Thermal energy

Lectures: 3 sessions / week, 1 hour / session

Recitations: 1 session / week, 1 hour / session

The typical student enrolled in 16.050 is a junior in the Department of Aeronautics and Astronautics at MIT. The student will have completed Unified Engineering while a sophomore. Unified Engineering (16.01-16.04) presents, among other disciplines, first courses in thermodynamics and propulsion.

Concepts Addressed in 16.050

Energy exchange in propulsion and power processes; the second law of thermodynamics; reversible and irreversible processes; quantification of irreversibility and connection to lost work; application of the first and second laws to engineering systems (propulsion cycles, gas and vapor power cycles, reacting flows); rates of energy transfer and heat exchange in aerospace devices.

Be able to:

Be able to:

Part 0 (Prelude): Introduction and Review of Unified Engineering Thermodynamics (3 lectures)
[IAW pp. 2-22, 32-41 (see IAW for detailed SB & VW references); VN Chapter 1]

Self-assessment on thermodynamic concepts and applications
Thermodynamic systems
Thermodynamic properties and states
Equilibrium
Energy, work and heat
The first law of thermodynamics
Enthalpy, a useful property
Relation between systems and control volumes; adaptation of system formulation to a fixed control volume, application to fluid processes
The first law for a control volume (steady flow energy equation)

1.A. Background to the Second Law of Thermodynamics (3 lectures)
[IAW 23-31 (see IAW for detailed SB & VW references); VN Chapters 2, 3, 4]

Some properties of engineering cycles; work and efficiency
Carnot cycles
The Brayton cycle (jet propulsion cycle)
Gas turbine technology and thermodynamics
Refrigerators and heat pumps; Carnot cycles in reverse
Reversibility and irreversibility in natural processes
Difference between free expansion of a gas and reversible isothermal expansion
Features of reversible processes

1.B. The Second Law of Thermodynamics (3 lectures)
[IAW 42-50; VN Chapter 5; SB & VW-6.3, 6.4, Chapter 7]

Concept and statements of the second law (Why do we need a second law?)
Axiomatic statements of the laws of thermodynamics
Combined first and second law expressions
Entropy changes in an ideal gas
Calculation of entropy change in some basic processes

1.C. Applications of the Second Law (4 lectures)
[VN-Chapter 6; SB & VW-8.1, 8.2, 8.5, 8.6, 8.7, 8.8, 9.6]

Limitations on the work that can be supplied by a heat engine
The thermodynamic temperature scale
Representation of processes in T-s coordinates
Brayton cycle in T-s coordinates
Irreversibility, entropy changes, and "lost work"
Entropy and "unavailable energy" (lost work by another name)
Examples of lost work in engineering processes
Interpretation of entropy from a microscopic perspective: entropy and randomness
Recap: How do we answer the question "What is entropy?"

2.A. Gas Power and Propulsion Cycles (6 lectures)
[SB & VW-11.8, 11.9, 11.11, 11.12, 11.13, 11.14, 11.15]

The internal combustion engine (Otto cycle)
Diesel cycle
Brayton cycle
Brayton cycle for jet propulsion; the ideal ramjet
The Breguet range equation
Performance of the ideal ramjet
Effect of departures from ideal behavior-real cycles

2.B. Power Cycles with Two-Phase Media (Vapor Power Cycles) (4 Lectures)
[SB & VW-Chapter 3, 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7]

Behavior of two-phase systems
Work and heat transfer with two-phase media
The Carnot cycle as a two-phase power cycle
Rankine power cycles
Enhancement of, and effect of design parameters on, Rankine cycles
Combined cycles in stationary gas turbines for power production

2.C. Introduction to Thermochemistry (3 lectures)
[SB & VW-14.1-14.6]

Fuels
Fuel-air ratio
Enthalpy of formation
First law analysis of reacting systems
Adiabatic flame temperature

3.A. Introduction to Conduction Heat Transfer (3 lectures)
[HT-1.0, 2.0 to 2.3]

1.0 Modes of heat transfer (conduction, convection and radiation)

2.0 Conduction heat transfer
Steady-state one-dimensional conduction
Thermal resistance circuits
Steady quasi-one dimensional heat flow

3.B. Introduction to Convection Heat Transfer (3 Lectures)
[HT-3.0 to 3.3, 4.0, 5.0, 6.0, 7.0]

3.0 Convective heat transfer
The Reynolds' analogy
Combined conduction and convection
Dimensionless numbers and analysis of results

4.0 Temperature distributions in the presence of heat sources

5.0 Heat transfer from a fin

6.0 Transient heat transfer (convective cooling or heating)

7.0 Some considerations in modeling complex physical processes

3.C. Applications of the Concepts: Heat Exchangers (2 Lectures)
[HT-8.0, 8.1]

8.0 Heat exchangers
Efficiency of a counterflow heat exchanger

3.D. Introduction to Thermal Radiation and Radiation Heat Transfer (3 lectures)
[HT-9.0 to 9.4]

9.0 Radiation heat transfer (heat transfer by thermal radiation)
Ideal radiators
Kirchoff's laws and "real bodies"
Radiation heat transfer between planar surfaces
Radiation heat transfer between black surfaces of arbitrary geometry

† Lecture divisions correspond to sections in 16.050 notes.
Relevant references given in brackets [ ]

Professor Zoltan Spakovszky

A design project related to gas turbine engines will be conducted with GE Aircraft Engines. Teams of 4 to 5 students will be formed and the workload will be equivalent to about two problem sets. The deliverables are a written report and the presentation of the work to a GE review committee. The best two teams will be awarded a prize and the GE project will count as two problem sets.

There will be two quizzes during the term plus a final exam. The homework (including reading assignments plus the GE design project) will count 35%, the quizzes will count 15% each, and the final exam will count 30%. The instructor reserves the right to alter the percentages slightly, depending on circumstances.

Each week, the 12 course hours are intended to be distributed approximately as follows:
3 hours of lecture, 1 hour of recitation, 2-3 hours of reading and reviewing notes, 5-6 hours of homework.

Homework assignments will be due at the beginning of class. Any unexcused late assignments will receive zero credit.

The remaining 5% of the grade will be based on student performance in various exercises (many of which will occur in class). These may include answering questions in class, either verbally or using the PRS system, submitting assessment surveys, or taking concept quizzes. In all cases the lowest 20% of the scores can be dropped to provide some flexibility for missed classes, etc. There will be no make-up opportunities granted for missing these activities.

[Note: A student's performance on quizzes is an assessment of individual performance (versus that of a study group, for example). Therefore if an individual's performance on the quizzes is significantly lower than on the homework, the average quiz grade may be given proportionally greater weight than described above.]

The basis for grading in the course is as described in the Rules of the MIT Faculty. The description of grades is given below under Basis for Grades.

The lectures are thrice a week. Each session is for one hour. These are the primary presentation of the subject material by the instructor.

There is a recitation once a week for one hour. The recitations will be given by (at different times) the graduate TA and the undergraduate TAs. The recitations review the material from previous lectures and introduce relevant examples, which may be related to the assigned homework.

As in Unified, attendance at lectures and recitations is considered mandatory. Although no formal roll call will be taken, participation during in-class exercises will represent part of your grade.

It is planned there will be help sessions given by the instructor prior to each quiz and to the final.

Each student will be distributed a remote transmitter to be used with the Personal Response System (PRS). Each one has its own number and is assigned to a particular student. Students are responsible for bringing their transmitter to every lecture, in order to participate in exercises that use PRS. Since class participation will be, in part, gauged by each student's responses, operating other student's transmitters in their place will be considered a violation of MIT's academic honesty policy.

The transmitters cost approximately $50. If a transmitter is lost the student will be responsible for paying for a replacement.

The policy on collaboration and cheating will be the same as that specified in Unified Engineering. The policy on Academic Honesty and Study Group Guidelines are given below.

The fundamental principle of academic integrity is that you must fairly represent the authorship of the intellectual content of the work you submit for credit. In the context of this class, this means that if you consult with others (such as fellow students, TA's, faculty) in the process of completing homework, you must acknowledge their contribution in any way that reflects their true ownership of the ideas and methods you borrowed.

Discussion among students to understand the homework problems or to prepare for laboratories or quizzes is encouraged. COLLABORATION ON HOMEWORK IS ALLOWED AS LONG AS ALL REFERENCES (BOTH LITERATURE AND PEOPLE) USED ARE NAMED CLEARLY AT THE END OF THE ASSIGNMENT. Word-by-word copies of someone else's solution or parts of a solution handed in for credit will be considered cheating unless there is a reference to the source for any part of the work which was copied verbatim. FAILURE TO CITE OTHER STUDENT'S CONTRIBUTION TO YOUR HOMEWORK SOLUTION WILL BE CONSIDERED CHEATING. The official Institute policy regarding academic honesty can be found in the MIT Bulletin Course and Degrees Issue under "Academic Procedures and Institute Regulations."

MIT's academic honesty policy can be found at the following link:

Study groups are considered an educationally beneficial activity. However, at the end of each problem on which you collaborated with another student you must cite the students and the interaction. The purpose of this is to acknowledge their contribution to your work. Some examples follow:

The rules of the MIT faculty define grades in terms of the degree of the mastery of course material:

A Exceptionally good performance, demonstrating a superior understanding of the subject matter, a foundation of extensive knowledge, and a skillful use of concepts and/or materials.

B Good performance, demonstrating capacity to use the appropriate concepts, a good understanding of the subject matter, and an ability to handle the problems and materials encountered in the subject.

C Adequate performance, demonstrating an adequate understanding of the subject matter, an ability to handle relatively simple problems, and adequate preparation for moving on to more advanced work in the field.

D Minimally acceptable performance, demonstrating at least partial familiarity with the subject matter and some capacity to deal with relatively simple problems, but also demonstrating deficiencies serious enough to make it inadvisable to proceed further in the field without additional work.

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