2020 Transport Phenomena at High Temperature - Momentum and Heat Flow -

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Academic unit or major
Graduate major in Materials Science and Engineering
Hayashi Miyuki  Kawamura Kenichi  Susa Masahiro  Kobayashi Yoshinao  Ueda Mitsutoshi 
Class Format
Media-enhanced courses
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Course description and aims

This course focuses on the momentum and energy transport. 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) Calculate the velocity distribution of laminar and steady-state fluids using Navier-Stokes equation.
3) Calculate the temperature distribution in solid materials using Fourier's law of heat conduction.
4) Calculate the radiant energy transfer between two bodies at different temperatures.


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 Definition of flux: Analogy among mass, momentum and heat fluxes, laminar and tubulent flows, steady and non-steady states Calculate mass flux
Class 2 Newton's law of viscosity: Momentum flux and momentum conservation theorem Calculate velocity distribution using momentum consentration theorem
Class 3 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 4 Viscosity measurement techniques: Relation between slag structure and viscosity Understand the principle of the cylinder rotating method
Class 5 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 6 Apparante heat transfer: Convection, heat transfer coefficient Calculate the temperature distribution due to convection and conduction
Class 7 Radiant heat transfer: Lambert's law, black body, emissivity Calculate the radiant heat transfer between two bodies at different temperatures

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


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

Assessment criteria and methods

Students' knowledge of 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)
  • MAT.A204 : Thermodynamics of Materials
  • MAT.M207 : Phase Diagram and Stability in Metals
  • MAT.M304 : Crystal Growth and Structure Formation

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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