1. SUNY Maritime College
Transport Processes Laboratory
Dr. Peter K. Domalavage
Heat Conduction Laboratory
Spring 2014
Group C3
05/01/2014
Hail Munassar- Leader
Andrew Butler- Analyst
Matt Thomas - Pictures
Josh Smith – Data Collector
Christopher Morsch – Called out Data
2. Abstract
The following report contains data, and analysis of said data, showing the results of heat
transfer through different materials and different shapes. The first data set that was collected was
for a rod made of carbon steel and copper with a single steady cross sectional area; this means
the diameter of the rod stayed consistent through its entire length. When we arrived the furnace
was already in a steady state condition, so we just turned the dial to the numbers that
corresponded to the thermocouples, the temperature for each thermocouple was recorded. This
was repeated for the next three materials; number two was a rod with a single, steady cross
sectional area and was made of aluminum and magnesium. The third set of data was different
from the first two because it was collected from a rod with a cross sectional area that got
gradually larger from a 1”diameter at the base to a 2”diameter at the top. The fourth and final set
of data was more similar to the first two in that it was a consistent cross sectional area, but it was
different because it was only one metal instead of two. Once all data was collected it was used to
graph and analyze temperature with respect to distance across all four materials.
5. `
1 | P a g e
Nomenclature
symbol definition units
Q rate of heat flow; qk, rate of heat flow by
conduction
S.I. - W
US - Btu/h
K thermal conductance; Kk, thermal
conductance for conduction heat
transfer
S.I. - W/K
US - Btu/h °F
A area; Ac cross-sectional area S.I. – M2
US – FT2
dT/dx Rate of temperature change; Temperature change over
distance
S.I. – ⁰C/cm
UM – ⁰F/in
Description of heat conduction
There are three modes of heat transfer: conduction, convection, and radiation. Heat that is
conducted through a material is heat that is transferred internally, through the vibrations of atoms
and molecules.1
It occurs in both solids and fluids. Conduction heat transfer is driven by
temperature differentials. For example, if one end of a metal rod is at a higher temperature,
energy will shift towards the colder end. The internal energy shift consists of disorganized
kinetic and potential energy. “For most engineering problems, it is impractical and unnecessary
to track the motion of individual molecules and electrons, which may instead be described using
the macroscopic averaged temperature.”2
1
N.d. TS 12-6-99. Boston University. Physics. Web. 1 May 2014.
2
"Heat Conduction." Thermal-Fluids Central. N.p., 5 Aug. 2010. Web. 1 May 2014.
6. `
2 | P a g e
The heat conduction process is modeled by Fourier’s law and thermodynamics of energy
conservation. 3
The resulting mathematical descriptions can be written as ordinary of partial
differential equations. Conduction heat transfer is the simplest of the three modes to solve
mathematically, and has been studied the longest. “Famous math mathematicians, including
Laplace and Fourier, spent part of their lives seeking and tabulating useful solutions to heat
conduction problems.” 4
Different engineering applications can be represented by one of two
situations; time dependent of not time dependent. A time dependent situation is referred to as
transient conduction. Situations that do not depend on time are referred to as steady state
conduction. All of our experiments are at a steady heat flow rate.
Fourier’s heat equation is Q=KA dT/dx. Q is the rate of heat flow (cal/s), K is the thermal
conductivity of the material (cal/sec-cm °C ), A is area (cm2
), and dT/dx is the rate of change of
temperature per unit length (°C/cm).
Introduction
This Labs purpose is to show a Maritime College Engineer the effects material and cross
sectional area have on heat transfer through conduction. By observing the system characteristics
students can see the change in temperature across the heat exchanger and compare how cross
sectional area and material type affects them. They can then relate this to the data they collect
and use it to get a better understanding on the reason for using different materials and sizes for
heat transfer in real world applications. It also helps the students to understand the best
applications for different materials and size configurations. By combining this usage of an actual
heat exchanger and relating it to real data gathered on it, a better understanding of heat transfer
can be gained.
3
Kreith, Frank, and Mark Bohn. "Heat Conduction." Principles of Heat Transfer. 7th ed.
4
Kreith, Frank, and Mark Bohn. "Heat Conduction." Principles of Heat Transfer. 7th ed.
7. `
3 | P a g e
Procedures
1. Set up heat exchangers and administer heat source.
2. Admit cooling water hose and adjust valve to maintain steady cooling water flow.
Note: Avoid unintentional valve adjustments. This will change the rate of cooling water flow
and skew data***
3. Allow for temperatures to stabilize.
4. Set digital meter to display readings from Material #1.
5. Cycle through thermocouples 1-10 while recording each temperature.
6. Set digital meter to display readings from Material #2.
7. Cycle through thermocouples 1-10 while recording each temperature.
8. Set digital meter to display readings from Material #3.
9. Cycle through thermocouples 1-10 while recording each temperature.
10. Set digital meter to display readings from Material #4.
11. Cycle through thermocouples 1-10 while recording each temperature.
12. Once you have recorded all data, repeat steps 4 – 11 and compare results.
Note: This will ensure that both experiments were completed under the same conditions
without any fluctuations.
13. Turn off heating supply.
14. Shut off cooling water and disconnect.
15. `
11 | P a g e
Materials Tested
For this experiment we are looking at thermal properties of various materials. Thermal
conductivity is a coefficient that represents the rate at which heat moves through a specific
material. Some materials allow heat to move quickly through them, some materials allow heat to
move very slowly through them.5
The higher the coefficient of thermal conductivity (K), the
faster the rate of heat transfer through that material. Copper has a thermal conductivity of 401
W/m°K while air as a coefficient of .026 W/m°K.
Specific heat tells us how much will the temperature of an object increase of decrease by
the gain or loss of energy.6
It is important to note that the specific heat is per unit mass therefore
the specific heat of a gallon of water is equivalent to the specific heat of a liter of water. For
example, the specific heat of copper is .385 J/g°C. This tells you that it takes .385 joules of heat
to raise 1 gram of copper 1 °C.7
Thermal diffusivity represents the ability of a material to conduct
thermal energy relative to its ability to store energy. The thermal coefficient of diffusivity is
calculated by thermal conductivity/ (coefficient of specific heat*density) at a constant pressure.
The thermal expansion coefficient is a standard measure of a substances expansion to
changes in temperature. It quantifies the magnitude of a material’s reaction to temperature
fluctuations. This is extremely important to structural engineers.
5
http://phun.physics.virginia.edu/topics/thermal.html, 1, May 2014
6
http://engineershandbook.com/Materials/thermal.htm, 1, May 2014
7
http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html, 1, May 2014
16. `
12 | P a g e
Conversions 8
1 W/( m°K) = 1 W/(m.o
C) = 0.85984 kcal/(hr.m.o
C) = 0.5779 Btu/(ft.hr.o
F)
1 J/(kg K) = 2.389x10-4
kcal/(kg o
C) = 2.389x10-4
Btu/(lbm
o
F)
1 kJ/(kg K) = 0.2389 kcal/(kg o
C) = 0.2389 Btu/(lbm
o
F)
1 Btu/(lbm
o
F) = 4,186.8 J/ (kg K) = 1 kcal/(kg o
C)
1 kcal/(kg o
C) = 4,186.8 J/ (kg K) = 1 Btu/(lbm
o
F)
Materials Data
Carbon Steel
Temperature (o
C) 25 125 225
Therm. Conductivity (W/(
m°K)
54 51 47
Thermal diffusivity 1.172 × 10−5
(m2/s)
Specific heat 0.49 (kJ/kg K)
Thermal expansion
coefficient
13.0 (10-6
m/m K)
Density 7.85 g/cm3
Copper
Temperature (o
C) 25 125 225
Therm. Conductivity (W/(
m°K)
401 400 398
Thermal diffusivity 1.11 × 10−4
(m2/s)
Specific heat 0.39 (kJ/kg K)
Thermal expansion
coefficient
16.6 (10-6
m/m K)
Density 8.96 g·cm−3
8
http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html, 1, May 2014
17. `
13 | P a g e
Aluminum
Temperature (o
C) 25 125 225
Therm. Conductivity (W/(
m°K)
205 215 250
Thermal diffusivity (m2/s) 8.418 × 10−5
Specific heat 0.91 (kJ/kg K)
Thermal expansion
coefficient
22.2 (10-6
m/m K)
Density 2.70 g·cm−3
Magnesium
Temperature (o
C) 25 125 225
Therm. Conductivity (W/(
m°K)
54 51 47
Thermal diffusivity (m2/s)
Specific heat 1.05 (kJ/kg K)
Thermal expansion
coefficient
25 (10-6
m/m K)
Density 1.738 g·cm−3
Discussion
Description of Curves
Configuration 1
The curve for the steady state heat flow of the copper and steel created two lines with
distinctly different slope. The slope (dt/dx) of copper is much less than that of carbon steel.
Therefore it can be said copper proves to have better conduction properties than steel. (With
steady state heat flow and same cross-sectional area.)
18. `
14 | P a g e
Configuration 2
The curve for the steady state heat flow of the aluminum and magnesium created two
lines with similar slopes. The slope (dt/dx) of aluminum is slightly less than that of magnesium.
Therefore it can be said aluminum proves to have better conduction properties than magnesium.
(With steady state heat flow, same cross-sectional.)
Configuration 3
The curve for steady state heat flow for a variable cross sectional area created a curve
with a declining slope. The slope starts out steeper at the start of the curve and decreases near the
end of the curve. The cylinder for this experiment had a narrow base (start of curve) and a wider
top (end of curve). This reveals that the temperature profile is greater for smaller cross-sectional
areas and lesser for larger cross-sectional areas.
Configuration 4
The curve for steady state heat flow for a constant cross section area creates a single line
with constant slope (temperature profile). This reveals that under constant area, steady state heat
flow, and same material that the temperature profile does not change. This configuration seems
to be a control group for experiment 2 (variable cross section).
Differences in Curves and Purpose
The purpose of these experiments was to develop relationships between the thermal
properties, as found in Fourier’s heat equation.
Experiment 1 (Steady state heat flow for different materials), provided two materials in
each configuration and allowed for comparisons to be made to develop relationships between
19. `
15 | P a g e
thermal gradient and conductivity. Looking at the curves, it is seen that copper has the least steep
thermal gradient, then aluminum, then magnesium, then carbon steel. These slope relationships,
with an understanding of the conductivity values, reveal that there is an inverse relationship
between conductivity and thermal gradient.
Experiment 2 (steady state heat flow for variable cross section), was used to display how
area affects temperature profile. Experiment 3 was used as a control group against experiment 2
to provide a basis of comparison. Experiment 2 yields a curve, whereas experiment 3 yielded a
straight line. Therefore, it is apparent that area does indeed affect temperature profile in a
material. It was concluded that a greater area is directly related to a lesser temperature profile.
This can be verified with Fourier’s equation, as seen on the equation sheet.
Question 1
Differences in thermal gradient and conductivity of materials
The data reveals that materials with higher conductivity values have lesser thermal
gradient. This can be seen from configuration 1: Steady State heat flow for copper and Carbon
Steel. In this configuration, area is constant and heat flow is assumed to be steady-state. The
graphs of our data clearly reveal that the line for copper has a lesser slope than that of steel. This
is unique because the conductivy of copper is k=0.9 (Cal/(cm-s ̊C) and the conductivity of
carbon steel is k=0.13 (Cal/(cm-s ̊C). Manipulating Fourier’s equation, as seen on the equation
sheet, it is proven that there is an inverse relationship between conductivity and temperature
gradient. Therefore, the more conductive a material is, the lesser temperature drop, or
temperature gradient, will be across the material, assuming constant area and steady state heat
flow.
20. `
16 | P a g e
Question 2
Cross-sectional area and temperature profile (dt/dx)
Comparing experiment 2: (Steady state heat flow for a variable cross section), and
experiment 3: (Steady state heat flow for a constant cross section) reveals the relationship
between cross-sectional area and temperature profile, assuming same material. Experiment 2
yielded a curve that had initially steep and then declining slope. This is interesting because the
cylinder that was used as the medium had a narrow base and wider top. Therefore, it can be
established that the temperature profile was greater near the base and lesser near the top. The
conclusion that is drawn from this is that there is an inverse relationship between temperature
profile and area. This relationship can be proved by Fourier’s equation, which can be seen on the
equation sheet. Experiment 3 acted as a sort of control for experiment 2. The slope of experiment
3 remained constant because the area remained constant.
Question 3
What is the material if Q, the heat flow, is the following?
a) 49.13 Cal/Sec
a. Copper
i. Assumed, as per Dr. Domalavage’s instruction. This makes sense because
copper has the highest conductivity, k=0.9 (Cal/(cm-s ̊C). Assuming area
and dt/dx to be constant/steady-state the material with the highest k value
will obviously have a correspondingly high Q value.
b) 26.23 Cal/sec
0.3
0.13
Material
Copper
Aluminum
Magnisum
Carbon Steel
K (Cal/(cm-s ̊C)
0.9
0.5
21. `
17 | P a g e
a. Aluminum
i. Using Fourier’s relation, as described above, it is sensible that Aluminum
would have the second highest Q value because it has the second highest
K value, k=0.5 (Cal/(cm-s ̊C). Once again, this is assuming area and dt/dx
to be constant/steady-state. Along with this relationship, this is also
sensible because K of aluminum is 55.5% of Copper. 55.5% of 49.13
(Copper Q) is 27.2, which is nearly the given Q assumed to be Aluminum.
c) 17.86 Cal/sec
a. Magnesium
i. Using Fourier’s relation, as described above, it is sensible that Magnesium
would have the third highest Q value because it has the third highest K
value, k=0.3 (Cal/(cm-s ̊C). Once again, this is assuming area and dt/dx to
be constant/steady-state. Along with this relationship, this is also sensible
because K of magnesium is 60.0% of Aluminum. 60.0% of 26.23
(Aluminum Q) is 15.7, which is nearly the given Q assumed to be
Magnesium.
d) 8.37 Cal/sec
a. Carbon Steel
i. Using Fourier’s relation, as described above, it is sensible that Magnesium
would have the least highest Q value because it has the least highest K
value, k=0.13 (Cal/(cm-s ̊C). Once again, this is assuming area and dt/dx
to be constant/steady-state. Along with this relationship, this is also
sensible because K of carbon steel is 43.3% of magnesium. 43.3% of
17.86 (Magnesium Q) is 7.74, which is nearly the given Q assumed to be
carbon steel.
22. `
18 | P a g e
Outcomes
The main outcome of this experiment was finding K values for each material, allowing us
to identify each of the unknown materials. Through this information we were all able to better
understand how heat is transferred through different materials. We also gained a better
understanding of how different heat transfer can be through materials that would otherwise be
seen as very similar to each other.
Improvements
This experiment can be improved by using a better method of supplying cooling water to
the equipment. The potential for the experiments data to be affected by someone either kicking
or standing on the hose is fairly high with the amount of people surrounding the table and as we
saw in our lab the equipment takes over an hour to stabilize after a change in cooling water flow
so reducing the risk of this happening is a priority.
23. `
19 | P a g e
References
Geiger, Gordon Harold, and D. R. Poirier. Transport Phenomena in Metallurgy. Reading, MA: Addison-
Wesley Pub., 1973. Print.
"Heat Conduction." Thermal-Fluids Central. N.p., 5 Aug. 2010. Web. 1 May 2014.
<https://www.thermalfluidscentral.org/encyclopedia/index.php/Heat_conduction>.
http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html, 1, May 2014
http://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html, 1, May 2014
http://phun.physics.virginia.edu/topics/thermal.html, 1, May 2014
http://engineershandbook.com/Materials/thermal.htm, 1, May 2014
http://en.wikipedia.org/wiki/Thermal_diffusivity, 1, May 2014
http://en.wikipedia.org/wiki/Magnesium , 1, May 2014
http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html, 1, May 2014
http://en.wikipedia.org/wiki/Aluminium, 1, May 2014
http://en.wikipedia.org/wiki/Copper, 1, May 2014
http://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html, 1, May 2014
Kreith, Frank, and Mark Bohn. "Heat Conduction." Principles of Heat Transfer. 7th ed. New York: Harper
& Row, 1986. 70-71. Print.
N.d. TS 12-6-99. Boston University. Physics. Web. 1 May 2014.
<http://physics.bu.edu/~duffy/py105/Heattransfer.html>.
