In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The vertical walls of the cavities are at different constant temperatures while the horizontal walls are adiabatic. Heat transfer between vertical walls occurs by laminar natural convection. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction, the local Bejan number and local entropy generation number are determined and related maps are plotted. The variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspect ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated. It is found that for a cavity with high value of Rayleigh number (i.e., Ra = 10 5 ), the total entropy generation due to fluid friction and total entropy generation number increase with increasing aspect ratio, attain a maximum and then decrease. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10 2 b Ra b 10 5 , 10 − 4 b ϕ b 10 − 2 , and Pr = 0.7.

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It is expected that fuel cells will play a significant role in a future sustainable energy system, due to their high energy efficiency and the possibility to use renewable fuels. A fully coupled CFD model (COMSOL Multiphysics) is developed to describe an intermediate temperature SOFC single cell, including governing equations for heat, mass, momentum and charge transport as well as kinetics considering the internal reforming and the electrochemical reactions. The influences of the ion and electron transport resistance within the electrodes, as well as the impact of the operating temperature and the cooling effect by the surplus of air flow, are investigated. As revealed for the standard case in this study, 90 % of the electrochemical reactions occur within 2.4 m in the cathode and 6.2 m in the anode away from the electrode/electrolyte interface. In spite of the thin electrochemical active zone, the difference to earlier models with the reactions defined at the electrodeelectrolyte interfaces is significant. It is also found that 60 % of the polarizations occur in the anode, 10 % in the electrolyte and 30 % in the cathode. It is predicted that the cell current density increases if the ionic transfer tortuosity in the electrodes is decreased, the air flow rate is decreased or the cell operating temperature is increased.

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Fuel cells are promising for future energy systems, because they are energy efficient and able to use renewable fuels. A fully coupled computational fluid dynamics (CFD) approach based on the finite element method, in twodimensions, is developed to describe a solid oxide fuel cell (SOFC). Governing equations for, gas-phase species, heat momentum, ion and electron transport are implemented and coupled to kinetics describing electrochemical and internal reforming reactions. Both carbon monoxide and hydrogen are considered as electrochemical reactants within the anode. The predicted results show that the current density distribution along the main flow direction depends on the local concentrations and temperature. A higher (local) fraction of electrochemical reactants increases the Nernst potential as well as the current density. For fuel mixtures without methane, the cathode air flow rate needs to be increased significantly to avoid high temperature gradients within the cell as well as a high outlet temperature.

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