EXPERIMENT:1
DETERMINE THE THERMAL CONDUCTIVITY OF GIVEN METAL ROD.
Date:
Competency and Practical Skills:
Relevant CO: 1
Objectives:
1 To calculate the thermal conductivity of metal rod.
2 Toplot the temperature distribution along the length of rod.
Introduction:
Thermal conductivity of substance is a physical property, defined as the ability of a substance
to conduct heat. Thermal conductivity of material depends on chemical composition; state of
matter, crystalline structure of a solid, the temperature, pressure and weather.
Theory:
The heater will heat the rod on its one end and heat will be conducted through the rod to the
other end. Since the rod is insulated from outside, it can be safely assumed that the heat transfer
along the copper rod is mainly due to axial conduction and at steady state the heat conducted
shall be equal to the heat absorbed by water at the cooling end. The heat conducted at steady
state shall create a temperature profile within the rod. (T = f(«)). The steady state heat balance
at the rear end of the rod is:
Hcat absorbed by cooling water,
Q= mCp 4T
Heat conducted through the rod in axial direction:
dT
Q=-KA
dX
At steady state:
dT
Q=-KA=m Cp 4T
So, thermal conductivity of rod may be expresscd as:
m Cp 47T
K=
-A
Description:
The apparatus consists of a metal rod, one end of which is heated by an electric heater while
the other end of the rod projects inside the cooling water jacket. The middle portion of the rod
is surrounded by a cylindrical shellfilled with the asbestos insulating powder. Six temperature
sensors are provided to measure temperature of rod at different section. The heater is provided
with a PID controller 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.
SENSOR NUT
OUTL9T
-cOPPER ROD HEATER
CONTROL PANEL
-GLASS wOOL
DRAN
T8
DRAN
SIAND
Apparatus for measurement of thermal conductivity of metal rod
2
Experimental procedure:
1. Close all the valves.
2. Connect continuous water supply to the inlet of water chamber
3. Ensure that mains ON/OFF switch given on the panel is at OFF position
4. Connect electric supply to the set up.
5. Switch ON the mains ON /OFF switch.
6. Set the heat input by the PID controller in the range of 50 to 80 °C.
7, Open the valve and start the flow of water.
8. Start the stop watch and collect the water in measuring cylinder.
9. Note down the time and volume of water.
10. After 1.5 hrs. note down the reading of temperaturesensors at every 10 minutes interval
(till observing change in consecutive readings of temperatures + 0.2° C)
11. When experiment is over stop the water supply by closing the valve
12. Switch OFF the mains ON/OFF switch.
13. Switch OFF electric supply to the set up.
Photographic view of apparatus for measurement of thermalconductivity of metal rod
3
Specification:
Length of the metal bar (total) 500 mm
Size of the metal bar (diameter) .25 mm
Test length of the bar : 300 mm
Number of thernocouple mounted on the Bar :6
No. of thermocouples in the insulation shell :4
Heater coil (Bend type) :Nichrome wire
Distance between two successive thermocouples : 40 mm
Distance of first thermocouple from the heater :50 mm
Distance of sixth thermocouple from the cooling zone :50 mm
Radial distance of thermocouple from the center of the rod : r;=25mm, ro= 50 mm
Axial Distance of thermocouple pairs embedded in the insulation from the heater end
X1: 100 mm, X>: 200 mm
Positions 1 to 6-Thermocouple positions on metal bar.
Positions 7 to 10- Thermocouple positions in the insulatingshell.
Positions 11& 12-Thermocouple positions to measure theCooling water
inlet and outlet temperature.
CONTROL PANEL:
Digital Temperature Indicator (0-299 °C with 0.1 °C Accuracy) with Selector switch (12
channel)
Dimmer stat for heater coil (0-230 V, 5A)
Digital Voltmeter (230V)
Digital Ammeter
Measuring flask for water flow rate 1000 cc Volume.
Insulating Powder Asbestos
4
Jnsulatrd
nclosur
motol Yod
WATER coLIHG
to scale
Test lerngth 30ma
length cf meta! bar ba0 mr
PROCEDURE:
Insert male socket of control panel and test set-up in properposition and start the main
switch of control panel.
Start the cooling water supply through the jacket and adjust it (about 150-250 cc
per minute).
Switch ON the electric supply.
Increase slowly the input to heater by the dimmer stat starting from 0 volts position.
Adjust input equal to 100watts maximum by voltmeter and ammeter.
See that this input remains constant throughout the experiment.
Go on checking the temperature at some specified time intervals say 10 minutes and
continue this till asatisfactory steady state (i.e. No change in temperature with respect
to time- it willtake about an hour toone and half hour) condition is reached.
THEORY/CALCULATION:
The heater willheat the bar at its cnd and heat will be conducted through the bar to other end.
After attaining the steady state.
Heat flowing out of section AA of bar (i.e. the other end at cooling jacket)
Qw=m x Cy XAT
where, m =mass flow rate of cooling water (kg/sec)
Cy = heat capacity of water (J/kg-K)
AT = (Tn-Twi) = Difference in cooling water outlet and inlet temperature
wo
Thermal conductivity of bar at cross scion AA can now becalculated as
QA = KAa xA x
AA
where, A = the cross-sectional area of the Metal bar (m')
KAA =ThermalConductivity of Metal bar at cross section AA.
The value of
). is obtained from experiment (i.e. from graph of Temperature vs.
Distance), which indicates the Temperature distribution in the bar along its length at
crosssection AA.
Heat conducted throughout the section BB (i.e. Middle of thetest section) of the
bar is,
Qaa =Qw or QA + Radial hcat loss between scctions BB and AA.
Qoe = Qw t+ {(2 x nx Kins XL (T5- T9- 10l/og(
where ro =50 mm and r; =12.5 mm, radial distance from the center of the rod.
Thermal conductivity Kag at cross section BB can be calculated as,
Q = Kg8 XA X
Heat conducted throughout the section CC (i.e. End of the test section) of the bar
Is,
Qcc=QB + Radial heat loss between sections BB and CC
Qcc = Qus +|2 x nXKins XL. (T2 T7 -&l/log)
where, ro =25 n1n and rË =12.5 mm, radial distance from the center of the rod.
6
Thermalconductivity KÍr at cross section CC can be
Qcc = Kcc XAx
Thus, the thermal conductivity of bar at two points can be calculated. We can do more
experimentation at different power inputs.
Note the mass flow rate of water in kg/minutes and temperature rise in it. And also note the
temperature readings from TË to T12 from temperature indicator by using selectorswitch.
Graph:
Plot the graph of the temperature distribution (at steady state) alongthe length of the
metal bar using observed values for determining the slopes at BB section and also at AA.
Slope is nothing but dx at various desired points on the plot of Temperature vs. Distance
(T vs. X).
Nature of the graph will be of curvature type (Convex Downward).
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OBSERVATION TABLE:
Sr. No. (1) (2)
Time
Voltage () V 97
Current (amp)
Heat Input (W) Q=VI L4g.5
Posit n) TË
(Thermocupl
75
T2 66
T3 58
T4 50
Ts
T6 36
Tempratue
(°C) T7
Tg
T9
50
46
B3
T10 32
TË|=Twi 22
T12=Two 26
Volume collected (ml) V 20
Time (sec)
8
SCA LE
--
y AXi5:1cM=5°c
X AXTS:1cMF 20 mm
-2l.5
mal-o.i95 c
T2
T3
T5
20
CALCULATIONS:
The heater will heat the bar at its end and heat willbe conductedthrough the bar to the other end.
After attaining the stcady state.
Heat supplied to the metal bar by heater, Q=VxI = 97x0-5
48.5 W
Arca, A=d'=xCo-025=4.91 X10-4 n2
Heat flowing out of bar (i.c. the far end, at cooling jacket),
Qw=QA4 =mxCp x(T12- Ti1)
-3
= 2x10 x 417 X C26-22)
= 33. 496
Qw QaA = 33.50 w
where rn = mass flow rate of cooling water (kg/sec)
rm = Density of water (kg/m') x Volume of Water Collected (m²) /time of collection (s)
l000 x 2X)o5
m =2 XIo kgs
Cp = heat capacity of water (J kg K)
T2 = Iwo= Water outlet Temperature
Tu =Iwi =Water inlet Temperature
Thermal Conductivity of metal rod at AA,
QAA = K A XAX
33.50 Kea X 4.9) Xo HX195
33-50 lTan XO.o 954
10
..KAA =3 49.W/m°C
Radial heat loss at point 9 and 10 (190 mm from the water flow end) can be calculated using the
temperature values of T9 and T10.
QRR = QA4 + Radial heat loss between sections BB and AA.
QBB = QAA t 2TtkinsL (Ts-Tg-10) where, To-10 Tg+T10
log() 2
33.5O 2T7Xo. o3 X 0-)90 X C:5)
Ln O.o5
O.o 125
33.50+ O. ||
Ly
- 33 "50 + O.29
QBB =33.o W
where r;=12.5 mm and ro= 50 mm, radial distance fron1 thecenter of the rod
L=Length of test section under consideration
Kins= Thermal conductivity of insulating powder =0.03 W/m°C.
Thermal conductivity of metal rod at BB,
QBB = KRR XAX
33-o = TBAX 4.9x x 195
7 BB - 353 02 W/m'
.Kpa = 353 W/m-°C
02
Similarly Radial heat loss at point 7and 8 (120 mm away from point 9 and 10) can be calculated
using the temperature values T7 and T.
2nkinsL(T2-T7-&)
Qcc = QBB + where, T;-8 = T;+Ts
log() 2
33.80-+ 2T X 0.03 xo.j20 XIg
Lh O.o125
O.0125
= 33.0+
Ln2
- 33-0+ 0.587
Qcc =34.39w
where r 12.5 mm and ro 25 mm, radial distance from thecenter ofthe rod
Thermal conductivity of rod at section CC,
(dT\
Qcc= Kcc xAx)
dX/ cC
34.39 = hcc X 4.91X lo
..Kcc =359.IN/m°C
The average conductivity of metal rod is, Kava = KAAtKBB+Kcc
3
3499+ 353.02 + 359./
Kavy -354.03W/mC
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RESULT:
1. The temperature of the bar decreases along the length of the bar.
2. Thermal conductivity of two sections can be calculated and itsvariation with
temperature can be studied.
3. From the data of the thermal conductivity and the temperature draw the graph
of the K vs. T. The nature of the graph willbestraight line following the linear
relationship (K= Ko (1+ «T)). The intercept of the copper rod and the slope
of the graph willbe the multiplication of the temperature coefficient and
thermal conductivity of copper rod at standard pressure temperature (Ko).
RESULT:
Sr. No. Q
(W) K (W/m°C)
1 33.5o 349.89
2 353. 02
33o
3
34.9 359. I
ITAV9 =354.03 W/m
CONCLUSION:
EXERCISES:
1. Explain the types of thermocouples.
2. Which type of heater is used in the experiment?
3. List the materials with their thermalconductivity.
4. Compare the experimental results with the standard oncs and justify the possible
deviation.
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