Analysis of Transport Phenomena
Graduate-level introduction to mathematical modeling
Program Information
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About this Program
In these MOOCs, you will learn to formulate mathematical models of transport phenomena based on partial differential equations and to solve them by pencil and paper. You will also learn the art of approximation—how to obtain useful solutions by simplifying a model without sacrificing the key physics. Applications include heat and mass transfer, fluid flow, waves, hydrodynamic instabilities, convection, phase transformations and electrochemical transport.
Analysis of Transport Phenomena is a series of the following nine MOOC modules:
- 10.50.CH01x Models
- 10.50.CH02x Mathematical Formulation
- 10.50.CH03x Scaling
- 10.50.CH04x Asymptotics
- 10.50.CH05x Series Expansions
- 10.50.CH06x Fluid Mechanics
- 10.50.CH07x Convection
- 10.50.CH08x Nonequilibrium Thermodynamics
- 10.50.CH09x Electrochemical Transport
At MIT, 10.50 is a required subject for all first-year graduate students in chemical engineering, but it also attracts students from other departments. This online course is suitable for anyone interested in learning the principles of continuum modeling. Although the examples are mostly from chemical engineering, no prior knowledge is assumed, beyond basic undergraduate applied mathematics.
The engineering applications and mathematical methods you learn in this course will advance your career in industry or academics. While your friends and co-workers may be able to run an experiment or computer simulation, you will also be able to formulate models, make scaling estimates, and derive simple analytical approximations. There is growing demand for such mathematical skills in most technical careers and graduate programs today.
What you'll learn
Models:
- Formulation of continuum models
- Integral and differential forms of conservation equations
- Interfacial conservation equations
- Models of diffusion
- Random walks
Mathematical Formulation:
- Formulation of continuum models and their exact and approximate solution
- Scaling, dimensional analysis, and similarity solutions
- Perturbation methods, matched asymptotic expansions
- Fourier series, eigenfunction expansions
- Fluid dynamics, waves, capillary phenomena, and instabilities
- Forced and natural convection
- Phase transformations and electrochemical transport
Scaling:
- Dimensional analysis
- Similarity solutions for linear and nonlinear diffusion
- Green functions and the method of images
Asymptotics:
- Asymptotic analysis
- Regular and singular perturbations for algebraic and differential equations
- Matched asymptotic expansions
Series Expansions:
- Fourier series and eigenfunction expansions
- Sturm–Liouville theory
- Generalized Fourier series: Bessel functions, spherical Bessel functions, and Legendre polynomials
Fluid Mechanics:
- Unidirectional Couette and Poiseuille flows
- Lubrication approximation and the Reynolds lubrication equation
- Linear and nonlinear waves and the method of characteristics
- Tensor algebra and calculus for continuum mechanics
- Navier–Stokes equations
- Creeping flow at low Reynolds number
- Inertial flow at high Reynolds number; turbulence
- Interfacial tension, wetting, and thin films
- Linear stability analysis
Convection:
- Boundary-layer and fully developed forced convection
- Taylor dispersion
- Natural convection and combined convection
- Turbulent convection
Nonequilibrium Thermodynamics:
- Nonequilirbrium phase transformations
- Calculus of variations
- Cahn–Hilliard and Allen–Cahn equations for phase separation
Electrochemical Transport:
- Electrochemical transport in neutral electrolytes
- Equilibrium double layers and linear electrokinetics in charged electrolytes
Courses
To complete this program, you must take 9 required courses.
Required Courses
Prerequisites
- Required: multivariable calculus and ordinary differential equations
- Recommended: undergraduate-level exposure to partial differential equations, heat and mass transfer, and fluid dynamics; and modules listed on the About Pages.
Meet your instructors
Martin Bazant
Professor of Chemical Engineering & Mathematics
After a PhD in Physics at Harvard University (1997), Professor Bazant first joined the MIT faculty in Mathematics (1998) and then in Chemical Engineering (2008), where he has served as Executive Officer (2016-2020) and now as the first Digital Learning Officer. His online teaching innovations in 10.50.1x have been recognized by the MITx Prize for Teaching and Learning in MOOCs and a finalist for the Edx Prize. His research combines mathematical theory with computation and experiments in electrochemical systems, electrokinetics, and transport phenomena. His honors and awards include the 2015 Alexander Kuznetsov Prize in Theoretical Electrochemistry (ISE), the 2018 Andreas Acrivos Award for Professional Progress in Chemical Engineering (AIChE), numerous distinguished lectureships and chairs, and Fellow status in the American Physical Society, the International Electrochemical Society, and the Royal Society of Chemistry. He also consults extensively for industry and serves as the Chief Scientific Advisor for Saint Gobain North America.
