İzmir Institute of Technology
CHEMICAL ENGINEERING DEPARTMENT
2008-2009 Spring Semester
CHE 310
CHEMICAL ENGINEERING LABORATORY I
Thermal Conductivity
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THERMAL CONDUCTIVITY
1. OBJECTIVES
 To understand the use of the Fourier’s law in determining heat rate through solids.
 To determine the thermal conductivityof a material, k.
 To determine the Overall Heat Transfer Coefficient for the flow of heat through a
combination of different materials in use.
 To demostrate the effect of cross sectional area on the heat rate.
 To demostrate the effect of contact resistance on thermal conduction between adjacent
materials.
 To measure the temperature distribution for unsteady state conduction of heat through
the uniform plane wall and the wall of the thick cylinder.
2. THEORY AND PRINCIPLES
Conduction (heat transfer by diffusion) is the transport of energy from the more
energetic to the less energetic particles of a substance due to a temperature gradient, and
the physical mechanism is that of random atomic and molecular activity. For onedimensional, steady-state heat conduction in a plane wall with no heat generation,
temperature is a function of the x coordinate only and heat is transferred exclusively in
this direction. Thus, the temperature distribution for the heat conduction through plane
wall must be linear as shown in Figure 1.
Ts,1
Ts,2
qx
x
x=L
Figure-1: Heat transfer through a plane wall
The heat transfer rate (qx) by conduction through a plane wall is directly
proportional to the cross sectional area (A) and the temperature difference (T), whereas
it is inversely proportional to the wall thickness (x).
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In addition to single plane wall, heat transfer through composite wall is also
important. Such walls may involve any number of series and parallel layers made of
different materials. In the case of steady state one-dimensional heat conduction with no
heat generation, temperature profile through each layer becomes linear as shown in
Figure 2. Heat transfer through composite systems is usually described by an overall heat
transfer coefficient. Simply, the overall heat transfer coefficient is related to the total
thermal resistance.
Ts,1
T2
T3
kA
kB
kC
A
B
C
xA
xB
xC
Ts,4
Figure-2: Heat transfer through composite systems.
Cylindrical and spherical systems often experience temperature gradients in the
radial direction only and may therefore treated as one dimensional. A common example
is the hollow cylinder, whose inner and outer surfaces are exposed to fluids at different
temperatures, as shown in Figure 3.
Thi
Temperature
distribution
Tco
Q
Flow
pattern
Hot
Fluid Ri
Thi
Cold
Fluid
Tco
Ro
Figure-3: Heat transfer through radial systems
The temperature distribution associated with radial conduction through a
cylindrical wall is logarithmic, not linear, as it is for the plane wall under the same
conditions.
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3) EXPERIMENTAL
3.1 THERMAL CONDUCTIVITY CALCULATION IN LINEAR SYSTEMS
Experimental set-up for the linear conductive heat transfer system is shown in
Figure 4.
Cooling water inlet
Filter
Regulator
Valve
Specimen position
Heater
Insulation
T8T7T6T5T4T3T2T1
Thermocouples
Figure 4: Linear heat conduction unit.
A. Determine the effect of change of heat flow for steady state conduction of energy
through a uniform plane
Procedure:
i) Smear the faces of the heated and cooled sections with thermal conducting paste
and clamp them together without any intermediate section in place as illustrated in the
following scheme.
ii) Ensure that the cooling water is flowing and then set the heater voltage V
iii) Monitor temperature T1, T2, T3, T6, T7 and T8 until steady-state is reached.
iv) When the temperatures are stabilized, record T1, T2, T3, T6, T7 and T8, V and I.
v) Reset the heater voltage and repeat the above procedure again recording the
parameters T1, T2, T3, T6, T7 and T8, V and I when temperatures have stabilised.
vi) Reset the heater voltage and repeat the above procedure again recording the
parameters T1, T2, T3, T6, T7 and T8, V and I when temperatures have stabilised.
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V, I
Q
T1
T2
T3
T6
T7
T8
FW
B. Determine heat rate through solid materials for one dimensional, steady flow of
heat
Procedure:
i)
Smear the faces of the heated and cooled sections with thermal conducting paste
and clamp them together with the Brass Intermediate Specimen in place as
illustrated in the following scheme.
V, I
BRASS
xint
Q
T1
T2
T3
T4
T5
T6
T7
T8
FW
ii) Ensure that the cooling water is flowing and then set the heater voltage V
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iii) Monitor temperature T1, T2, T3, T4, T5, T6, T7 and T8 until steady-state is
reached.
iv) When the temperatures are stabilized, record T1, T2, T3, T4, T5, T6, T7 and T8, V
and I.
v) Reset voltage and repeat the above procedure again recording the parameters T1,
T2, T3, T4, T5, T6, T7 and T8, V and I when temperatures have stabilised.
C. Determine overall heat transfer coefficient for the flow of heat through a
combination of different materials in use and determine the thermal conductivity k
of a metal specimen
Procedure:
i) Smear the faces of the heated and cooled sections with thermal conducting paste and
clamp them together with the Stainless steel and Aluminium Intermediate Specimens in
place as illustrated in the following scheme.
V, I
V, I
Q
Q
Stainless steel
xint
FW
Aluminium
T1
T2
T3
T4
T5
T6
T7
T8
xint
T1
T2
T3
T4
T5
T6
T7
T8
FW
ii) Ensure that the cooling water is flowing and then set the heater voltage V for
stainless steel specimen and for aluminium specimen.
iii) Monitor temperature T1, T2, T3, T6, T7 and T8 until steady-state is reached.
iv) When the temperatures are stabilized, record T1, T2, T3, T6, T7 and T8, V and I.
v) Reseet the voltage and repeat the above procedure again recording the parameters
T1, T2, T3, T4, T5, T6, T7 and T8, V and I when temperatures have stabilised.
D. Determine the effect of cross sectional area on the heat rate
Procedure:
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i) Smear the faces of the heated and cooled sections with thermal conducting paste and
clamp them together with the reduced diameter brass intermediate specimen in place as
illustrated in the following scheme.
ii) Ensure that the cooling water is flowing and then set the heater voltage V
iii) Monitor temperature T1, T2, T3, T6, T7 and T8 until steady-state is reached.
iv) When the temperatures are stabilized, record T1, T2, T3, T6, T7 and T8, V and I.
v) Reset the voltage and repeat the above procedure again recording the parameters T1,
T2, T3, T4, T5, T6, T7 and T8, V and I when temperatures have stabilised.
V, I
Q
T1
T2
T3
xred
dred
T6
T7
T8
FW
E. Determine the effect of contact resistance on thermal conduction between
adjacent materials
Procedure:
i) Ensure that the faces of the heated and the cooled sections are cleaned of thermal
conducting paste and that the brass intermediate section is also similarly cleaned.
ii) Lightly coat the mating faces between the cooled section and the brass intermediate
specimen with thermal paste and assemble them together.
iii) Do not coat the mating faces of the heated section and the brass intermediate
specimen with thermal paste and assemble.
iv) Finally, do not clamp the assembly together as normal but leave the clamps open as
illustrated in the following scheme.
v) Ensure that the cooling water is flowing and then set the heater voltage V to
approximately 12 volts
vi) Monitor temperature T1, T2, T3, T4, T5, T6, T7 and T8 until steady-state is
reached.
vii) When the temperatures are stabilized, record T1, T2, T3, T4, T5, T6, T7 and T8, V
and I.
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viii) Reset the voltage and repeat the above procedure again recording the parameters
T1, T2, T3, T4, T5, T6, T7 and T8, V and I when temperatures have stabilised.
ix) Clamp the sections together on the unit. Monitor temperatures T1, T2, T3, T4, T5,
T6, T7 and T8 until they become stable and then repeat the above readings.
V, I
Q
BRASS
T1
T2
T3
T4
T5
T6
T7
T8
No thermal paste
xint
Thermal paste
FW
F. Determine the thermal conductivity,k of an insulation material
Procedure:
i) Ensure that the faces of the heated and cooled sections are cleaned of thermal
conducting paste.
ii) Select the thin cork disc provided, measure and record the thickness xint of the disc
as accurately as possible ( A vernier gauge or micrometer is suitable). Place this between
the heated and cooled sections then clamp the assembly together as illustrated in the
following scheme.
V, I
Insulator
xint
Q
T1
T2
T3
T6
T7
T8
FW
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ii) Ensure that the cooling water is flowing and then set the heater voltage V
iii) Monitor temperature T1, T2, T3, T6, T7 and T8 until steady-state is reached.
iv) When the temperatures are stabilized, record T1, T2, T3, T6, T7 and T8, V and I.
v) Reset the voltage and repeat the above procedure again recording the parameters T1,
T2, T3, T4, T5, T6, T7 and T8, V and I when temperatures have stabilised.
G. Observe unsteady state conduction of heat
Procedure:
i) Ensure that the faces of the heated and cooled sections are cleaned of thermal
conducting paste.
ii) Select the thin cork disc provided and place this between the heated and cooled
sections then clamp the assembly together as illustrated in the following scheme.
V, I
Insulator
xint
Q
T1
T2
T3
T6
T7
T8
FW
ii) Ensure that the cooling water is flowing.
iii) Then disconnect the heater dc supply and then set the heater voltage V
iv) Start a stopwatch to record regular time intervals and then reconnect the dc supply
to the heater with the voltage still set at approximately 9 volts.
v) Record V, I and T1 at regular time intervals of say 5 minutes.
USEFUL DATA FOR LINEAR HEAT CONDUCTION UNIT
Heated Section
Material: Brass, 25 mm diameter, Thermocouples T1, T2, T3 at 15 mm spacing
Thermal conductivity: Approximately 121 W/ mK
9
Cooled Section
Material: Brass, 25 mm diameter, Thermocouples T6, T7, T8 at 15 mm spacing
Thermal conductivity: Approximately 121 W/ mK
Brass Intermediate Specimen
Material: Brass, 25 mm diameter  30 mm long. Thermocouples T4, T5 at 15 mm
spacing centrally spaced along the length
Thermal conductivity: Approximately 121 W/ mK
Stainless Steel Intermediate Specimen
Material: Stainless steel, 25 mm diameter  30 mm long. No thermocouples fitted.
Thermal conductivity: Approximately 25 W/ mK
Aluminium Alloy Intermediate Specimen
Material: Aluminium alloy, 25 mm diameter  30 mm long. No thermocouples fitted.
Thermal conductivity: Approximately 180 W/ mK
Reduced Diameter Brass Intermediate Specimen
Material: Brass, 13 mm diameter  30 mm long. No thermocouples fitted.
Thermal conductivity: Approximately 121 W/ mK
Hot and Cold Face Temperatures
Due to the need to keep the spacing of the thermocouples constant at 15 mm with, or
without the intermediate specimens in position, the thermocouples are displaced 7.5 mm
back from the end faces of the heated and cooled specimens and similarly located for the
brass Intermediate Specimen.
T1 T2 T3 T4 T5 T6 T7 T8
hot
Thot face
Tcold face
cold
Thus, the temperatures of the hot and cold faces can be calculated from the following
equations:
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Thot face = T3 -
T 2  T 3
Tcold face = T6 +
2
T 6  T 7 
2
3.2 THERMAL CONDUCTIVITY CALCULATION IN RADIAL SYSTEMS
Experimental set-up for the radial conductive heat transfer system is shown in
Figure-5.
Thermocouples
T1 T2 T3 T4 T5 T6
Thermal insulation
Metal disc
Heater
Cooling water outlet
Valve
Pressure
regulator
Filter
Cooling water
inlet
Figure-5: Radial heat conduction unit.
A. Determine the effect of a change in heat flow for steady-state conduction of heat
energy through the wall of a thick cylinder (radial energy flow) and determine the
thermal conductivity, k, of the material
Procedure:
i) Ensure that the cooling water is flowing and then set the heater voltage V.
ii) Monitor temperature T1, T2, T3, T4, T5 and T6 until steady-state is reached.
iii) When the temperatures are stabilized, record T1, T2, T3, T4, T5 and T6, V and I.
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iv) Reset the voltage and repeat the above procedure again recording the parameters T1,
T2, T3, T4, T5, T6, V and I when temperatures have stabilised.
v) Reset the heater and repeat the above procedure again recording the parameters T1,
T2, T3, T4, T5, T6, V and I when temperatures have stabilised.
B. Determine unsteady-state conduction of heat energy through the wall of a thick
cylinder (radial energy flow)
Procedure:
i) Ensure that the cooling water is flowing.
ii) Then disconnect the heater dc supply and set the heater voltage V, but do not
reconnect the dc supply at this stage.
iii) Start a stopwatch to record regular time intervals and then reconnect the dc supply to
the heater with the voltage still set
iv) Record T1, T2, T3, T4, T5 and T6 at regular time intervals of 1 minute.
USEFUL DATA FOR RADIAL HEAT CONDUCTION UNIT
Heated Disc
Material: Brass outside diameter: 0.110 m
Diameter of heated copper core: 0.014 m
Thickness of disc: 0.032 m
Radial position of thermocouples:
T1 = 0.007 m
T2 = 0.010 m
T3 = 0.020 m
T4 = 0.030 m
T5 = 0.040 m
T6 = 0.050 m
Thermal conductivity of brass disc:121 W/m.K
4) DATA ANALYSIS
a. Sketch temperature distribution for each experiment.
b. Determine the thermal conductivity of aluminium and compare this value with that
given in the manual. If the values are not similar, discuss possible reasons.
c. Determine the thermal conductivity of stainless steel and compare this value with that
given in the manual. If the values are not similar, discuss possible reasons.
d. Determine the thermal conductivity of brass using all temperature measurements. Is
thermal conductivity similar in every case? If not, discuss possible reasons.
e. Determine the overall heat transfer coefficient using temperature measurements and
compare this value with that resulting from the thermal resistance of the composite
material.
f. Calculate the temperature gradients in the heated and reduced diameter bar. Is the
ratio of these gradients similar to the ratio of areas? If not, discuss possible reasons.
g. Determine the thermal conductivity of the insulation material.
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5) QUESTIONS FOR CONSIDERATION
i) How would a change in the heating rate affect the temperature distribution for both
linear and radial systems?
ii) How would a change in the flowrate of the cooling water affect the results?
iii) Discuss the effect of varying cross-sectional area of the specimen on the temperature
gradient.
iv) Discuss the effect of contact resistance between two adjacent surfaces. What can be
done to reduce the contact resistance?
v) Under the same conditions (cross sectional area, thickness, heating/cooling rate),
hypothetically sketch the temperature distributions if the intermediate specimen is brass,
stainless steel and paper? Explain the differences.
vi) How does a change in insulation thickness affect the total resistance to flow?
vii) For unsteady-state conductive heat transfer, what modifications should be
introduced to both linear and radial systems in order to shorten the time to reach the
steady-state conditions?
viii) Why do you think it takes longer time for the unsteady-state linear conductive
heat transfer system to reach steady-state when compared to the radial system?
6) REFERENCES
i) Incropera, F. P., De Witt, D.P., Fundamentals of Heat and Mass Transfer, John Wiley
& Sons, Singapore, 1990.
ii) McCabe, W. L., Smith, J.C., Harriot, P., Unit Operations of Chemical Engineering,
McGraw-Hill, Singapore, 1985,
Acknowledgment: Author thanks Dr. S. Alsoy Altunkaya for her help in preparing this
manual.
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CONFIGURATION OF CONTROL PANEL
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
R
Q
S
T
U
V
X
W
on/off switch
Manual/Remote control
Voltage control potentiometer
Display Volts (V), Current (I), Thermal radiation (R), Light illumination (L),
air velocity (Ua), Cooling water flow rate (Fw)
Rotary selector switch for V, I, R, L, Ua, and Fw
IO port
Measurement selector switch fro thermocouples
Display temperature
Allow connection of specific transducers to record parameter
Power supply sockets for current loads up to 4 Amps maximum
DC voltage sockets
Circuit breaker
Circuit breaker
Circuit breaker
Power supply sockets for current loads up to 1 Amps maximum
Power supply sockets for DC voltage
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LINEAR HEAT CONDUCTION UNIT
1
2
3
4
6
7
11
12
13
14
15
heating section
intermediate section
cooling section
manual control valve
hose coupling
pressure regulator
outlet hose
toggle clamps
PVC base plate
thermocouple plugs (extreme right)
plug and lead
15
RADIAL HEAT CONDUCTION UNIT
1
2
3
4
5
6
7
8
9
11
13
15
brass disc
solid disc of brass (110mm diameter)
heating section
central heater
solid copper core (14mm diameter)
insulation material
six fixed thermocouples
miniature plug
manual control valve
pressure regulator
hose coupling
plug and lead
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