
Thermodynamic analysis of solid oxide cells
Vágner, Petr ; Maršík, František (advisor) ; Grmela, Miroslav (referee) ; Pekař, Miloslav (referee)
Thermodynamic analysis of solid oxide cells Petr Vágner The thesis deals with continuum thermodynamic modeling and analysis of phe nomena in solid oxide electrochemical cells. A general description of the evo lution of charged mixtures using partial mass densities, momentum density, entropy density, electric induction, magnetic field, polarization, and magnetiza tion based on the GENERIC framework is formulated. The formulation is used to recover the LandauLifshitz magnetization relaxation model, the Single Re laxation Time model for dielectrics, and the generalized PoissonNernstPlanck model. The latter model is consequently linked to the second part, where a novel double layer model of an yttriastabilized zirconia interface is formulated within nonequilibrium thermodynamics. The model is solved for numerically in the time domain, and cyclic voltammetry of the system is analyzed. The last part of the thesis demonstrates the limits of Exergy Analysis on a simple solid oxide hydrogen fuel cell model with nonisothermal boundary. It is demon strated that the minimization of entropy production does not necessarily lead to the maximization of the electric power for certain optimization scenarios. The thesis consists of a compilation of published and unpublished results of the author.


Mathematical analysis of bone and vascular remodelling model
Matajová, Adéla ; Maršík, František (advisor) ; Souček, Ondřej (referee)
Bone is a tissue that is constantly being renewed during the whole life. This complex biological process, controling among others adaptation to environ mental loads, is called bone remodelling. It is due to this complexity that the process hasn't been fully biomechanically described yet. However, sev eral mathematical models of bone remodelling have been conjectured, one of which we will introduce and analyze in this thesis. The model describes bone metabolism by five chemical equations. Using the biothermodynamical laws we will derive from these equations a system of ordinary differential equations. Then we will effectuate a qualitative analysis, while focusing on existence, uniqueness and stability of a stationary solution. Finally the im pact of the mechanical loading on bone remodelling will be outlined.We will also mention the relation with vascular remodelling. 1


Numerical modelling of unstable fluid flow past heated bodies
Pech, Jan ; Maršík, František (advisor) ; Feistauer, Miloslav (referee) ; Rohan, Eduard (referee)
Title: Numerical modeling of unstable fluid flow past heated bodies Author: Jan Pech Department: Mathematical Institute of Charles University Supervisor: prof. Ing. František Maršík, DrSc., Mathematical Institute of Charles University Abstract: Presented work brings new results to numerical computations of flow influenced by temperature changes. Constructed numerical algorithm takes into account variable coefficients of the differential operators in the system of in compressible NavierStokes equations coupled with thermal heat equation. The spatial discretisation of the problem targets to application of high order method, the spectral element method. Phenomenons connected with high order approxi mations are discussed on a number of examples and comparisons with methods of lower order, which are more common. Results were achieved for two fluids with opposite response to heating, air and water. The observed quantity is par ticularly a frequency of vortex shedding, the Strouhal number, as dependent on temperature and Reynolds number. The calculated values were compared with experimental results and exhibit a good coincidence. Numerical analysis of sep aration angle in flow around heated circular cylinder may give a new impulse to verification of accuracy and reliability of the developed method. Keywords:...


Optimization of operation of renewable electric energy sources based on fuel cells, accumulators and FV panels for small powers.
Holeček, Martin ; Maršík, František (advisor) ; Beran, Zdeněk (referee)
The first part of the research is motivated to provide citations deeper to the literature of optimal control principles that could be linked to the system optimization problem, discuss these principles and various ways to apply them. Then we describe one fuel cell, accumulator and photovoltaic standalone system along with the most used equations from the literature. Next, we formulate the problem of optimal control for this system to optimize the system financial cost in the best case and we process to describe and discuss the numerical optimal control algorithm  multiple shooting  that will be used to solve the problem, that was not used in literature so far in conjunction with the problem. The codes and numerical simulations are also provided. Powered by TCPDF (www.tcpdf.org)


Numerical modelling of unstable fluid flow past heated bodies
Pech, Jan ; Maršík, František (advisor)
Title: Numerical modeling of unstable fluid flow past heated bodies Author: Jan Pech Department: Mathematical Institute of Charles University Supervisor: prof. Ing. František Maršík, DrSc., Mathematical Institute of Charles University Abstract: Presented work brings new results to numerical computations of flow influenced by temperature changes. Constructed numerical algorithm takes into account variable coefficients of the differential operators in the system of in compressible NavierStokes equations coupled with thermal heat equation. The spatial discretisation of the problem targets to application of high order method, the spectral element method. Phenomenons connected with high order approxi mations are discussed on a number of examples and comparisons with methods of lower order, which are more common. Results were achieved for two fluids with opposite response to heating, air and water. The observed quantity is par ticularly a frequency of vortex shedding, the Strouhal number, as dependent on temperature and Reynolds number. The calculated values were compared with experimental results and exhibit a good coincidence. Numerical analysis of sep aration angle in flow around heated circular cylinder may give a new impulse to verification of accuracy and reliability of the developed method. Keywords:...


Physical analysis of the main processes in the solid oxide fuel cells and their mathematical description
Vágner, Petr ; Maršík, František (advisor) ; Souček, Ondřej (referee)
Solid oxide fuel cells (SOFC) are mainly used as large stationary elec tricity sources, therefore an every little improvement in their performance leads to considerable savings. In order to understand the fundamentals of the SOFC operation, we have developed a new model describing the main physical processes. The thermodynamical model of SOFC, developed in this thesis, concerns the gas transport, the transport of the charged particles in cluding the thermoelectric effect and the electrochemical reactions. Linear irreversible thermodynamics is the key modelling framework, in which the dusty gas model and the ButlerVolmer equations are used. A new relation between the electrochemical affinity and the overpotential is introduced into the ButlerVolmer equation. A weakly formulated statinonary system en dowed with boundary conditions is solved with the finite element method in one dimensional approximation. 1


Relation between forces induced by fluid flow and dissipative processes in boundary layers
Mináriková, Petra ; Maršík, František (advisor) ; Lanzendörfer, Martin (referee)
Práce se zabývá vlivem disipativních proces· v mezních vrstvách, konkrétně vlivem viskozity tekutiny a dále vlivem difúze vodní páry ve vzduchu na vznik sil p·sobících na obtékaná tělesa. Z Croccovy věty plyne, že gradient entropie má sv·j podíl na vzniku cirkulace a d·sledkem toho i na vznik vztlakové síly. Práce zkoumá vznik vztlakové síly při obtékání rotujícího válce, v soft waru FEniCS modeluje tuto situaci, porovnává s modelem nevazké nestlačitelné tekutiny a následně i s experimentem provedeným Ing. Zdeňkem Trávníčkem a Ing. Zuzanou Broučkovou. Taktéž zkoumá vznik vztlakové síly při vypařování na horní straně válce a srovnává s případem rotujícího válce. 1


Biomechanical aspects of the dynamics of intracranial pressure in traumatic brain injury
Mayer, Martin ; Jelen, Karel (advisor) ; Maršík, František (referee) ; Pokorný, Jan (referee)
Title: Biomechanical aspects of the dynamics of intracranial pressure in traumatic brain injury Author: Ing. Martin Mayer email: mayercz@seznam.cz Department: Department of Anatomy and Biomechanics Supervisor: doc. PaedDr. Karel Jelen, CSc. This PhD thesis "Biomechanical aspects of the dynamics of intracranial pressure in traumatic brain injury" is about the dynamics of intracranial pressure, particularly in relation to the external mechanical action of the patient. Severe head injury is the leading cause of death in patients under 35 years of age. Despite constantlyimproving medical and nursing care only one third of patients, after recovery, regained the ability to live independently in the long term. Twothirds of patients were severely disabled or died. The lifetime cost of such a patient who was not completely cured has been calculated to be $4,000,000. A significant consequence of craniocerebral injuries are secondary brain lesions, which among other means the rise in intracranial pressure (ICP), which can further exacerbate due to intracerebral or extracerebral causes. Therefore, the objective of the treatment is minimizing secondary injury, optimally at the phase of the primary lesion. However, realization of this requirement, about which we can say that is a conditio sine qua non, sometimes leads...


Thermodynamic analysis of processes in Hydrogen fuel cells.
Pavelka, Michal ; Maršík, František (advisor) ; Grmela, Miroslav (referee) ; Sciacovelli, Adriano (referee)
Nonequilibrium thermodynamics, which serves as a framework for formulating evolution equations of macroscopic and mesoscopic systems, is briefly reviewed and further developed in this work. For example, the relation between the General Equation for the Nonequilibrium Reversible Irreversible Coupling (GENERIC) and (ir)reversibility is elucidated, and OnsagerCasimir reciprocal relations are shown to be an implication of GENERIC. Nonequilibrium thermodynamics is then applied to describe fuel cells and related devices, and theoretical conclusions are compared to experimental data. Moreover, a generalization of standard exergy analysis is developed bringing a new method for revealing a map of useful work losses in electricity producing devices. This method requires a nonequilibrium thermodynamic model, and so the general theory of non equilibrium thermodynamics and optimization of real power generating devices stand side by side.


Modeling of phase transformations in shape memory materials
Frost, Miroslav ; Maršík, František (advisor) ; Rohan, Eduard (referee) ; Seiner, Hanuš (referee)
Title: Modeling of phase transformations in shape memory materials Author: Miroslav Frost Department: Mathematical Institute of Charles University Supervisor: Prof. Ing. František Maršík, DrSc., Mathematical Institute of Charles University Abstract: This thesis presents a new thermomechanical threedimensional con stitutive model of NiTibased shape memory alloys. The model was formulated within the framework of generalised standard models and it features a novel form of the dissipation function, which combines contributions stemming from the phase transformation between austenite and martensite and from the reorienta tion of martensite. The change in the material response associated with the phase transformation between austenite and Rphase as well as material anisotropy and tensioncompression asymmetry are also covered. The timeevolutionary problem of a quasistatic mechanical loading of a NiTi body with prescribed temperature evolution was formulated and analyzed within the framework of energetic so lutions. The corresponding timeincremental minimization problem provided a conceptual algorithm utilized in the numerical treatment. The constitutive mod el was implemented into the finite element package Abaqus. Several numerical simulations were performed and compared with experiments. Keywords:...
