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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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Thermomechanical interaction between outer ice shells and deep oceans on icy moons of Jupiter and Saturn
Malík, Jiří ; Souček, Ondřej (advisor) ; Tůma, Karel (referee)
The thesis contains a survey of numerical tools for studying thermomechanical interactions of a two-phase system contained in a domain with an upper bound- ary that forms a free surface. The enthalpy diffused-interface formulation is used for an approximation of the phase change interface and the computing algorithm is benchmarked against an analytical solution of the Stefan problem. Arbitrary Lagrangian-Eulerian kinematical description of the continuum is applied to over- come the difficulty in the form of the free surface. The validity of the approach is examined on a thermal convection benchmark problem. 1
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Deformation and thermal evolution of the ice shell on Enceladus
Kvorka, Jakub ; Čadek, Ondřej (advisor) ; Souček, Ondřej (referee)
In the last two decades, successful space missions to Jupiter and Saturn provi- ded important data bearing information about topography and internal structure of icy bodies in the outer Solar System. Some of these bodies contain subsurface reservoirs of liquid water in contact with an outer shell made of solid ice. One of the possibilities how to explain the observed topography of a moon is to use its thermal production as the energy source that produces deformation of the ice crust covering the body. In this study, we develop a simplified mathematical mo- del of thermal-mechanical evolution of the ice crust including the effect of phase transition at its bottom boundary. The appropriate system of partial differential equations is coded in Fortran95 and used to study the surface features developed in response to heat flux anomalies imposed on the top of the subsurface ocean. The results obtained for Enceladus, Europa and Titan show that the observed topography of these moons can be explained only for a large grain size and the ice crust behaving elastically near the upper boundary. 1
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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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