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Heat Transfer Lab
Conduction Heat Transfer Unit
LAB 1
HEAT CONDUCTION
1.0
OBJECTIVES
A)
To investigate Fourier’s Law for the linear conduction of heat along a
homogeneous bar
B)
To examine the temperature profile and determine the rate of heat transfer
resulting from radial conduction through the wall of a cylinder
2.0
INTRODUCTION
Thermal conduction is the mode of heat transfer, which occurs in a material by
virtue of a temperature gradient. A solid is chosen for the demonstration of pure
conduction since both liquids and gases exhibit excessive convective heat transfer. In a
practical situation, heat conduction occurs in three dimensions, a complexity which often
requires extensive computation to analyze. In the laboratory, a single dimensional
approach is required to demonstrate the basic law that relates rate of heat flow to
temperature gradient and area.
The Heat Conduction Study Bench consists of two electrically heated modules
mounted on a bench support frame. One module contains a cylindrical metal bar
arrangement for a variety of linear conduction experiments while the other consists of a
disc for radial conduction experiment. Both test modules are equipped with an array of
temperature sensors. Cooling water, to be supplied from a standard laboratory tap is fed
to one side of the test pieces in order to maintain a steady temperature gradient.
The instrumentation provided permits accurate measurement of temperature and
power supply. Fast response temperature probes with a resolution of 0.1°C are used. The
power control circuit provides a continuously variable electrical output of 0-100 Watts.
The test modules are designed to minimize errors due to true three-dimensional
heat transfer. The basic principles of conduction can be taught without knowledge of
radiation or convective heat transfer. The linear test piece is supplied with
interchangeable samples of conductors and insulators to demonstrate the effects of area,
conductivity and series combinations. Contact resistance may also be investigated, and
the important features of unsteady state conditions may be demonstrated.
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Heat Transfer Lab
3.0
Conduction Heat Transfer Unit
EQUIPMENTS/UNIT ASSEMBLY
The equipment comprises two heat-conducting specimens, a multi-section bar for the
examination of linear conduction and a metal disc for radial conduction. A control panel
provides electrical and power digital for display heaters in the specimens as well as the
selector switch for data acquisition system
A small flow of cooling water provides a heat sink at the end of the conducting path in
each specimen.
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3
4
7
5
6
8
9
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Figure 1: Unit Assembly for Heat Conduction Study Bench
1. Control Panel
2. Heater Power Indicator
3. Heater Power Regulator
4. Heater Power
5. Temperature Indicator
6. Temperature Selector
7. Main Power Switch
8. Temperature Sensors
9. Radial Module
10. Linear Module
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Heat Transfer Lab
Conduction Heat Transfer Unit
2.1 Specifications
a) Linear Module
Consists of the following sections:
i) Heater Section
Material : Brass
Diameter : 25 mm
ii) Cooler Section
Material : Brass
Diameter : 25 mm
iii) Interchangeable Test Section
- Insulated Test Section with Temperature Sensors Array (Brass)
(Diameter = 25mm, Length = 30 mm)
- Insulated Test Section (Brass)
(Diameter = 13mm, Length = 30 mm)
- Insulated Test Section (Stainless Steel)
(Diameter = 25mm, Length = 30 mm)
b) Radial Module
Material : Brass
Diameter : 110 mm
Thickness : 3 mm
c) Instrumentations
Linear module consists of a maximum of 9 temperature sensors at 10 mm interval.
For radial module, 6 temperature sensors at 10 mm interval along the radius are
installed.
Each test modules are installed with 100 Watt heater.
2.2 Overall Dimensions
Height
: 0.80 m
Width
: 0.80 m
Depth
: 0.35 m
2.3 General Requirements
Electrical : 240 VAC, 1-phase, 50Hz
Water
: Laboratory tap water, 20 LPM @ 20 m head
Drainage point
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Heat Transfer Lab
Conduction Heat Transfer Unit
2.4 Linear Module
Fourier's Law of Heat Conduction is most simply demonstrated with the linear
conduction module. This comprises a heat input section fabricated from brass fitted
with an electrical heater. Three thermistor temperature sensors are installed at 10mm
intervals along the working section, which has a diameter of 25mm. A separate heat
sink section also of brass is cooled at one end by running water while its working
section is also fitted with thermistor temperature sensors at 10mm intervals.
The heat input section and the heat sink section may be clamped directly together
to form a continuous brass bar with temperature sensor at 10mm intervals,
alternatively any one of three intermediate sections can be fitted between these two.
The first of these is a 30mm length of the same material (brass) and is the same
diameter as the heat input and heat sink sections and is again fitted with thermistor
sensors at 10mm intervals. This section is clamped between the two basic sections
forms a relatively long uniform bar with nine regularly spaced temperature sensors.
The second center section, which may be fitted, is again brass and 30-mm long
but has a diameter of 13mm and is not fitted with temperature sensors. This section
allows a study of the effect of a reduction in the cross-section of the heat-conducting
path.
The third center section, which may be fitted, is of stainless steel and has the same
dimensions as the first brass section. No temperature sensors are fitted. This section
allows the study of the effect of a change in the material while maintaining a constant
cross-section.
The mating ends of the five sections are finely finished to promote good thermal
contact although heat- conducting compound may be smeared over the surfaces to
reduce thermal resistance. The heat-conducting properties of insulators may be found
by simply inserting a thin specimen between the heated and cooled metal sections. An
example of such an insulator is a piece of paper.
Heat losses from the linear module are reduced to a minimum by a heat-resistant
casing enclosing an air space around the module. The interchangeable center sections
have their own attached casing pieces, which fit with those of the heat input and heat
sink sections.
The thermistor temperature sensors are connected to miniature plugs fitted to the
casing and connections from the sensors to the temperature input module are made
via nine sensor leads fitted with appropriate sockets. Therefore temperature gradients
can be plotted.
2.5 Radial Module
The radial conduction module comprises a brass disc 110mm diameter and 3mm
thick heated in the center by an electrical heater and cooled by cold water in a
circumferential copper tube. Thermistor temperature sensors are fitted to the center of
the disc and at 10mm intervals along a radius there being six in all. Again heat losses
are minimised by preserving an air gap around the disc with a heat-resistant casing.
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Heat Transfer Lab
Conduction Heat Transfer Unit
As in the linear module, the thermistor connections are brought out to plugs in the
casing to which six sensor leads fitted with appropriate sockets may be connected to
obtain the temperature.
2.6 Control Panel
Either of the heat-conduction modules may be connected to a control panel which
allows the heater input power to be set and the temperature at any of the sensors to be
shown in °C. Heater power is controlled by a variable autotransformer and displayed
on a digital indicator. Power outputs from 0 to 100 watts may be obtained.
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Heat Transfer Lab
3.0
Conduction Heat Transfer Unit
SUMMARY OF THEORY
3.1
Linear Conduction Heat Transfer
dx
Q
dT
Figure 2: Linear temperature distribution
It is often necessary to evaluate the heat flow through a solid when the
flow is not steady e.g. through the wall of a furnace that is being heated or
cooled. To calculate the heat flow under these conditions it is necessary to
find the temperature distribution through the solid and how the distribution
varies with. Using the equipment set-up already described, it is a simple
matter to monitor the temperature profile variation during either a heating
or cooling cycle thus facilitating the study of unsteady state conduction.
THS
kH
kS
kC
THI
TCI
XH
XS
XC
TCS
Figure 3: Linear temperature distribution of different materials
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Heat Transfer Lab
Conduction Heat Transfer Unit
Fourier’s Law states that:
Q  kA
dT
dx
(1)
where,
Q = heat flow rate, [W]
W 
k = thermal conductivity of the material,  
 Km 
A = cross-sectional area of the conduction, [m2]
dT = changes of temperature between 2 points, [K]
dx = changes of displacement between 2 points, [m]
From continuity the heat flow rate (Q) is the same for each section of the
conductor. Also the thermal conductivity (k) is constant (assuming no
change with average temperature of the material).
Hence,
AH (dT ) AS (dT ) AC (dT )
(2)


(dx H )
(dx S )
(dx C )
i.e. the temperature gradient is inversely proportional to the cross-sectional
area.
AC
AH
AC
XH
XS
Q
AC
XC
Figure 4: Temperature distribution with various cross-sectional areas
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Heat Transfer Lab
3.2
Conduction Heat Transfer Unit
Radial Conduction Heat Transfer (Cylindrical)
Temperature
Distribution
Ti
To
Ri
Ro
Ri
Ro
Figure 5: Radial temperature distribution
When the inner and outer surfaces of a thick walled cylinder are each at a
uniform temperature, heat rows radially through the cylinder wall. From
continuity considerations the radial heat flow through successive layers in
the wall must be constant if the flow is steady but since the area of
successive layers increases with radius, the temperature gradient must
decrease with radius.
The amount of heat (Q), which is conducted across the cylinder wall per
unit time, is:
2Lk (Ti  To )
R
ln o
Ri
where,
Q
(3)
Q = heat flow rate, [W]
L = thickness of the material, [m]
W 
k = thermal conductivity of the material,  
 Km 
Ti = inner section temperature, [K]
To = outer section temperature, [K]
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Ro = outer radius, [m]
Ri = inner radius, [m]
Heat Transfer Lab
4.0
Conduction Heat Transfer Unit
EXPERIMENTAL PROCEDURES
4.1 General Start-up Procedures
1. Make sure that the main switch is off. Insert an intermediate section into the linear
module and clamp together.
2. Connect one of the cooling water tubes to the water supply and the other to the
drain.
3. Connect the heater supply lead for the linear conduction module into the power
supply socket on the control panel.
4. Connect the nine sensor leads to the nine plugs on top of the linear conduction
module. Connect the left-hand sensor lead from the module to the place marked
TT1 on the control panel. Repeat this procedure for the remaining eight sensor
leads, connecting them from left to right on the module and in numerical order on
the control panel.
5. Turn on the water supply and ensure that water is flowing from the free end of the
water pipe to drain. This should be checked at intervals.
6. Turn the heater power control knob on the control panel to 0 Watt position by
turning the knob fully anti clockwise.
7. Switch on the main switch and the digital readouts will be illuminated.
8. Set the heater power control to give a reading of 20 watts on the digital indicator.
9. Make sure that the temperature reading decreases towards the water-cooled end
for the entire temperature sensor.
10. Turn off the heater power control and switch off the main switch.
11. Exchange the two-heater supply leads at the control panel.
12. Remove the central specimen from the linear module, leaving the three sensor
leads still connected to the specimen.
13. Connect the remaining six sensor leads to the radial module, with the TT1
connected to the innermost plug on the radial. Connect the remaining five sensor
leads to the radial module correspondingly, ending with TT 9 sensor lead at the
edge of the radial module.
14. Set the heater power control to give a reading of 20 watts on the digital indicator.
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Heat Transfer Lab
Conduction Heat Transfer Unit
15. Make sure that the temperature reading decreases towards the edge of the disc.
16. The equipment is now pre-checked for experiment.
Note:
i. Care should be exercised to avoid overheating the linear
conduction module especially when poor heat conductors are used
as the intermediate section. The temperature at the hot end of the
module should be checked at regular intervals to ensure that it does
not rise above 100 °C.
ii) Always switch off the main switch before connecting the power
and sensor leads.
4.2
Experiment Procedures
Experiment A: To investigate Fourier’s Law for the linear conduction of heat
along a homogeneous bar
1. Make sure that the main switch is initially off. Then Insert a brass conductor
(25mm diameter) section intermediate section into the linear module and
clamp together.
2. Turn on the water supply and ensure that water is flowing from the free end of
the water pipe to drain. This should be checked at intervals.
3. Turn the heater power control knob control panel to the fully anticlockwise
position and connect the sensors leads.
4. Switch on the power supply and main switch, the digital readouts will be
illuminated.
5. Turn the heater power control to 40 Watts and allow sufficient time for a
steady state condition to be achieved before recording the temperature at all
nine sensor points and the input power reading on the wattmeter (Q). This
procedure can be repeated for other input power between 0 to 40 watts. After
each change, sufficient time must be allowed to achieve steady state
conditions. Record all your data in Table 1.
6. End of experiment
7. Plot the temperature, T versus distance, x. Calculate the thermal conductivity
at heater power is 5 watts.
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Heat Transfer Lab
Conduction Heat Transfer Unit
Note:
i) When assembling the sample between the heater and the cooler
take care to match the shallow shoulders in the housings.
ii) Ensure that the temperature measurement points are aligned along
the longitudinal axis of the unit.
Experiment B: To examine the temperature profile and determine the rate of
heat transfer resulting from radial conduction through the
wall of a cylinder
1. Make sure that the main switch is initially off.
2. Connect one of the water tubes to the water supply and the other to drain.
3. Connect the heater supply lead for the radial conduction module into the
power supply socket on the control panel.
4. Connect the six sensor (TT1, 2, 3 & 7, 8, 9) leads to the radial module, with
the TT1 connected to the innermost plug on the radial. Connect the remaining
five sensor leads to the radial module correspondingly, ending with TT 9
sensor lead at the edge of the radial module.
5. Turn on the water supply and ensure that water is flowing from the free end of
the water pipe to drain. This should be checked at intervals.
6. Turn the heater power control knob control panel to the fully anticlockwise
position.
7. Switch on the power supply and main switch, the digital readouts will be
illuminated.
8. Turn the heater power control to 40 Watts and allow sufficient time for a
steady state condition to be achieved before recording the temperature at all
six sensor points and the input power reading on the wattmeter (Q). This
procedure can be repeated for other input power between 0 to 40 watts. After
each change, sufficient time must be allowed to achieve steady state
conditions. Record all your data in Table 2.
9. End experiment
10. Plot of the temperature, T(°C) versus distance, r
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Heat Transfer Lab
Conduction Heat Transfer Unit
11. Plot the temperature T(K) versus ln(r) Calculate the amount of heat
transferred at heater power of 5 watts.
4.3 General Shut-down Procedures
1. Turn the heater power control knob on the control panel to 0 Watt position by
turning the knob fully anti clockwise. Keep the cooling water flowing for at least
5 minutes through the module to cool down the test metal.
2. Switch off the main switch and power supply. Then, unplug the power supply
cable.
3. Close the water supply and disconnect the cooling water connection tubes if
necessary. Otherwise, leave the connection tubes for next experiment.
4. Disconnect the heater supply lead for the linear conduction module into the power
supply socket on the control panel.
Disconnect the sensor leads if necessary
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Heat Transfer Lab
Conduction Heat Transfer Unit
KOLEJ KEJURUTERAAN UTARA MALAYSIA
LAB 1
CONDUCTION HEAT TRANSFER
Result Lab Sheet
GROUP NUMBER
:___________________________
STUDENT NAME
:
DATE OF EXPERIMENT :___________________________
GROUP MEMBERS NAME:
1)_______________________________signature:__________
2)_______________________________signature:___________
3)_______________________________signature:__________
4)_______________________________signature:___________
5)_______________________________signature:___________
Mark :
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Heat Transfer Lab
5.0
Conduction Heat Transfer Unit
DATA & RESULTS
Experiment A
Table 1
Heater
TT1
Power, Q
(°C)
(Watts)
5
TT2
(°C)
TT3
(°C)
TT4
(°C)
10
15
20
14
TT5
(°C)
TT6
(°C)
TT7
(°C)
TT8
(°C)
TT9
(°C)
Heat Transfer Lab
Conduction Heat Transfer Unit
Experiment B
Table 2
Test
A
Node
Radius
Heater
TT1
Power, Q
(°C)
(Watts)
5
B
10
C
15
D
20
TT1
TT2
TT2
(°C)
Table 3
TT3
ln r
Temperature
(°C)
Temperature
(K)
15
TT3
(°C)
TT7
(°C)
TT7
TT8
(°C)
TT8
TT9
(°C)
TT9
Heat Transfer Lab
Conduction Heat Transfer Unit
Graph Experiment A
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Heat Transfer Lab
Conduction Heat Transfer Unit
Graph Experiment B
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Heat Transfer Lab
6.0
Conduction Heat Transfer Unit
QUESTIONS
Answer all questions below:
6.1 Give 3 sources of error in the experiment?
6.2 What is the physical mechanism of heat conduction in a solid, a liquid, and a gas?
6.3 What is meant by thermal resistance?
6.4 Define thermal conductivity and explain its significance in heat transfer?
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Heat Transfer Lab
6.4
Conduction Heat Transfer Unit
Consider a 3-m-high, 5-m-wide, and 0.3-m-thick wall whose thermal
conductivity k=0.9 W/m.°C(Fig.1). On a certain day, the temperatures of the
inner and the outer surface of the wall are measured to be 32°C and 27°C,
respectively. Determine the rate of heat loss through the wall on that day?
Wall
H=3m
W=5m
L=0.3m
Figure 1
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Heat Transfer Lab
6.4
Conduction Heat Transfer Unit
A thick-walled tube of stainless steel [18%Cr, 8%Ni, k=19W/m.°C] with
2-cm inner diameter (ID) and 4-cm outer diameter (OD) is covered with a
3-cm layer of asbestos insulation [k=0.2W/m.°C] (Fig.2). If the inside wall
temperature of the pipe is maintained at 600°C, calculate the heat loss per
meter of length.
Stainless steel
T1= 600°C
r1
r2
r3
Asbestos
T2 = 100°C
Figure 2
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Heat Transfer Lab
7.0
Conduction Heat Transfer Unit
DISCUSSION
Include a discussion on the result noting trends in measured data, and comparing measurements with theoretical
predictions when possible. Include the physical interpretation of the result, the reasons on deviations of your findings from
expected results, your recommendations on further experimentation for verifying your results and your findings.
8.0
CONCLUSION
Based on data and discussion, make your overall conclusion by referring to experiment objective
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