Abstract. In this work, methods of numerical modelling of the coronary vessels system of the human heart have been studied. This investigation includes transient flow of the liquid -blood and dynamics of zones of shear stress at vessels. The main goal of the research is obtaining of hemodynamic and shear stress for creating the digital twin of coronary heart vessels. The results were obtained for low Reynolds numbers about 20 of three-dimensional laminar flow. With this Reynolds number the turbulent flow of the blood is modelled by Realizable k-ε model, and SST models to the narrowing, expansions, and blocks inside the vessels. Loads caused by the additional energy consumption because of the turbulent flow of the blood (increase in arterial blood pressure) have been analyzed. A twodimensional model of a separated vessel with fixed blood back-flow prevention is developed. Presence of a turbulent flow core is discovered. By the means of stress-strain properties of the model, visual representation of the wearing process of the blood back-flow preventer, and heart diseases progression is obtained.

Thermodynamic equilibrium analysis of the steam methane reforming process to synthesis gas was studied. For this purpose, the system of chemical reactions for carbon production and consumation as well as other side reaction in the steam methane reforming process were analysed. The material balance and the equations of law mass action were obtained for various chemical reactions. The system of those equations were solved by dichotomy method. The investigation was performed for a wide range of operational conditions such as a temperature, pressure, and inlet steam-to-methane ratio. The results obtained, with the help of developed algorithms, were compared with the results obtained via different commercial and open-source programs. All results are in excellent agreement. The operational conditions for the probable formation of carbon were determined. It was established that for the temperature range above 1100K the probability of carbon formation is absent for steam-to-methane ratio above units. The presented algorithm of thermodynamic analysis gives an appearance of the dependence of the product composition and the amount of required heat from operating conditions such as the temperature, pressure and steam-to-methane ratio.

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