2022 Numerical Analysis of Heat Transfer and Fluid Flow

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Academic unit or major
Graduate major in Systems and Control Engineering
Kosaka Hidenori 
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Course description and aims

This course focuses on the fundamentals of numerical analysis of thermo-fluid dynamics. Firstly the governing equations of thermo-fluid dynamics, which express the conservation of mass, momentum, and energy, are presented. Secondly the discretization of governing equations, numerical solving method of discretized equations, and the numerical errors in numerical analysis are explained. Finally the numerical simulation on the simple steady flow is conducted as an exercise.

Computational fluid dynamics (CFD) is widely used for designing the energy conversion systems such as internal combustion engines, turbo-charger. We need to understand the principles of numerical simulation of thermo-fluid dynamics and apply the numerical analysis to the actual systems for the validation of the computed results by CFD and developing the new models of thermo-fluid phenomena. In this course, the processes of numerical analysis of heat transfer and fluid flow are explained with examples of analysis in the simple field. By combining lectures and exercises, the course enables students to understand and acquire the fundamentals of numerical analysis of thermo-fluid dynamics widely applicable to analysis of energy conversion systems.

Student learning outcomes

By the end of this course, students will be able to:
1) Explain the physical meaning of governing equations of heat transfer and fluid flow.
2) Discrete the governing equations.
3) Explain the source of error in the numerical analysis.
4) Explain the methods for solving the discretized governing equations.


thermo-fluid dynamics, numerical analysis, discretization, control volume method, pseudodiffusion

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 Governing equations of heat transfer and fluid flow Derivation of Fourier equation and Navier-Stokes equations
Class 2 Discretization of governing equations Understand discretization of equations by control volume method
Class 3 Numerical analysis of heat transfer Numerical analysis of 1-D heat transfer
Class 4 Convection and diffusion Understand the upwind difference method, exponential method, stability of solution, pseudodiffusion
Class 5 Numerical analysis of fluid flow Understand the analysis of incompressible fluid flow, discretization with staggered grid
Class 6 Numerical simulation of fluid flow in simple field Numerical simulation of 2-D steady flow field
Class 7 Models for multi-phase flow and combustion Understand the concepts of models for multi-phase flow and combustion

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 will be provided if they are required.

Reference books, course materials, etc.

Reference book: Patankar, S. V., Numerical Heat Transfer and fluid flow, Hemisphere Publishing Co., 1980

Assessment criteria and methods

Students' knowledge on numerical analysis of heat transfer and fluid flow will be assessed.
The report on assignment is used to determine the score.

Related courses

  • SCE.M302 : Fundamentals of Thrmal Engineering
  • SCE.S302 : Fundamentals of System Science

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

Students are expected to have successfully completed Fundamentals of Thrmal Engineering or have equivalent knowledge.

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