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

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.

Table of Contents

Nomenclature ……………...…………………………………………… 1

Description of heat conduction ……………………………………… 1

Introduction ……...…………………………………………………… 2

Procedures ………………………………...………………………… 3

System Schematic …………………………………………………… 4

Data ………………….……………………………………………… 5

Raw of Data …………………………………………………… 5

Configuration 1 …………………………………………………… 6

Basic Diagram …………………………………………………… 6

Analysis …………………………………………………… 6

Results …………………………………………………… 7

Configuration 2 …………………………………………………… 7

Basic Diagram …………………………………………………… 7

Analysis …………………………………………………… 8

Results …………………………………………………… 8

Configuration 3 …………………………………………………… 9

Basic Diagram …………………………………………………… 9

Analysis …………………………………………………… 9

Results …………………………………………………… 9

Configuration 2 …………………………………………………… 10

Basic Diagram …………………………………………………… 10

Analysis …………………………………………………… 10

Results …………………………………………………… 10

Materials Tested .…………………..……………………………………… 11

Conversions …………………………………………………… 12

Material Data …………………………………………………… 12

Carbon Steel …………………………………………………… 12

Copper …………………………………………………… 12

Aluminum …………………………………………………… 13

Magnesium …………………………………………………… 13

Discussion ……...…………………..……………………………………… 13

Description of Curves ………………………...…………………. 13

Differences in Curves and Purpose …………...…………………. 14

Question 1 ……….………………………...…………………. 15

Question 2 ……….………………………...…………………. 16

Question 3 ……….………………………...…………………. 16

Outcome ……...…………………..……………………………………… 18

Conclusion ……...…………………..……………………………………… 18

References ……...…………………..……………………………………… 19

Appendix ……...…………………..……………………………………… 20

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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.

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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.

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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.

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System Schematic

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Data

Raw Data

Temperature for Each Thermocouple for Each Configuration

Conductivity (K) Values

1 2 3 4

1 239 243 260 296

2 165 166 252 292

3 115 104 245 288

4 110 96 240 284

5 107 88 235 281

6 104 80 231 277

7 91 66 227 274

8 76 58 224 271

9 62 50 222 268

10 49 41 220 265

Ther

mo

cou

ple

#

Configuration # (Temps in ̊C)

0.3

0.13

MaterialCopper

Aluminum

Magnisum

Carbon Steel

K (Cal/(cm-s ̊C)0.9

0.5

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Configuration 1

Steady State Heat Flow for Different Materials

Basic Diagram

Analysis

Temperature Change with Distance

Material Thermo # Distance (cm) Temp( ̊C)

Steel 1 0 239

2 0 165Steel

Copper

3 2.54 115

4 6.98 110

5 11.42 107

6 15.86 104Coppe

r

Carbon

Ste

el

7 23.48 91

8 27.92 76

9 32.36 62

10 36.8 49Carbon

Ste

el

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Results

Configuration 2

Steady State Heat Flow for Different Materials

Basic Diagram

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Analysis

Temperature Change with Distance

Results

Material Thermo # Distance(cm)Temp ( ̊C)

Steel 1 0 243

2 0 166Steel

Alumin

um

3 2.54 104

4 6.98 96

5 11.42 88

6 15.86 80Alum

inum

Mag

nesiu

m

7 23.48 66

8 27.92 58

9 32.36 50

10 36.8 41

Mag

nesiu

m

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Configuration 3

Steady-state heat flow for a variable cross-section

Basic Diagram

Analysis

Temperature Change with Distance

Results

Thermo # Distance Temp

1 4.92125 260

2 7.381875 252

3 9.8425 245

4 12.30313 240

5 14.76375 235

6 17.22438 231

7 19.685 227

8 22.14563 224

9 24.60625 222

10 27.06688 220

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Configuration 4

Steady-state heat flow for constant cross section

Basic Diagram

Analysis

Results

Thermo # Distance Temp

1 4.92125 296

2 7.381875 292

3 9.8425 288

4 12.30313 284

5 14.76375 281

6 17.22438 277

7 19.685 274

8 22.14563 271

9 24.60625 268

10 27.06688 265

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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

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Conversions 8

1 W/( m°K) = 1 W/(m.oC) = 0.85984 kcal/(hr.m.

oC) = 0.5779 Btu/(ft.hr.

oF)

1 J/(kg K) = 2.389x10-4

kcal/(kg oC) = 2.389x10

-4 Btu/(lbm

oF)

1 kJ/(kg K) = 0.2389 kcal/(kg oC) = 0.2389 Btu/(lbm

oF)

1 Btu/(lbm oF) = 4,186.8 J/ (kg K) = 1 kcal/(kg

oC)

1 kcal/(kg oC) = 4,186.8 J/ (kg K) = 1 Btu/(lbm

oF)

Materials Data

Carbon Steel

Temperature (oC) 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 (oC) 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

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Aluminum

Temperature (oC) 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 (oC) 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.)

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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

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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.

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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

MaterialCopper

Aluminum

Magnisum

Carbon Steel

K (Cal/(cm-s ̊C)0.9

0.5

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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.

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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.

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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>.

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