thermal conductivity of metal rod

THERMAL CONDUCTIVITY OF METAL ROD

Heat Transfer & Metrology Lab

Name : Anil Chejara Roll No. : 9003022 Group : 5

ME-314 IIT-Gandhinagar

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


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:

Hand Watch

A/C supply

Water supply at constant Rate

Beaker

PROCEDURE:

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.


Repeat the above procedure for two different Temperatures.

Closing Procedure: -

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 : 450mm Diameter of the Metal Bar : 25mm Test length of the bar : 235mm Total no. of temperature sensors in the setup : 8 Nos. Number of Temperature Sensors mounted on bar : 6 Nos. Number of Temperature Sensors mounted on water jacket : 2 Nos. Type of Temperature Sensors : RTD PT-100 Heater : Nichrome heater Cooling Jacket Dia : 100mm Length of cooling jacket : 75mm Dimmer stat for heater coil : 2Amp, 230VAC Digital Voltmeter : 0 to 250 Volts Digital Ammeter : 0 to 2.5 Amps. Temperature indicator : 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 =𝑴𝑪𝒑𝜟𝑻

−𝑨(𝒅𝑻𝒅𝒙

)


OBSERVATIONS: -

Observation table:

Thermocouple Distance from the leading edge (mm)

At V=165V At V=199V

T1 35 126.4 162.5

T2 75 119.9 154.1

T3 115 105.9 135.4

T4 155 94.8 120.2

T5 195 83.4 104.6

T6 235 70.5 87

T8 Water inlet 22.8 22.5

T9 Water outlet 25.1 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:

𝒌 =40.91

−0.000491 x (−440)= 189.363 W/m0C


GRAPH OBTAINED: -

T v/s X

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: -

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.

0

20

40

60

80

100

120

140

160

180

0 50 100 150 200 250

V=199V

V=165V

thermal conductivity of metal rod

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