Multidisciplinary Senior Design Conference
Kate Gleason College of Engineering
Rochester Institute of Technology
Rochester, New York 14623
Project Number: 13623
EDUCATIONAL APPARATUS TO DEMONSTRATE 1-D CONDUCTIVE HEAT
TRANSFER
David Olney
Project Manager
Chemical Engineering
Edward Turfitt
Chemical Engineering
Ian Abramson
Chemical Engineering
Todd Jackson
Project Engineer
Mechanical Engineering
Charles Pueschel
Chemical Engineering
Alysha Helenic
Chemical Engineering
ABSTRACT
Heat Transfer is part of the core curriculum for chemical engineering students. In order to reinforce the principles
of conductive heat transfer, the Chemical Engineering Process Lab currently includes a project where a group of
students design and build their own apparatus to measure a temperature gradient across a copper rod and then calculate
the thermal conductivity for copper using Fourier’s Law. Historically, the apparatuses have produced inaccurate
results for the thermal conductivity of copper thereby failing to enhance student learning of conductive heat transfer.
An improved instrument was designed and built that can create a consistent steady state temperature gradient
along the sample and, using Fourier’s Law, produce results for thermal conductivity that are within 15% accuracy
compared to textbook values. The apparatus is modular and can accept samples of a range of materials, shapes, and
sizes; support different types of insulation; and create a variety of temperature gradients in order to enforce the material
learned from Heat Transfer. The new system includes safe guards to prevent any injury to students. This paper will
outline the design, build, and initial testing of the new instrument and suggestions for future utilization and
improvements.
INTRODUCTION
Sophomore Chemical Engineering students at Rochester Institute of Technology enroll in Chemical Engineering
Principles Lab, a lab designed to demonstrate principles from multiple courses including Continuum Mechanics I.
This course includes the study of the core topics of Heat Transfer. One of the first concepts that students learn in Heat
Transfer is that Fourier’s Law governs conduction heat transfer. Fourier’s Law for 1-dimensional heat transfer can be
written as follows1:
qx
dT
 k
(1)
A
dx
''
In the Fourier’s Law equation qx is heat flux, qx is heat rate, A is this cross sectional area, and k is thermal
q''x 
conductivity. Under steady state conditions where the temperature distribution is linear the derivative can be
T
L where T is the
temperature difference along a sample of length L .
The Chemical
Engineering Department at RIT
desired to include an experiment in
the Principles Lab that would

expressed as
demonstrate 1-dimensional conductive heat transfer and allow students the ability to measure and calculate the thermal



Copyright © 2013 Rochester Institute of Technology
conductivity of a material using the concept of Fourier’s Law. The first year the Chemical Principles Lab was offered
the department created a project for the students to design and build an instrument that would create a steady state
temperature gradient in a copper rod and allow them to calculate the thermal conductivity of the copper. Several
apparatuses were built, however, none produced results that were sufficiently accurate to demonstrate the core
principles of conductive heat transfer.
DESIGN PROCESS
In order to improve the conductive heat transfer experiment, the team was charged with creating an educational
apparatus that can create and allow measurement of a steady state temperature gradient along a sample within a lab
period (20-40 minutes per trial). The hardware should create a consistent temperature at both boundaries of the
specimen to develop a temperature difference of over 80 K (176 F). It must be able to accept a variety of solid
specimens with a range of thermal conductivities. The apparatus should allow for manual data collection of at least
two temperatures along the sample and the heat flux. The resulting calculated thermal conductivity must be within
15% of the textbook value and multiple tests must result in a standard deviation of less than 5%. The instrument is
required to have a small footprint of about 0.9 m by 0.4 m (2.9 ft by 1.3 ft) and a low weight so it can fit and be
transported on a laboratory cart. The experiment and apparatus must be safe for all users and is within a budget limit
of $1200. The students will be able to use the data to calculate the thermal conductivity of each sample and compare
the results to principles learned in class. Emphasis is on enhancing class learning and engaging a team of students by
assigning them to set up and conduct the experiment independently.
Figure 1. Diagram of 1-Dimensional Conductive Heat Transfer Experiment1
Structure & Safety Features
The structure of the apparatus should protect the students from the elevated temperatures of the heating element
and be able to withstand repeated and extended exposure to heat without degrading. In addition, the structure ideally
is able to hold samples and insulation of different shapes and sizes as well as provide the ability the view inside when
closed.
In order to accommodate samples of different shapes and sizes, the heating element is placed on two rails and
backed with a screw to allow for different lengths of samples. A hand wheel outside the structure allows the student
to rotate the screw and move the heater to different positions and an LED light with a range from blue to red displays
relatively how much pressure is being exerted on the sample.
The frame is built from aluminum T-slotted rails and four sides are built from plexiglass for viewing while the
two end sides are built from stainless steel for rigidity and strength against the pressure of the screw. A door on top
of the apparatus allows the student to access to the inside of the box. A magnetic strip on the door ensures that the
apparatus is closed before the heater is turned on or the sample is tightened. The heater will not turn on if the door is
open and the LED light will flash and an alarm will sound if pressure is applied before the door is closed. These
ensure that the student is safe from burns from the heater and crushed fingers from the screw.
Figure 2. Conceptual Structure Design
Sample Selection
Proceedings of the Multi-Disciplinary Senior Design Conference
Page 3
The team desired to have several different samples available to test so the students could observe material and
size effects on the experiment and resulting conductivity constant. All samples were required to be conductive enough
to enable the heat transfer to reach steady state in less than an hour.
Stainless steel, aluminum, and copper samples were chosen because they are relatively conductive but have
significantly different conductivity constants (167 W/m*K and 391 W/m*K respectively [1159 Btu inch/hour/square
foot/°F and 2713 Btu inch/hour/square foot/°F])2. Four copper rods are provided: 1” (2.54 cm) diameter at 4” (10.16
cm) and 8” (20.32 cm) long and ½” (1.27 cm) diameter at 4” (10.16 cm) and 8” (20.32 cm) long to allow the student
to observe that the conductivity constants remains the same between different sizes of materials. An aluminum rod
with a diameter of 1” (2.54 cm) is also provided. The department can choose to purchase more samples of varying
shapes and sizes as needed.
DC Power Supply
The power supply provides 108 watts and delivers 1-36 V and 0-3 A from its main output3. The student can
manipulate and monitor either the voltage or the current using the touchpad and LCD screen located on the power
supply. It also has a USB port that can be used to power the Arduino Mega when the Arduino is not connected to the
computer
Heating
The heating element must create a steady state temperature gradient across any samples in less than the time of a
lab period. It also must be small enough to be contained in the apparatus. A small flexible silicone-rubber heat sheet
is used as the heating element because it is compact and can withstand a large range of relatively low temperatures,
from -40 C to 300 C (-40 F to 572 F).
The heater is backed with a wooden block for insulation in order to ensure maximum heat is transferred in the
direction of the sample and limit heat loss. The front of the heater is covered with a 0.5 in (1.3 cm) thick aluminum
plate to distribute the heat across a larger surface area to accommodate samples of different sizes and to allow
measurement of heat flux across the plate at steady state. The heat flux at steady state across the plate is assumed to
be the same heat flux across the sample, allowing for calculation of thermal conductivity.
The heater was tested for functionality by setting up the heater subsystem as shown in Figure 3, connecting it to
the power supply, and placing a 12” (20.48 cm) long and 1” (2.54 cm) diameter copper rod on top and observing the
temperatures at the ends of the rod over time. No insulation or cooling portion was included. With the power supply
set to 24V and reading 1.76A, the copper rod reached steady state after 17 minutes. The temperature at the bottom of
the rod nearest the heater 100 C (212 F) and farthest was 43 C (109 F) for a temperature gradient of 57 C (135
F). The resulting thermal conductivity was 457 W/m*K (3171 Btu inch/hour/square foot/°F), which is approximately
15% greater than the accepted value. According to the customer requirements, 15% is the maximum acceptable value
for error. With added insulation the error is expected to decrease.
Figure 3. Conceptual Diagram of Heater
Figure 4. Flexible Silicone-Rubber Heat Sheet
Cooling
Copyright © 2013 Rochester Institute of Technology
To create a larger temperature gradient across the sample the team decided to include a contact-cooling element
to the instrument. The cooling element is placed on the end of the sample opposite from the heating element. Similar
to the heating element, the cooling element must maintain a consistent temperature and accommodate a range of sizes
and shapes of samples.
For these reasons, a cold plate was chosen. This type of cooling element reduces the temperature of the sample
through direct contact. The cold plate is made of a conductive metal, in this case stainless steel, and a cool fluid is sent
through the piping in the cold plate to cool the entire element. Stainless steel was chosen because it is relatively robust
allowing different cooling fluids to be sent through the cold plate. If desired, a student could test the impact of using
cold water versus glycol to cool the sample and observe the impact on the temperature gradient, time to reach steady
state, and the resulting calculated conductivity.
The cold plate was tested by placing the 1” (2.54 cm) diameter and 8” (20.32 cm) long copper rod between the
plate and the heater. Tap water was used as the cooling fluid. It was maintained at 10 C (50 F) by continuously
circulating the flow through a temperature-controlled tank. The power supply for the heater was set to 24V and read
1.74A. During this experiment there was only a 30 C (86 F) temperature gradient across the sample. This difference
is less than the test using just the heater partly because a shorter sample was used, but also because the heat sink
provided by the cooling plate was too large. It was decided from the results of this test to cool the water to 20 C (68
F) in future tests in order to maintain room temperature at the ‘cool’ end of the rod.
Figure 5. Cooling plate mounted in structure
Temperature Data Collection and Display
To calculate the temperature gradient along the sample at least two temperature measurements are required. The
team decided to include 6 temperature measurements in order to allow for monitoring whether the gradient has reached
steady state. Initially, thermistors were selected due to their larger operating temperature range of -55 C to 200 C (67F to 392F); however, the thermistors were too small to manually solder connecting wires to and they were replaced
with temperature sensors with a range of -40 C to 125 C (-40F to 257F), which is sufficient for the purposes of
this laboratory.
To allow for testing of different size samples the temperature sensors were attached to small plastic arms
extending from a metal rail that runs parallel to the sample. The arms are able to be moved to different pre-drilled
holes along the rail and can be placed closer together for shorter samples or father apart for longer ones. The rail can
be moved up or down along the side of the structure depending on the size of the sample and the arms may be tightened
using butterfly screws to ensure good contact between the sample and the temperature sensor to ensure consistent
readings with a standard deviation of less than 4% and a final thermal conductivity value within 15% of the accepted
textbook value.
Figure 6. Temperature Sensor Rail and Arms
The chemical engineering department requires manual data collection capabilities on the instrument at
minimum. The team designed the instrument to allow for both manual data collection and collection through
Proceedings of the Multi-Disciplinary Senior Design Conference
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Labview. A display box containing the Arduino Mega connects to both an LCD screen and a computer. The LCD
screen displays the temperatures at the different temperature sensors along the sample, giving students the
opportunity to manually collect temperature data and then use Fourier’s Law to calculate the thermal conductivity of
the sample. By connecting the Arduino to the computer, Labview can display graphs of the temperature gradient
along the sample and automatically calculate the thermal conductivity of the sample. Transient conduction can be
observed using the Labview programming. Additionally, red to blue led lights are placed on the box parallel to the
sample and display a color relative to the temperature at that point along the same. Blue indicates a cooler
temperature while red indicates a hotter temperature. This allows for students to gain a visual understanding of how
the samples heat up with time and can suggest when steady state is reached.
Figure 7. Manual Temperature Display Box (PLACEHOLDER)
In order to use Fourier’s Law to determine thermal conductivity, heat flux must also be measured. As described
in an earlier section there is a thin aluminum plate with a known thermal conductivity placed on top of the heat sheet.
A temperature sensor is placed on both sides of the sheet. A steady state temperature gradient can be quickly achieved
due to the thinness of the plate and a temperature difference can be measured and used with the known thermal
conductivity to calculate heat flux. This flux is assumed to be the same flux sent through the test sample with no major
losses to the surroundings.
Insulation
The structure is built to enable different sizes and types of temporary insulation to be added or no insulation at
all. The insulation must be able to withstand the temperature of the heater without burning or melting. For this reason,
the team decided to choose to provide fiberglass insulation and allow the lab coordinators to choose future insulation
if desired. By using temporary insulation, students have the ability to test the effect of insulation on the accuracy of
the resulting thermal conductivity.
Include detail about effectiveness of insulation chosen
Labview Programming
Talk to Charles
Copyright © 2013 Rochester Institute of Technology
Figure 10. Temperature Gradient Output from Labview (PLACEHOLDER)
Arduino Mega Design and Programming
Talk to David
Figure 9. Arduino Mega (PLACEHOLDER)
RESULTS AND DISCUSSION
After assembly, the team tested the apparatus to ensure it would operate efficiently and effectively in the time
constraints of a laboratory period. The cold plate was maintained at 20 C (68 F) and the power supply for the heater
was set to 24V. The first tests were performed by reading the temperatures from the LCD screen manually, as manual
temperature measurements are minimally required. The later tests were performed by using the capabilities of Labview
to view the transient temperature gradient and automatic calculation of thermal conductivity. The goal was to produce
and measure a temperature gradient along all samples in approximately 20 minutes and confirm the functionality of
the temperature sensors, LED temperature lights, safety features, and Labview programming.
CONCLUSIONS AND RECOMMENDATIONS
REFERENCES
[1] Incropera, F., Dewitt, D., Bergman, T., Lavine, A., 2007, Fundamentals of Heat and Mass Transfer, John Wiley
& Sons, New York, pp. 4-59, Chap. 1 and Chap 2.
[2] McMaster Carr. Web. <http://www.mcmaster.com>
[3] BK Precision. Web. <http://www.bkprecision.com>
ACKNOWLEDGMENTS
Group 13623 would like to acknowledge the Rochester Institute of Technology Chemical Engineering Department
for their funding for this project. The group would also like to thank Paul Gregorius and Karuna Koppula for their
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Page 7
funding and support for this project, the guide Michael Antoniades for his guidance, and Reginald Rogers and Patricia
Taboada-Serrano for their advice at the reviews.
Copyright © 2013 Rochester Institute of Technology