**Unit 2: Conduction**
*In this Unit, you will be introduced to heat conduction, which is the
primary mode of heat transfer in solid systems. Heat conduction occurs
when there is temperature gradient in the system and involves transfer
of thermal energy from regions with higher temperature (higher molecular
kinetic energy) to regions with lower temperature (lower molecular
kinetic energy) by collisions of molecules and interactions of
electrons. The process of heat conduction plays a vital role in many
engineering systems, ranging from metal casting, cooling of
microelectronic devices, to dissipation of energy generated by nuclear
fuel.
In this Unit, you will learn about the basic concepts and equations of
heat conduction and how to obtain solutions for heat conduction problems
in simple geometric configurations.*

**Unit 2 Time Advisory**

This unit will take you approximately 24 hours to complete.

☐ Subunit 2.1: 3 hours

☐ Video Lecture: 1 hour

☐ Reading: 2 hours

☐ Subunit 2.2: 4 hours

☐ Video Lecture: 1 hour

☐ Reading: 3 hours

☐ Subunit 2.3: 4 hours

☐ Video Lecture: 1 hour

☐ Reading: 3 hours

☐ Subunit 2.4: 6 hours

☐ Video Lecture: 1 hour

☐ Reading: 5 hours

☐ Subunit 2.5: 6 hours

☐ Video Lecture: 1 hour

☐ Reading: 5 hours

☐ Subunit 2.6: 6 hours

☐ Video Lecture: 1 hour

☐ Reading: 5 hours

**Unit2 Learning Outcomes**

Upon successful completion of this unit, the student will be able to:
- Derive basic equations for heat conduction.
- Solve heat conduction in one-dimensional steady-state systems (i.e.
in plane wall, radial and spherical systems).
- Calculate fin resistance and fin efficiency for different fin
geometries.
- Use analytical and finite difference to obtain solutions for
steady-state and transient two-dimensional heat conduction.

**2.1 Introduction to Conduction**
- **Web Media: YouTube: Julius Summer Miller’s “Heat Energy Transfer
by Conduction – Part 1” and “Heat Energy Transfer by Conduction –
Part 2”**
Link: YouTube: Julius Summer Miller’s “Heat Energy Transfer by
Conduction – Part
1” and “Heat Energy
Transfer by Conduction – Part
2”

Instructions: Please watch this science demonstration video, in
which Dr. Julius Summer Miller performed several simple experiments
to illustrate heat conduction. You may want to repeat some of these
experiments at home.

Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.

**Reading: MIT: Professors John Lienhard IV and John Lienhard V’s A Heat Transfer Textbook: “Chapter 2”**Link: MIT: Professors John Lienhard IV and John Lienhard V’s*A Heat Transfer Textbook: “Chapter 2”*(PDF)

Instructions: For this unit, please read section 2.1 of “Chapter 2: Heat conduction Concepts, Thermal Resistance, and Heat Transfer Coefficient” (pages 49-56) of Professors John Lienhard IV and John Lienhard V’s*A Heat Transfer Textbook*. The reading discusses the basic concepts (e.g. thermal conductivity, Fourier’s law, etc.) and the governing equations of heat conduction. Pay special attention to Example 2.1. Work through Example 2.6 which illustrates the concept of “boundary condition.” Note that the reading will cover the material that you need to know for subunits 2.1.1-2.1.5.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.**Lecture: YouTube: Indian Institute of Technology (IIT) Bombay: Professor S.P.Sukhatme and Professor U.N.Gaitonde’s “Lecture 4: Heat Conduction-1”**Link: YouTube: Indian Institute of Technology (IIT) Bombay: Professor S.P.Sukhatme and Professor U.N.Gaitonde’s “Lecture 4: Heat Conduction-1” (YouTube)

Instructions: Please watch this video lecture (54:42 minutes), which will introduce you to the basic equations of heat conduction. The video will cover the material that you need to know for subunits 2.1.1-2.1.5. Pay attention to example discussed at 17:00 minute mark. At the 31:00 minute mark, Professor S.P. Sukhatme discussed how to calculate thermal resistance of an infinite composite slab. Compare this with Examples 2.2 and 2.4 in the Lienhard-Lienhard chapter in this unit.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**2.1.1 Rate of Conduction Equation - Fourier's Law**
*Note: This topic is covered by the resources below subunit 2.1.*

**2.1.2 Thermal Conductivity**
*Note: This topic is covered by the resources below subunit 2.1.*

**2.1.3 Thermal Diffusivity**
*Note: This topic is covered by the resources below subunit 2.1.*

**2.1.4 Heat Diffusion Equation**
*Note: This topic is covered by the resources below subunit 2.1.*

**2.1.5 Boundary Conditions**
*Note: This topic is covered by the resources below subunit 2.1.*

**2.2 Plane Wall Conduction**
- **Reading: MIT: Professors John Lienhard IV and John Lienhard V’s A
Heat Transfer Textbook: “Chapter 2”**
Link: MIT: Professors John Lienhard IV and John Lienhard V’s *A
Heat Transfer Textbook: “Chapter
2”* (PDF)

```
Instructions: For this unit, please read pages 56-63 in section 2.2
of “Chapter 2: Heat Conduction Concepts, Thermal Resistance and Heat
Transfer Coefficient.” This reading will introduce to you solutions
of the heat conduction equations in plane wall geometry. Plane wall
conduction is an example of one-dimensional, steady-state
conduction; one example of this is a wall separating an
air-conditioned room from the hot outdoors. Assuming constant
outside temperature, we can use one-dimensional, steady-state
analysis to determine the amount of heat is conducted between the
cool air inside and the hot air outdoor through the wall. Note that
the reading will cover the material that you need to know for
subunits 2.2.1-2.2.3.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**2.2.1 Temperature Distribution**
*Note: This topic is covered by the reading below subunit 2.2.*

**2.2.2 Thermal Resistance**
*Note: This topic is covered by the reading below subunit 2.2.*

**2.2.3 Composite Walls**
*Note: This topic is covered by the reading below subunit 2.2*

**2.2.4 Contact Resistance**
- **Reading: MIT: Professors John Lienhard IV and John Lienhard V’s A
Heat Transfer Textbook: “Chapter 2”**
Link: MIT: Professors John Lienhard IV and John Lienhard V’s *A
Heat Transfer Textbook: “Chapter
2” *(PDF)

Instructions: Please click on the link “Download *A Heat Transfer
Textbook,*” which will take you to a download request form. After
you fill in relevant information about you, you will be able to
download the book. Note that the only information required on the
form is your city, country, and occupation. The book is in PDF
format (17.2 MB). Save a copy of the book for future use.

```
For this unit, please read pages 64-66 in section 2.3 of “Chapter
2: Heat conduction concepts, thermal resistance and heat transfer
coefficient." This reading will introduce to you to contact
resistance. Please pay attention to Example 2.4 and Table 2.1
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**2.3 Radial System Conduction**
- **Reading: Professor Z. S. Spakovszky’s Lecture Notes on
Thermodynamics and Propulsion: “Section 16.5: Steady
Quasi-One-Dimensional Heat Flow in Non-Planar Geometry”**

```
Link: MIT: Professor Z. S. Spakovszky’s Lecture Notes on
Thermodynamics and Propulsion: “[Section 16.5: Steady
Quasi-One-Dimensional Heat Flow in Non-Planar
Geometry](http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node119.html)”
(HTML)
Instructions: Please read the entire page. In this reading, you
will learn how to obtain solutions for one-dimensional steady-state
heat conduction problems in spherical and cylindrical geometries.
Note that this reading will cover the material that you need to
know for subunits 2.3.1-2.3.3.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Lecture: YouTube: Indian Institute of Technology (IIT) Bombay: Professor S.P.Sukhatme and Professor U.N.Gaitonde’s “Lecture 5: Heat Conduction-2”**Link: YouTube: Indian Institute of Technology (IIT) Bombay: Professor S.P.Sukhatme and Professor U.N.Gaitonde’s “Lecture 5: Heat Conduction-2” (YouTube)

Instructions: Please watch this video (52:44 minutes), which will introduce you to heat conduction in radial systems and how to calculate thermal resistance. The example solved at 8:40 minute mark illustrates how to solve heat conduction problems in a radial system. Note that this video covers the material that you need to know for subunits 2.3.1-2.3.3.Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**2.3.1 Cylinders**
*Note: This topic is covered by the resources below subunit 2.3.*

**2.3.2 Spheres**
*Note: This topic is covered by the resources below subunit 2.3*

**2.4 Fins**
- **Reading: MIT: Professors John Lienhard IV and John Lienhard V’s A
Heat Transfer Textbook: “Chapter 4”**

```
Link: MIT: Professors John Lienhard IV and John Lienhard V’s A Heat
Transfer Textbook: “[Chapter
4”](http://web.mit.edu/lienhard/www/ahtt.html) (PDF)
Instructions: Please click on the link “Download A Heat Transfer
Textbook,” which will take you to a download request form. After
you fill in relevant information about you, you will be able to
download the book. Note that the only information required on the
form is your city, country, and occupation. The book is in PDF
format (17.2 MB). Save a copy of the book for future use. For this
subunit, please read section 4.5 in “Chapter 4: Analysis of Heat
Conduction and Some Steady-state One-Dimensional Problems.” This
reading will introduce to you to heat conduction in extended
surfaces, such as fin. You will learn to calculate fin resistance
and fin efficiency for a wide range of fin geometries.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Reading: MIT: Professor Z. S. Spakovszky’s Lecture Notes on Thermodynamics and Propulsion: “Section 18.2: Heat Transfer from A Fin”**Link: MIT: Professor Z. S. Spakovszky’s Lecture Notes on Thermodynamics and Propulsion: “Section 18.2: Heat Transfer from A Fin” (HTML)

Instructions: Please read the entire page. This reading will provide you a brief introduction to fin heat transfer.

Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**2.4.1 Introduction to Fins**
*Note: This topic is covered by the resources below subunit 2.4.*

**2.4.2 Fin Effectiveness**
*Note: This topic is covered by the resources below subunit 2.4.*

**2.4.3 Fin Resistance**
*Note: This topic is covered by the resources below subunit 2.4.*

**2.4.4 Fin Efficiency**
*Note: This topic is covered by the resources below subunit 2.4.*

**2.4.5 Fins with Non-Uniform Cross-Sectional Area**
*Note: This topic is covered by the resources below subunit 2.4.*

**2.4.6 Overall Surface Efficiency**
*Note: This topic is covered by the resources below subunit 2.4.*

**2.5 Two-Dimensional, Steady State Conduction**
**2.5.1 Separation of Variables**
- **Reading: MIT: Professors John Lienhard IV and John Lienhard V’s A
Heat Transfer Textbook: “Chapter 4”**

```
Link: MIT: Professors John Lienhard IV and John Lienhard V’s A Heat
Transfer Textbook: “[Chapter
4”](http://web.mit.edu/lienhard/www/ahtt.html) (PDF)
Instructions: Please click on the link “Download A Heat Transfer
Textbook,” which will take you to a download request form. After
you fill in relevant information about you, you will be able to
download the book. Note that the only information required on the
form is your city, country, and occupation. The book is in PDF
format (17.2 MB). Save a copy of the book for future use. For this
sub-subunit, please read section 4.2 in “Chapter 4: Analysis of Heat
Conduction and Some Steady-state One-dimensional Problems.” Pay
attention to pages 146-150. This section introduces you to
separation of variables, which is a method often used to obtain
solutions to multi-dimensional and transient heat conduction
problems.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**2.5.2 Shape Factor and Heat Rate**
- **Reading: MIT: Professors John Lienhard IV and John Lienhard V’s A
Heat Transfer Textbook: “Chapter 5”**

```
Link: MIT: Professors John Lienhard IV and John Lienhard V’s A Heat
Transfer Textbook: “[Chapter
5](http://web.mit.edu/lienhard/www/ahtt.html)” (PDF)
Instructions: Please click on the link “Download A Heat Transfer
Textbook,” which will take you to a download request form. After
you fill in relevant information about you, you will be able to
download the book. Note that the only information required on the
form is your city, country, and occupation. The book is in PDF
format (17.2 MB). Save a copy of the book for future use. For
this sub-subunit, please read section 5.7 in “Chapter 5: Transient
and Multidimensional Heat Conduction.” Read pages 240-248
carefully. This reading will introduce you to shape factor and how
to calculate shape factor for a number of geometrical
configurations.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above
```

**2.6 Transient Conduction**
- **Reading: MIT: Professors John Lienhard IV and John Lienhard V’s A
Heat Transfer Textbook: “Chapter 5”**

```
Link: MIT: Professors John Lienhard IV and John Lienhard V’s A Heat
Transfer Textbook: “[Chapter
5”](http://web.mit.edu/lienhard/www/ahtt.html) (PDF)
Instructions: Please click on the link “Download A Heat Transfer
Textbook,” which will take you to a download request form. After
you fill in relevant information about you, you will be able to
download the book. Note that the only information required on the
form is your city, country, and occupation. The book is in PDF
format (17.2 MB). Save a copy of the book for future use. Please
read sections 5.1-5.6 (pages 193-235) in “Chapter 5: Transient and
Multidimensional Heat Conduction.” In this reading, you will
learn how to obtain solutions for transient heat conduction problems
using lumped capacitance method. The lumped capacitance method
assumes that the solid object in question has no internal
temperature differences. Always be sure to check that this method
is applicable to your situation by first calculating the object’s
Biot Number (based on its physical and geometric properties). Note
that this reading will cover the material that you need to know for
subunits 2.6.1-2.6.3.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
```

**Lecture: YouTube: Indian Institute of Technology (IIT) Bombay: Professor S.P.Sukhatme and Professor U.N.Gaitonde’s “Lecture 8: Heat Conduction-5”**Link: YouTube: Indian Institute of Technology (IIT) Bombay: Professor S.P.Sukhatme and Professor U.N.Gaitonde’s Lecture Series on Heat Mass Transfer: “Lecture 8: Heat Conduction-5” (YouTube)

Instructions: Please watch this video (53:29 minutes). In this video, you will learn about unsteady state conduction in an infinite slab. Compare what you learn here with section 5.3 in the Lienhard-Lienhard textbook. Professor S.P. Sukhatme will also work through an example of transient heat conduction in a radial coordinate at the 38:00 minute mark. This video covers the material that you need to know for subunits 2.6.1-2.6.3.Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

**2.6.1 Introduction to Unsteady States**
*Note: This topic is covered by the resources below subunit 2.6.*

**2.6.2 Lumped Capacitance Method**
*Note: This topic is covered by the resources below subunit 2.6*

**2.6.3 Spatial Effects**
*Note: This topic is covered by the resources below subunit 2.6*

**Assessment: The Saylor Foundation’s “Unit 2 Assessment”**Link: The Saylor Foundation’s “Unit 2 Assessment” (PDF)

Instructions: Please download the quiz linked above, and answer each question before checking your answers against The Saylor Foundation’s “Unit 2 Assessment Answer Key” (PDF).**Assessment: The Saylor Foundation’s “ME 204 Heat Transfer: Radial Heat Conduction”**Link: The Saylor Foundation’s “ME 204 Heat Transfer: Radial Heat Conduction” (PDF)

Instructions: Read the document and complete the assessment as instructed. The solution to the problem is given in the "Answer Key" (PDF).