Course Notes

• Syllabus
• Course Notes
• Exams
• Homework
• References
• Schedule
• Learning Suite

These are notes, examples, derivations, links and handouts related to the course. I provide these notes for your benefit in case you want update your personal notes or check something from class. I strongly encourage you to take notes in class and to read your book. I make no guarantee that these notes are free of error, nor do I promise to post them before an assignment is due. For copyright reasons, I may not be able to publish all of the handouts from class on the web.

Course Outcomes and Concepts

• Course Concepts is a detailed list of the concepts covered in the course.

Course Notes

Unit 1 - Math Review

• Lec 1 – Vector and Tensor Algebra
• Lec 2 – Curvilinear Coordinates
  • Supplement – Vector Algebra in Curvilinear Coordinates
• Lec 3 – Vector and Tensor Calculus
• Lec 4 – Differential Equations
  • Supplement – Definite and Indefinite Integrals
  • Supplement – Bessel Functions (Jupyter Notebook)

Unit 2 - Transport Equations

• Lec 5 – Constitutive Equations
• Lec 6 – Transport Coefficients
  • Supplement – Slides on Corresponding States
  • Supplement – Tracer vs Mutual Diffusion Coefficients
• Lec 7 – Conservation Equations
• Lec 8 – Conservation of Energy
• Lec 9 – Conservation of Species Mass

Unit 3 - Solutions to 1D Transport Equations

• Lec 10 – Solving 1D Transport Equations
  • Supplement – Diffusive Flux and Bulk Flow
  • Supplement – Examples of 1D Problems (Jupyter Notebook)
• Lec 11 – Scaling
  • Supplement – Scaling of the Heated Wire Solution
  • Supplement – Scaling of the Irreversible Homogeneous Reaction Problem
  • Supplement – Dimensionless 1D Solutions (Jupyter Notebook)
• Lec 12 – Simplifying 1D Transport Equations
  • Supplement – Pseduosteady example: Evaporating Liquid Column
  • Supplement – Evaporating Liquid Column (Jupyter Notebook)

Unit 3 - Solutions to Multidimensional Transport Equations

• Lec 13 – Similarity Method
  • Supplement – Example: Semi-Infinite Diffusion
• Lec 14 – Perturbation Analysis
  • Supplement – Example: Heated wire (with variable conductivity)
• Lec 15 – Linear PDEs
• Lec 16 – FFT Method
  • Supplement – Example: Transient Diffusion in Finite Domain

Unit 4 - Fluid Mechanics

• Lec 17 – Navier Stokes
• Lec 18 – Unidirectional Flows
• Lec 19 – Creeping Flow
  • Supplement – Example: Creeping flow around a sphere
• Lec 20 – Inviscid Flow
  • Supplement – Example: Potential flow around a cylinder
• Lec 21 – Boundary Layers
  • Supplement – Notes on Blasius Solution
  • Supplement – Example: Blasius Numerical Solution

Unit 5 - Convective Heat Transfer

• Forced Convection in Laminar Confined Flow and the Graetz Problem
  • Supplement – Notes on Graetz Problem
  • Supplement – Example: Graetz Problem Plot

Other Resources

• Qualifier Review
• Link to Videos and Notes from Fall 2020
• Link to Notes from Winter 2024
• National Committee for Fluid Mechanics Films. These are awesome videos made in the 1960s for teaching fluid mechanics.
• Notes from ME 505 (Applied Engineering Math)
  • Finite Fourier Transforms