The provided article comprehensively explores the modelling and analysis of solid oxide fuel cell (SOFC) systems within the context of thermodynamic energy cycles. The paper provides insight into various applications of these cells, with a specific emphasis on their role as the primary source of electrical energy in systems that work with biogas and heat recovery. The technological structure of these systems is delineated, with a focus on their principal components and the chemical reactions occurring within SOFCs. Moreover, the article incorporates a mathematical model of SOFCs and presents calculation results that illustrate the influence of air and fuel temperature on the cells’ efficiency. The research indicates that optimal SOFC efficiency is attained at higher temperatures of supplied air and fuel. The presentation of the results of calculations for the solid oxide fuel cell and its thermodynamic cycle, considering fuel supply and its thermodynamic parameters under both steady-state and transient conditions, is the main aim of the article.

The present paper describes a cycle, which may be applied in sewage treatment plants as a system to convert biological waste into process heat and electricity. In sludge stabilization processes anaerobic fermentation acts as the source of methane, which can be used then to generate heat and electric current in gas turbines. Products of high-temperature oxidation can be utilized in organic Rankine cycles to generate electric power. Waste heat is used for heating the fermenting biomass. Energy balance equations mentioned in the thesis: organic Rankine cycle, regenerative gas turbine engine, anaerobic sludge stabilization system.

This study elucidates the technologies employed in membranebased water purification processes. The theoretical underpinnings of semipermeable membrane functionalities are expounded upon through the lens of Onsager’s reciprocal relations in non-equilibrium thermodynamics, delineating the fluxes and the driving forces that instigate them. Utilising a simplified Onsager matrix tailored for the ion-exchange membrane electrodialysis process, computational fluid dynamics (CFD) simulations were conducted. The computations presented herein depict the intricacies of both dialysis and electrodialysis in saline water solutions.

The paper presents the calculations for the failure conditions of the ORC (organic Rankine cycle) cycle in the electrical power system. It analyses the possible reasons of breakdown, such as the electrical power loss or the automatic safety valve failure. The micro-CHP (combined heat and power) system should have maintenance-free configuration, which means that the user does not have to be acquainted with all the details of the ORC system operation. However, the system should always be equipped with the safety control systems allowing for the immediate turn off of the ORC cycle in case of any failure. In case of emergency, the control system should take over the safety tasks and protect the micro-CHP system from damaging. Although, the control systems are able to respond quickly to the CHP system equipped with the inertial systems, the negative effects of failure are unavoidable and always remain for some time. Moreover, the paper presents the results of calculations determining the inertia for the micro-CHP system of the circulating ORC pump, heat removal pump (cooling condenser) and the heat supply pump in failure conditions.