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.

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.