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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 barwith 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 resistanceand 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 meansof 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 (X) and area (A)

supports a temperature difference (T) then theheat transfer rate per unit time (Q) by conduction

through the wall is found to be:

Q AT

x

If the material of the wall is homogeneous and

has a thermal conductivity (k) then:

Q kA dTdx

=

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 withradius, the temperature gradient must

decrease with radius.

The amount of heat (Q) which is conducted across the cylinder wall per unit time is:

Q LKT T

LogR

R

i o

e

o

i

=

2( )

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Plots of the temperature

profile along the radius

should be drawn and thetemperature Toat the outer

radius Roof 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 differencebetween 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 unitthe 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 ofCommerce, National Bureau of Standards, Washington, D.C., 1973 (QC 176.8.T4 C47 1973)

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EQUIPMENT

1. 250 mL beaker

2. Stop watch

3. Micrometer

4. Tissues5. 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 adrain 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 conductionthrough 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 EngineeringStockroom Checkout slip

The Heat Conduction Bench ChE 3211

Name: Date:

(print name)

Lab No.: Lab 1 Tuesday 12:00 - 4:50 PM Lab 2: Thursday 12:00 - 4:50 PM

Lab No.: Lab 3 Tuesday and Thursday morning (9:30 - 11:50 AM)

(circle one)

Equipment Out In Equipment Out In

250 mL Beaker Stopwatch

Micrometer 1-100 mL grad cyl

Name:

(Signature)