619-0801/01 – Transport Phenomena I (PJ I)
| Gurantor department | Department of Physical Chemistry and Theory of Technological Processes | Credits | 7 |
| Subject guarantor | doc. RNDr. Věra Dobrovská, CSc. | Subject version guarantor | doc. RNDr. Věra Dobrovská, CSc. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2005/2006 | Year of cancellation | 2014/2015 |
| Intended for the faculties | FMT | Intended for study types | Follow-up Master |
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.
Additional study materials
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
Other requirements
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction