2016 Transport Phenomena at High Temperature

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Academic unit or major
Graduate major in Materials Science and Engineering
Susa Masahiro  Kobayashi Yoshinao  Kawamura Kenichi  Hayashi Miyuki  Ueda Mitsutoshi 
Class Format
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(S8-501)  Fri3-4(S8-501)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

This course focuses on the diffusion in solids, and the momentum and energy transport, which are lectured in parallel. The `diffusion in solids' part deals with the kinetics of charged particles in solid. It starts with the expression of point defects in ionic crystals. Devices, which are related to the motion of charged particles, are introduced. The `momentum and energy transport' starts with the comparison of these transports with the mass transport so as to understand the analogy of these three transports in terms of the relation between flux and driving force. With respect to the momentum transport, Newton's law of viscosity and Navier-Stokes equation are explained and applied to the calculation of the velocity profile of fluid and the shear stress acted on the wall assuming that the fluid is laminar. Dimensionless factors such as Reynold's number and friction factors are also introduced. Viscosity will be related with the structure of materials. With respect to the thermal conduction, Fourier's law of heat conduction is applied to the calculation of temperature distribution in solid materials. As for the radiation heat transfer, absorption and emission at solid surfaces are explained so as to introduce the calculation method of radiant energy transfer between two bodies at different temperatures.
The studies in this course will give you the important concepts on the research and development of high temperature materials and processes.

Student learning outcomes

By the end of this course, students will be able to:
1) Understand the analogies between mass, momentum and energy transports.
2) Describe the point defects in solid.
3) Calculate the defect concentration as a function of activity.
4) Explain the principal of high temperature electrochemical devices.
5) Calculate the velocity distribution of laminar and steady-state fluids using Navier-Stokes equation.
6) Calculate the temperature distribution in solid materials using Fourier's law of heat conduction.
7) Calculate the radiant energy transfer between two bodies at different temperatures.


ionic transport, mass transport, momentum transport, Newton's law of viscosity, Navier-Stokes equation, dimensionless factors, Fourier's law of heat conduction, radiant energy transfer

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

At the beginning of each class, solutions to exercise problems that were assigned during the previous class are reviewed. Towards the end of class, students are given exercise problems related to the lecture given that day to solve. To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Transport equation of charged particles. Express the Fick's first law by using potential.
Class 2 Point defect in ionic crystals. Express the point defects in ionic crystals.
Class 3 Activity dependence of point defect. Draw the Kröger-Vink diagram.
Class 4 Electrical conductivity by charged particles. How to measure the total conductivity.
Class 5 Partial electrical conductivity. How to measure the partial conductivity.
Class 6 Principal of concentration cells. Describe the electromotive force.
Class 7 Application of charged particle. Introduce the high temperature elctrochemical devices.
Class 8 Definition of flux: Analogy among mass, momentum and heat fluxes, laminar and tubulent flows, steady and non-steady states Calculate mass flux.
Class 9 Newton's law of viscosity: Momentum flux and momentum conservation theorem Calculate velocity distribution using momentum consercation theorem.
Class 10 Navier-Stokes equation and its dementionless form: Reynolds number and friction factor, dimension analysis, Buckingham' pai theorem Calculate the average fruid velocity using Reynolds number and friction factor.
Class 11 Viscosity measurement techniques: Relation between slag structure and viscosity Understand the principle of the cylinder rotating method
Class 12 Fourier's law of heat conduction: Energy flux, thermal conductivities of metals, ceramics, multiphase structures and slags Calculate the temperature distribution using energy balance.
Class 13 Apparante heat transfer: Convection, heat transfer coefficient Calculate the temperature distribution due to convection and conduction.
Class 14 Radiant heat transfer: Lambert's law, black body, emissivity Calculate the radiant heat transfer between two bodies at different temperatures.
Class 15 Test level of understnading with exercise problems to summarize the course: Solve exercise problems covering the contents of classes 1-14. Solve exercise problems covering the contents of classes 1-14.


Materials relevent to the lecture are provided.

Reference books, course materials, etc.

R. Byron Bird, Warren E. Stewart and Edwin N. Lightfoot, 『Transport Phenomena』 John Wiley&Sons, Inc., ISBN: 0-471-41077-2
R. A. Swalin, 『Thermodynamics of Solids』, John Wiley & Sons, Inc., New York

Assessment criteria and methods

Students' knowledge of the diffusion in solids, and the momentam and energy transport, and their ability to apply them to problems will be assessed.
Midterm and final exams 70%, exercise problems 30%.

Related courses

  • MAT.M302 : Physical Chemistry in Metals
  • MAT.M203 : Chemical Reaction Dynamics(M)

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed both `Chemical Reaction Dynamics(M)(MAT.M203)', `Physical Chemistry in Metals(MAT.M302)', or have equivalent knowledge.

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