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A Stefan problem of heat conduction with phase change and its exact solution
Kesler, René ; Mauder, Tomáš (referee) ; Klimeš, Lubomír (advisor)
This bachelor's thesis deals with analytical solutions of heat conduction problems with phase change which are known as classical Stefan problems. At the beginning a differential equation of heat conduction is derived and a mathematical model of Stefan problem is formed. The greatest attention is paid to the derivation of analytical solutions for cases in which these solutions are obtainable. The MATLAB environment was chosen for implementation of the obtained solutions. The thesis also includes a description of the program and its graphical interface in MATLAB. The applicability of the program is demonstrated in several phase change problems.
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The usage of Salome Meca workbench for task solution in the field of solid mechanics
Nytra, Michal ; Návrat, Tomáš (referee) ; Vosynek, Petr (advisor)
Submitted bachelors thesis deals with solution of tasks of body mechanics in open-source workbench Salome Meca and FEM solver Code_Aster. In the beginning is short theoretical introduction to finite element method a basic theory to strength of materials. Then follows series of tasks, which will test solver and workbench. We will compare results with analytical solution (if exists), eventually with available commerical software Ansys. There are 3 static structural tasks (beams, axisymetric bodies). Next task is from dynamics, searching of natural frequencies and vibration of plate during harmonic excitation. The last one is steady-state-thermal combined with static structural. In the conclusion are summarized advantages and disadvantages of open-source softwares. Results of workbench Salome Meca vary from analytical solution maximal to 10 %, what is in engineering praxis suffcient accuracy.
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FLow in cracs
Ocásek, Adam ; Veselý, Jindřich (referee) ; Haluza, Miloslav (advisor)
This Master’s thesis investigates the flow in sealing gaps of impeller within pumps and turbines. Sealing gaps are installed to improve the volumetric efficiency in this type of fluid machinery. Despite present extensive research this subject has not been entirely documented and the thesis’ aim is to improve our knowledge in this matter. At the beginning, the practical experiment is used in order to establish appropriate numerical description of flow in seals and to calibrate software FLUENT. In chapter five, the thesis analyses the influence of seal design on volumetric efficiency of pumps and turbines and defines its optimal construction to improve the efficiency. The thesis then examines the effect of rotor eccentricity on flow properties, flow rate and pressure distribution within the sealing gap. In the last section, through chapters six to eight, the flow results provided by numerical solution in FLUENT and selected analytical equations, or their modified forms, are being discussed. The degree of correspondence between the results is also studied.
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Comparision of methods for nonlinear dynamic sytems solution
Krejčí, Jaroslav ; Lošák, Petr (referee) ; Dušek, Daniel (advisor)
The aim of this work is to make a solution of nonlinear dynamic system with one degree of freedom using various approximate analytical methods and perform their comparison. The beginning of the work describes the basic characteristics of nonlinear dynamic systems, methods of modelling and a description of the basic analytical methods of solution. In the following part is the solution of the system using described methods and comparing of results. In conclusion the methods are compared with final element method by program ANSYS.
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Modelling of dynamics systems with multi degrees of freedom
Ondra, Václav ; Donát, Martin (referee) ; Dušek, Daniel (advisor)
The aim of this work is for a dynamic system with multiple degrees of freedom to assemble and solve the equations of motion. In the beginning of work are summarized the basic knowledge about the dynamic oscillating systems, their distribution, method of mathematical description etc. In the following part of work are for the given set of particles assembled equations using Lagrange equations of the second kind. The solution of equation is made in mathematical system MAPLE for frequency domain. To determine the position of particles in time was used MATLAB. Research results are graphs of amplitude and frequency characteristics and graph of positions of particles in time. There is discussion on the influence of systems parameters on oscillation. The conclusion is a comparison of analytical solution with the solution of finale elements conclusion in ANSYS.
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