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Non-Newtonian Fluid Mechanics - NDIR057

Title:	Mechanika nenewtonovských tekutin
Guaranteed by:	Mathematical Institute of Charles University (32-MUUK)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Note:	you can enroll for the course repeatedly enabled for web enrollment

Guarantor:	prof. RNDr. Josef Málek, CSc., DSc.
Class:	DS, matematická analýza
Classification:	Mathematics > Differential Equations, Potential Theory
Interchangeability :	NMMO402
Is incompatible with:	NMMO402
Is interchangeable with:	NMMO402

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: JOSEF/MFF.CUNI.CZ (06.05.2008)

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: JOSEF/MFF.CUNI.CZ (06.05.2008)

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.

Literature - Czech

Last update: Prof. PhDr. Alan Josef, CSc. (23.05.2006)

[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: JOSEF/MFF.CUNI.CZ (06.05.2008)

Lecture course

Syllabus -

Last update: Prof. PhDr. Alan Josef, CSc. (23.05.2006)

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.