Search result: Catalogue data in Autumn Semester 2020

Mathematics Master Information
Application Area
Only necessary and eligible for the Master degree in Applied Mathematics.
One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area.
Material Modelling and Simulation
327-1201-00LTransport Phenomena IW5 credits4GJ. Vermant
AbstractPhenomenological approach to "Transport Phenomena" based on balance equations supplemented by thermodynamic considerations to formulate the undetermined fluxes in the local species mass, momentum, and energy balance equations; Solutions of a few selected problems relevant to materials science and engineering.
ObjectiveThe teaching goals of this course are on five different levels:
(1) Deep understanding of fundamentals: local balance equations, constitutive equations for fluxes, entropy balance, interfaces, idea of dimensionless numbers and scaling, ...
(2) Ability to use the fundamental concepts in applications
(3) Insight into the role of boundary conditions
(4) Knowledge of a number of applications.
(5) Flavor of numerical techniques: finite elements and finite differences.
ContentPart 1 Approach to Transport Phenomena
Diffusion Equation
Refreshing Topics in Equilibrium Thermodynamics
Balance Equations
Forces and Fluxes
1. Measuring Transport Coefficients
2. Pressure-Driven Flows and Heat exchange
Lecture notesThe course is based on the book D. C. Venerus and H. C. Öttinger, A Modern Course in Transport Phenomena (Cambridge University Press, 2018) and slides are presented
Literature1. D. C. Venerus and H. C. Öttinger, A Modern Course in Transport Phenomena (Cambridge University Press, 2018)
2. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd Ed. (Wiley, 2001)
3. L.G. Leal, Advanced Transport Phenomena (Oxford University Press, 2011)
4. W. M. Deen, Analysis of Transport Phenomena (Oxford University Press, 1998)
5. R. B. Bird, Five Decades of Transport Phenomena (Review Article), AIChE J. 50 (2004) 273-287
Prerequisites / NoticeComplex numbers. Vector analysis (integrability; Gauss' divergence theorem). Laplace and Fourier transforms. Ordinary differential equations (basic ideas). Linear algebra (matrices; functions of matrices; eigenvectors and eigenvalues; eigenfunctions). Probability theory (Gaussian distributions; Poisson distributions; averages; moments; variances; random variables). Numerical mathematics (integration). Equilibrium thermodynamics (Gibbs' fundamental equation; thermodynamic potentials; Legendre transforms). Maxwell equations. Programming and simulation techniques (Matlab, Monte Carlo simulations).
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