619-0801/01 – Transport Phenomena I (PJ I)

Gurantor departmentDepartment of Physical Chemistry and Theory of Technological ProcessesCredits7
Subject guarantordoc. RNDr. Věra Dobrovská, CSc.Subject version guarantordoc. RNDr. Věra Dobrovská, CSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Year1Semesterwinter
Study languageCzech
Year of introduction2005/2006Year of cancellation2014/2015
Intended for the facultiesFMTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
DOB40 doc. RNDr. Věra Dobrovská, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+3

Subject aims expressed by acquired skills and competences

The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to: analyze problems, suggest a method of solution, analyze correctness of achieved results with respect to given conditions, aply these methods while solving technical problems.

Teaching methods

Lectures
Individual consultations
Tutorials
Other activities

Summary

The course includes the selected chapters on tensor calculus, a field theory and the solution methods of boundary value problems for both ordinary and partial differential equations. Acquired knowledge can be used in mathematical modelling of heat, mass and momentum transfer.

Compulsory literature:

Farrashkhalvat,J.P.: Tensor methods for engineers. Publ. Ellis Horwood, New York, London 1990. Bick,T.A.: Elementary boundary value problems. Marcel Dekker, New York 1993. Carrier,G.F., Pearson,C.E.:Partial differential equations, theory and technique. Academia press, Boston 1988. Evans,L.C.: Partial differential equations. American Math. Society Providence 1998. Bird,R.B.,Stewart,W.E.,Lightfoot,E.N.: Transport phenomena. John Wiley & Sons, New York 1965.

Recommended literature:

Carrier,G.F., Pearson,C.E.:Partial differential equations, theory and technique. Academia press, Boston 1988.

Way of continuous check of knowledge in the course of semester

Course-credit -participation on tutorials is obligatory, 20% of absence can be apologized, -elaborate programs, -pass the written tests, Point classification: 5-20 points. Exam Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points. Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtains at least 5 points. Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0 National grading scheme excellent very good satisfactory failed

E-learning

Další požadavky na studenta

No other activities required.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Tensor calculus. Scalar, vector, tensor. Algebra of vectors, differential operations on vectors. 2. Cartesian tensors of second-rank. Algebra of tensors, differential operations on tensors. Tensor diagonalization. 3. Field theory. The gradient of scalar fields. Scalar potential. The divergence and rotation in vector fields. The curl theorem due to Stokes. The divergence theorem due to Gauss. 4. Orthogonal curvilinear coordinates. The gradient, divergence and curl in cylindrical and spherical systems. An application of transport phenomena: Equation of continuity. Heat and mass transfer. 5. Boundary value problems for ordinary differential equation (ODE). Formulation of boundary value problems. Boundary conditions. Second-order linear differential equations. Orthogonal system of functions. Fourier series. Homogeneous boundary problem. The eigenvalues and eigenfunctions. 6. Sturm-Liouville problem. The Bessel’s differential equation. Some method of solution of non- homogeneous boundary value problems. Method of direct integrations. Fourier method. 7. Method of variation of constants. Finite difference method. Application: Stationary heat conduction equation. Stationary, one-dimensional heat transfer in a plane sheet, cylinder and sphere. 8. Boundary value problems for partial differential equation (PDE). Linear second-order homogeneous partial differential equations and their classification. Boundary conditions, initial conditions. Formulation of boundary value problems for parabolic and elliptic equations. Some method of solutions of boundary value problem. 9. The method of separation of variables. Application: The one-dimensional heat conduction equation. Non-dimensional variables. 10. The method of combination of variables. Application: The one-dimensional diffusion equation in semi- infinite medium. 11. The method of Green’s function. Application: The one-dimensional heat conduction equation in infinite medium. 12. The difference method. Finite-difference solution: explicit method, Crank-Nicolson implicit method. Compatibility, convergence, stability. 13. Solution of the two-dimensional Laplace equation: The method of separation of variables. Finite difference method. 14. Reserve

Conditions for subject completion

Full-time form (validity from: 2012/2013 Winter semester, validity until: 2014/2015 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Exercises evaluation Credit 20 (20) 5
                Project Project 20  0
        Examination Examination 80 (80) 30
                Written examination Written examination 60  0
                Oral Oral examination 20  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2014/2015 (N3909) Process Engineering (3911T008) Chemical and Physical Methods of Material Testing P Czech Ostrava 1 Choice-compulsory study plan
2014/2015 (N3909) Process Engineering (2807T004) Chemical Engineering P Czech Ostrava 1 Compulsory study plan
2013/2014 (N3909) Process Engineering (2807T004) Chemical Engineering P Czech Ostrava 1 Compulsory study plan
2013/2014 (N3909) Process Engineering (3911T008) Chemical and Physical Methods of Material Testing P Czech Ostrava 1 Choice-compulsory study plan
2012/2013 (N3909) Process Engineering (2807T004) Chemical Engineering P Czech Ostrava 1 Compulsory study plan
2012/2013 (N3909) Process Engineering (3911T008) Chemical and Physical Methods of Material Testing P Czech Ostrava 1 Choice-compulsory study plan
2011/2012 (N3909) Process Engineering (2807T004) Chemical Engineering P Czech Ostrava 1 Compulsory study plan
2011/2012 (N3909) Process Engineering (3911T008) Chemical and Physical Methods of Material Testing P Czech Ostrava 1 Choice-compulsory study plan
2010/2011 (N3909) Process Engineering (2807T004) Chemical Engineering P Czech Ostrava 1 Compulsory study plan
2010/2011 (N3909) Process Engineering (3911T008) Chemical and Physical Methods of Material Testing P Czech Ostrava 1 Choice-compulsory study plan
2009/2010 (N3909) Process Engineering (3911T008) Chemical and Physical Methods of Material Testing P Czech Ostrava 1 Choice-compulsory study plan
2009/2010 (N3909) Process Engineering (2807T004) Chemical Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (N3909) Process Engineering (2807T004) Chemical Engineering P Czech Ostrava 1 Compulsory study plan
2008/2009 (N3909) Process Engineering (3911T008) Chemical and Physical Methods of Material Testing P Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N3909) Process Engineering (2807T004) Chemical Engineering P Czech Ostrava 1 Compulsory study plan
2007/2008 (N3909) Process Engineering (3911T008) Chemical and Physical Methods of Material Testing P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N3909) Process Engineering (2807T004) Chemical Engineering P Czech Ostrava 1 Compulsory study plan
2006/2007 (N3909) Process Engineering (3911T008) Chemical and Physical Methods of Material Testing P Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N3909) Process Engineering (2807T004) Chemical Engineering P Czech Ostrava 1 Compulsory study plan
2005/2006 (N3909) Process Engineering (3911T008) Chemical and Physical Methods of Material Testing P Czech Ostrava 1 Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner