ENT233 Thermo Fluid
Laboratory Module
EXPERIMENT 5
HEAT CONDUCTION
1.0
OBJECTIVES
1.1
1.2
2.0
To investigate Fourier’s Law for the linear conduction of heat along a
homogeneous bar
To examine the temperature profile and determine the rate of heat transfer
resulting from radial conduction through the wall of a cylinder
INTRODUCTION & THEORY
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.
2.1 Linear Conduction Heat Transfer
dx
Q
dT
Figure 1: 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.
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ENT233 Thermo Fluid
Laboratory Module
THS
kH
kS
kC
THI
TCI
XH
XS
XC
TCS
FiFigure 2: Linear temperature distribution of different materials
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 )


(dx H )
(dx S )
(dx C )
(2)
i.e. the temperature gradient is inversely proportional to the cross-sectional area.
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ENT233 Thermo Fluid
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AC
AH
AC
XH
Q
XS
AC
XC
Figure 3: Temperature distribution with various cross-sectional areas
2.2 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.
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ENT233 Thermo Fluid
Laboratory Module
The amount of heat (Q), which is conducted across the cylinder wall per unit time, is:
Q
2Lk (Ti  To )
R
ln o
Ri
(3)
where,
Q = heat flow rate, [W]
L = thickness of the material, [m]
W 
Ro = outer radius, [m]
Ri = inner radius, [m]
k = thermal conductivity of the material, 
 Km 
Ti = inner section temperature, [K]
To = outer section temperature, [K]
3.0
EQUIPMENT
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.
1
2
3
4
7
5
6
8
9
10
Figure 4: Unit Assembly for Heat Conduction Study Bench
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ENT233 Thermo Fluid
1. Control Panel
2. Heater Power Indicator
3. Heater Power Regulator
4. Heater Power
5. Temperature Indicator
Laboratory Module
6. Temperature Selector
7. Main Power Switch
8. Temperature Sensors
9. Radial Module
10. Linear Module
3.1 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)
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.
3.2 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.
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ENT233 Thermo Fluid
Laboratory Module
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.
3.3 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 minimized by preserving an air gap around the disc with a heat-resistant
casing. 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.
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4.0
Laboratory Module
EXPERIMENTAL PROCEDURE
Experiment A: To investigate Fourier’s Law for the linear conduction of heat along
a homogeneous bar
No
Procedure
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 20 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). Repeat this procedure for
input power between 10 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
Plot the temperature, T (°C) versus distance, x(meter) in figure 1 from data in Table
7
1. From the graph calculate the thermal conductivity at heater power is 10 watts
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
No
Procedure
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
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ENT233 Thermo Fluid
7
8
9
10
11
Laboratory Module
Switch on the power supply and main switch, the digital readouts will be illuminated
Turn the heater power control to 20 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). Repeat this procedure for
input power between 10 watts. After each change, sufficient time must be allowed
to achieve steady state conditions. Record all your data in Table 2
End experiment
Plot of the temperature, T(°C) versus distance, r (meter) in figure 2 from data in
Table 2
Plot the temperature T(K) versus ln(r) in figure 3 from data in Table 3 at heater
power of 10 watts and calculate the thermal conductivity
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ENT233 Thermo Fluid
Laboratory Module
Name :
______________________________
Matrix No :
______________________________
5.0
Date : ______________
DATA & RESULTS
EXPERIMENT A
Table 1
Heater
Power, Q
(Watts)
5
TT1
(°C)
TT2
(°C)
TT3
(°C)
TT4
(°C)
TT5
(°C)
TT6
(°C)
TT7
(°C)
TT8
(°C)
TT9
(°C)
10
15
20
Figure 1
Temperature versus Distance
Calculate the thermal conductivity at Heater Power, Q = 10 watts (show your
calculation)
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ENT233 Thermo Fluid
Laboratory Module
Name :
______________________________
Matrix No :
_____________________________
Date : ______________
EXPERIMENT B
Table 2
Test
A
Heater
Power, Q
(Watts)
5
B
10
C
15
D
20
TT1
(°C)
TT2
(°C)
TT3
(°C)
TT7
(°C)
TT8
(°C)
TT9
(°C)
Figure 2
Temperature(oC) versus radial(x)
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ENT233 Thermo Fluid
Laboratory Module
Name :
______________________________
Matrix No :
______________________________
Date : ______________
Table 3
Node
Radius
TT1
TT2
TT3
TT7
TT8
TT9
ln r
Temperature
(°C)
Temperature
(K)
Figure 3
Temperature(K) versus ln(r)
Calculate the thermal conductivity (show your calculation)
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ENT233 Thermo Fluid
Laboratory Module
Name :
______________________________
Matrix No :
______________________________
6.0
Date : ______________
QUESTIONS
Answer all questions below:
6.1 What is the physical mechanism of heat conduction in a solid, a liquid, and a gas?
6.2 What is meant by thermal resistance?
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ENT233 Thermo Fluid
Laboratory Module
Name :
______________________________
Matrix No :
______________________________
7.0
Date : ______________
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.)
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ENT233 Thermo Fluid
Laboratory Module
Name :
______________________________
Matrix No :
______________________________
Date : ______________
8.0
CONCLUSION
(Based on data and discussion, make your overall conclusion by referring to experiment objective)
The conclusion for this lab is…
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