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Course, academic year 2018/2019
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Thermodynamics and Mechanics of Non-Newtonian Fluids - NMMO402
Title in English: Termodynamika a mechanika nenewtonovských tekutin
Guaranteed by: Mathematical Institute of Charles University (32-MUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Note: enabled for web enrollment
Guarantor: RNDr. Karel Tůma, Ph.D.
Class: M Mgr. MOD
M Mgr. MOD > Povinné
Classification: Mathematics > Differential Equations, Potential Theory
Incompatibility : NDIR057
Interchangeability : NDIR057
Annotation -
Last update: T_MUUK (14.05.2013)
Description of non-Newtonian phenomena and explanation how to model these phenomena within the complete thermomechanical framework using the concept as natural configuration, maximization of rate of entropy production, implicit constitutive theory. Basic mathematical insights on equations describing steady and unsteady flows of Newtonian and non-Newtonian incompressible fluids will be also given.
Aim of the course -
Last update: T_MUUK (14.05.2013)

The course aims to describe basic phenomena that cannot be captured by Newtonian (Navier-Stokes) fluids and then to provide a derivation of models that have the ability of capturing these phenomena.

Course completion requirements -
Last update: RNDr. Karel Tůma, Ph.D. (11.06.2019)

Credit must be received before the exam. Credit is obtained for successfully solved homeworks. The exam consists of a written test and an oral part.

Literature - Czech
Last update: T_MUUK (14.05.2013)

[1] W. R. Schowalter: Mechanics of Non-Newtonian Fluids, Pergamon Press (Oxford), 1978.

[2] R. R. Huilgol: Continuum mechnaics of viscoelastic liquids, Hindusthan Publishing Co. (Delhi), 1975.

[3] J. Malek, K. R. Rajagopal: Mathematical issues concerning the Navier-Stokes equations and some of its generalizations, Handbook of Differential Equations, Evolutionary Equations, Vol. 2 (eds. C. Dafermos and E. Feireisl),

Elsevier, 2005, 371-459.

Teaching methods -
Last update: T_MUUK (14.05.2013)

Lecture course

Requirements to the exam -
Last update: RNDr. Karel Tůma, Ph.D. (22.02.2019)

You can enroll for the exam only if you already got credits for the tutorials.

The exam consists of the test and the oral part. The test will contain four examples corresponding to the syllabus of the lecture and examples trained at the tutorial. The requirements to the oral part of the exam correspond to the syllabus of the lecture in the range presented in the lecture.

Syllabus -
Last update: RNDr. Karel Tůma, Ph.D. (22.02.2019)

The lecture course, offerred only in the winter semesters, is scheduled for two years. In the even calendar year, we focus on modeling of the non-Newtonian phenomena in the full thermomechanical framework. In the odd year, we analyze selected models within the modern theories on nonlinear partial differential equations.

The key topics: foundation of continuum fluid mechanics and thermodynamics (what is a fluid, incompressibility, inhomogeneity, duitable description, balance equations); Newtonian (Navier-Stokes) fluids, description of non-Newtonian phenomena (shear-thinning/shear-thickenning, pressure-thichening, stress relaxation, nonlinear creep, normal stress differences, jump discontinuities in stress)accompanied by sample models that can capture these non-Newtonian features and by several important materials (biological fluids, granular materials, mixtures) that exhibit such non-Newtonian behavior; derivation of an hierarchy of models within an unified thermomechanical setting - from the Navier-Stokes equations upto the equations for viscoelastic materials; various types of boundary conditions; a link between the principle physical concepts and mathematical analysis of relevant models.

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