MEAM664 homepage

Advanced modeling and solutions of heat conduction and mass diffusion, with emphasis on the similarities and analogies between these phenomena. Analytical and numerical solutions, including the use of available general and specific software for the solution of the associated differential equations. Inverse problem solution techniques. Applications including basic and combined problems as well as moving interfaces, effects of energy sources and chemical reactions, interfacial contact resistance, advanced insulation, thermal stresses, composite materials, and microscale and non-continuum systems.

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Course Outline

1. Introduction

1.1 The physics of conduction, and engineering applications
1.2 The heat conduction equation and its initial and boundary conditions
1.3 The physics of mass diffusion, and engineering applications
1.4 The mass diffusion equation and its initial and boundary conditions
1.5 Heat and mass transfer analogy

2. Steady state problems and methods for their solution

2.1 A review of the solution of one-dimensional problems by analytical and integral methods.
2.2 Contact resistance
2.3 The inverse problem and approaches to its solution
2.4 Multi-dimensional problems
2.5 Heat and mass transfer in composite materials
2.6 Advanced thermal insulation

3. Transient problems

3.1 One-dimensional problems, solutions by analytical, integral and numerical methods
3.2 Multi-dimensional problems

4. Melting and solidification

4.1 Analytical solutions
4.2 Numerical solutions

5. Thermal stresses: a conjugate problem of solid mechanics and heat transfer
6. Microscale heat conduction

6.1 Microscale energy transport in solids
6.2 Heat transport in thin films and at solid-solid interfaces
6.3 Heat conduction in semiconductor devices and interconnects.

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Prerequisites

Students planning on taking this course are expected to have completed ENM 510 or equivalent, and undergraduate level heat and/or mass transfer, or equivalent.

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Course Meeting Time and Room

TuTh 6-7:30pm, 212 Moore

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Course Conduct
Homework, small project, and final exam (1/3 of grade each).

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Online Schedule

Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Week 12
Week 13
Week 14
Week 15
Final

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Textbooks

Required Text:

B. Gebhart, Heat Conduction and Mass Diffusion, McGraw-Hill, 1993.

Optional Texts:

K. Kurpisz and A.J. Nowak, Inverse Thermal Problems, Computational Mechanics Publications, Southampton UK and Boston, USA, 1995.
M. A. Porter, FEA Step by Step with Algor®, Second Edition, Dynamic Analysis, KS.
C.L. Tien, A. Majumdar and F.M. Gerner (eds), Microscale Energy Transport, Taylor & Francis, Washington, 1998.
C.V. Madhusadana, Thermal Contact Conductance, Springer-Verlag, NY, 1996.

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Software
It is recommended that the program Algor®, as well as as the MATLAB pde Toolbox be used in some of the numerical analysis. Both are available on the SEAS network

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General Information

Instructor:

Name: Professor Noam Lior

Office: 212 Towne

Phone: (215) 898-4803

Email: lior@seas.upenn.edu

Instructor Office Hours:

By appointment or walk-in.

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Handouts

N. Lior, "Melting", Section 507. 9 in Heat Transfer and Fluid Flow Data Books, Genium Publishing Corp., 1996.

N. Lior, "Freezing", Section 507.8 in Heat Transfer and Fluid Flow Data Books, Genium Publishing Corp., 1996.

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Homework

Homework Due Dates:

2 weeks after assignment.

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Homework Assignments:

Read Gebhart Chs. 1-3, 7.1-7.3, 4, 5

Do problems:
#1: 1.2.2, 1.2.3, 1.2.4, 1.2.5, 1.2.7, 1.4.1
#2: 2.1.2. 2.3.1, 2.4.16
#3: 7.3.1
#4: 2 problems on inverse solutions given in class
#5: 4.2.3, 4.4.2, 5.1.4, 5.1.17
#6: 4.4.7, 4.8.1, 4.8.3
#7: 9.3.5
#8: 4.6.2

MEAM 664 Course Project (in lieu of midterm)

The project

The main project is the development of an inverse method for computing heat transfer coefficients on the surface of a cylindrical test probe used to determine heat-treatability of metals.

If you prefer to do another project in heat conduction or mass diffusion you may recommend one to the instructor for consideration.

Inverse analysis of the heat treatment probe

In heat treatment of metals the metal is preheated to a certain temperature, usually above 800 C, and is then cooled rapidly by immersion in a cold liquid or in a fast gas stream. Such rapid cooling changes the internal microstructure of the metal to obtain higher hardness and strength. If liquids are used, they extract heat from the metal by boiling. If a gas is used, it by convection. In either case it is important to get sufficiently high cooling rates (i.e., heat transfer coefficients) so that the internal phase transformation is obtained. These coefficients are hard to determine a-priory, and therefore a test probe, similar in shape to the part to be heat treated, is used, with an internal thermocouple . The temperatures are measured at several times during the quenching period (which is typically shorter than 30 s), and the surface-average transient external heat withdrawal rate is calculated by using an inverse heat conduction analysis method.

In your problem, this probe, is either

1. Cylindrical, 12.5 mm diameter and 60 mm long (described in ISO-standard 9950) with an imbedded thermocouple located in the center of gravity, (for first 3 students alphabetically: Hu, Muto, Pasquarella)

2. A ring with the thermocouple in the center of the ring cross-section (for Quinones the ring dimensions are 140 mm o.d., 128 mm i.d., 40 mm high; for Shimizu, 280, 232, 80; for Xiong, 72.37, 59.70, 22.28) ).

The required solution (independent, and not team work, is a requirement)

1. Develop an inverse heat conduction method to find the surface-average transient heat flux from the interior temperature measurements. Assume the heat transfer coefficients are uniform on the exterior surface.

2. Apply the model to calculate these heat fluxes and the surface-average transient convective heat transfer coefficients for SAE 52100 steel, based on the transient temperature measurement data given in the heat treatment curve below, for Re=10⁶.

3. Propose a method for constructing a probe and solving the problem if the case was more realistic where the heat transfer coefficients over the surface are nonuinform. For EXTRA CREDIT (you can still get full credit without doing that) solve the problem for the case where the heat transfer coefficient at the flat surfaces was different from that on the curved ones. Make some logical assumption about the values of h to use on the different types of surface.

Project submission

The project is due on 16 December 1998. Submit also a diskette and annotated printout of any software you may have developed for the solution.

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