod which is not totally true.
PRECAUTIONS:
 Never switch on mains power supply before ensuring that all the ON/OFF switches given on
the panel are at OFF position.
 Voltage to heater should be increased slowly.
 Never run the apparatus if power supply is less than 180 volts and above than 230 volts.
 Operate selector switch of temperature indicator gently.
 There is a possibility of getting abrupt result if the supply voltage is fluctuating or if the
satisfactory steady state condition is not reached.
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