UNIVERSITY OF MINNESOTA DULUTH
DEPARTMENT OF CHEMICAL ENGINEERING
ChE 3211-4211
THE HEAT CONDUCTION BENCH
OBJECTIVE
The objective of the heat conduction bench is to teach the basic principles of heat transfer
that occurs in a solid material by virtue of a temperature gradient within it. The study of the
conduction of heat along a brass and stainless steel bar of the same diameter and a brass bar of a
smaller diameter and the evaluation of their thermal conductivity constants will be conducted.
The effect of surface contact on thermal conduction between adjacent bars of metal will be
studied by using (heat conducting paste) and calculation of contact resistance. The influence of
thermal insulation (paper or cardboard) upon the conduction of heat between adjacent metals
will be investigated. The thermal conductivity of the insulating material (paper or cardboard)
will be determined. Monitoring the temperature profile during either a heating or cooling cycle
can be useful in studying unsteady state conduction. An investigation into the temperature
profile and the determination of the rate of heat transfer resulting from radial steady conduction
through the wall of a cylinder will be made.
INTRODUCTION
The apparatus comprises two heat-conducting specimens, a sectioned bar for the
examination of linear conduction and a disc for radial conduction. A console provides electrical
power to heaters in the specimens and digital readout of the temperature at selected points along
the heat-conducting paths. A stream of cold water provides a heat sink at the end of the
conducting path in each specimen.
The general view of the Bench is shown in Figure 1. More detail is shown in the schematic
view shown in Figure 2, where the numbers relate to references in parentheses found in the text
that follows below.
The Linear Module
This consists of a section (1) manufactured from brass fitted with an electrical heater (2).
Three temperature sensors (thermistors) are installed at 10 mm intervals along the working
section, which has a diameter of 25 mm. The separate section that forms the heat sink (4) is
made of brass; it is cooled at one end by flowing water (5) and its working section is fitted with
three temperature sensors (6) at 10 mm intervals. The heated and the cooled section may be
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clamped together to form a continuous bar of brass with temperature sensors at 10 mm intervals.
Alternatively, there are three metallic bars that can be fitted between the heated and cooled brass
sections.
The first (7) is a brass bar of the same diameter as the heated and cooled sections and 30 mm
in length. There are three temperature sensors (8) along its length at 10 mm intervals. This
section (7) is shown clamped between the heated and cooled bars; it forms a relatively long bar
with nine regularly spaced temperature sensors.
The second section (9) is also made of brass, and is 30 mm long. However, its diameter is
13 mm and it is not fitted with sensors. Use heat conducting paste when determining the thermal
conductivity of this section. The effect of a reduction in the cross-section of the heat conducting
path may be studied with this section.
The third section (10) is stainless steel, and it has the same dimensions as the first section.
There are no temperature sensors fitted in this section. Use heat conducting paste when
determining the thermal conductivity of this section. The effect of a change in material along the
heat conducting path may be studied with this section.
The ends of the sections that come together are finely finished to provide good thermal
contact. Heat conducting paste may be smeared over the surfaces to reduce thermal resistance
and demonstrate the effect of surface contact on thermal conduction between adjacent bars of
metal. The paste may be wiped off using a paper tissue or cotton swab moistened with
isopropyl alcohol when finished.
The properties of insulators may be studied by inserting a thin specimen between the heated
and the cooled sections. A piece of paper or thin piece of cardboard is a useful example.
Heat losses from the module are reduced to a minimum by a heat-resistant casing (11)
enclosing an air gap (12) around the module. The interchangeable center sections (7, 9, & 10)
have their attached casings, which mesh those of the heated and cooled sections.
There are nine sensor leads to connect the thermistors to the electrical console. The
temperature readings are given on the digital meter on the front of the console. The required
reading is selected by the nine-position switch.
The Radial Module
This comprises a brass disc (17) that is 110 mm in diameter and 3 mm thick. It is heated
electrically in the center and cooled by water in a circumferential copper tube (9). Temperature
sensors (20) are fitted to the center of the disc and at 10 mm intervals along the radius. In all,
there are six sensors. The heat-resistant casing (22) encloses an air gap (21) around the disc; this
reduces heat loss. The sensors are connected to the console. This module can be used to
investigate the temperature profile and determine the rate of heat transfer resulting from radial
steady conduction through the wall of the cylinder.
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Figure 1. The general arrangement of the heat conduction bench showing interconnections
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Figure 2. Heat Conduction apparatus showing the location of temperature sensors, etc. The
numbers are those referenced in the text.
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The Electrical Console
One module may be connected to the electrical console, but not both simultaneously. The
power delivered to the heated sections is controlled by a variable auto transformer; the power is
displayed on a digital wattmeter. The power output may be controlled from 0 to 100 W. The
temperature gradient along the specimen is obtained by switching through the sensors by means
of the nine-position switch.
Overheating is prevented by means of a thermostat attached to the heated sections. The
thermostat will trip if excessive heating or insufficient cooling is provided so that the
temperature exceeds 100EC.
THEORY
Linear Conduction of heat along a simple bar.
If a plane wall of thickness (ΔX) and area (A)
supports a temperature difference (ΔT) then the
heat transfer rate per unit time (Q) by conduction
through the wall is found to be:
Q∝ A
ΔT
Δx
If the material of the wall is homogeneous and
has a thermal conductivity (k) then:
Q = kA
dT
dx
Heat flow is positive in the direction of temperature fall. What is the effect of average
temperature on the values of thermal conductivity for brass?
The heat flow through a material can not always be evaluated at steady state 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 time. Using the equipment set-up described above, it is a simple matter of
monitoring the temperature profile variation during either a heating or cooling cycle thus
facilitating the study of unsteady state conduction.
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Radial steady conduction through the wall of a cylinder.
When the inner and outer surfaces of a
thick walled cylinder are each at a uniform
temperature, heat flows 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:
Q = 2πLK
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(Ti − To )
R
Log e o
Ri
Plots of the temperature
profile along the radius
should be drawn and the
temperature To at the outer
radius Ro of the disc should
be determined from the
curve. This data should be
used to calculate the rate of
radial head conduction from
the equation and the result
compared to the measured
heat input (Q) from the
wattmeter. Students should
account for any difference
between the measured input
and the calculated
conduction rate. A straight
line plot can be obtained on
log/linear paper with the
radius on the logarithmic
axis and temperature on the
linear axis. NOTE:
Depending on which order
the thermistors are
connected to the radial unit
the numbers may be
opposite those shown on the
Figure to the right
.
REFERENCES
Any respectable text on heat transfer
Childs, G.E., Ericks, L.J., Powell, R.L., “Thermal Conductivity of Solids at Room Temperature
and Below, A review and compilation of the literature”, NBS Nomograph 131, U. S. Bureau of
Commerce, National Bureau of Standards, Washington, D.C., 1973 (QC 176.8.T4 C47 1973)
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EQUIPMENT
1.
2.
3.
4.
5.
250 mL beaker
Stop watch
Micrometer
Tissues
Cotton swabs (Q-tips)
CHEMICALS/MATERIALS
1. Isopropyl alcohol
EXPERIMENTAL PROCEDURE
The apparatus should be installed on a firm level work surface next to a water supply with a
drain and an electrical power supply. Check that the ON/OFF switch on the console is OFF. If
working with the linear module, configure it in the way desired. One water tube is connected to
the supply and the other to the drain. The tube going to the drain may be routed through a flow
meter to control the water flow. The heater supply cord for the requisite module is plugged into
the power supply socket on the front panel of the console. The leads from the temperature
sensors are connected to the rear of the console paying close attention to the correct numbering
of the leads and the sensors.
Make sure that the water tubing and electrical cords are not entangled. Keep them away
from each other as much as possible. Turn on the water supply and ensure that water is flowing
freely to the drain. Set the flow meter if required. Check water connections for leaks, especially
those under the Bench. Do this periodically during use.
Rotate the heater power control on the console to the fully anti-clockwise position. Set the
main ON/OFF switch to the on position; the digital panel meters will be illuminated. The heater
power control is then set to the desired power. Maximum power should not be set greater than
20 watts. Power for the smaller diameter brass section may have to be set lower than 20 watts.
Power for the insulator test (paper) should be about half the power used in the other tests. The
power slowly drifts so it will require adjustment from time to time. Temperatures along the
conducting specimen can now be recorded. They should be recorded at known times to
determine when steady state has been reached and to study unsteady state conduction.
Experimental runs that should be carried out include: 1) heat conduction through the 25 mm
brass bar and stainless steel bar (heat conducting paste should be used); 2) heat conduction
through the 13 mm Brass Bar; 3) Comparison of heat conduction using heat conducting paste
and no heat conducting paste to determine the contact resistance. (Two ways this can be done
would be: 1. Make two runs, one run with heat conducting paste on both sides of the center
section and one run with no paste on either side. Compare the contact resistance of the two runs;
2. Make one run with heat conducting paste on one side of the center section and no paste on the
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other side of the center section. Compare the contact resistance on both sides of the center
section.); 4) Make a run with paper or light cardboard between the sections to determine the
thermal conductivity of paper; 5) make runs using the radial conduction set-up.
SAFETY NOTES
1. Personal protective equipment shall include safety glasses with side shields.
2. The unit is heated. Be careful when removing the specimen from the unit, it may still
be hot. Let it cool or wear thermal mitts. Thermal mitts shall be worn whenever items
at temperatures above ambient are handled.
3. Turn on the cooling water slowly. Hoses can be popped off their connections,
spraying water all over, if the water is turned on too fast.
WASTE DISPOSAL PROCEDURES
There should be no waste from this experiment. Let the liquid on the Q-tips and tissues
evaporate and then place them in the garbage container.
08/2012
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Department of Chemical Engineering
Stockroom Checkout slip
The Heat Conduction Bench
ChE 3211
Date:
Name:
(print name)
Lab No.: Lab 1 Tuesday 12:00 - 4:50 PM
Lab No.:
Lab 3
Lab 2: Thursday
12:00 - 4:50 PM
Tuesday and Thursday morning (9:30 - 11:50 AM)
(circle one)
Equipment
Out
In
Equipment
250 mL Beaker
Stopwatch
Micrometer
1-100 mL grad cyl
Name:
(Signature)
10
Out
In