PurposeThe aim of this paper is to investigate performance improvements of a monolithic solid oxide fuel cell geometry through an entropy generation analysis.Design/methodology/approachThe analysis of entropy generation rates makes it possible to identify the phenomena that cause the main irreversibilities in the fuel cell, to understand their causes and to propose changes in the design and operation of the system. The various contributions to entropy generation are analyzed separately in order to identify which geometrical parameters should be considered as the independent variables in the optimization procedure. The local entropy generation rates are obtained through 3D numerical calculations, which account for the heat, mass, momentum, species and current transport. The system is then optimized in order to minimize the overall entropy generation and increase efficiency.FindingsIn the optimized geometry, the power density is increased by about 10 per cent compared to typical designs. In addition, a 20 per cent reduction in the fuel cell volume can be achieved with less than a 1 per cent reduction in the power density with respect to the optimal design.Research limitations/implicationsThe physical model is based on a simple composition of the reactants, which also implies that no chemical reactions (water gas shift, methane steam reforming, etc.) take place in the fuel cell. Nevertheless, the entire procedure could be applied in the case of different gas compositions.Practical implicationsEntropy generation analysis allows one to identify the geometrical parameters that are expected to play important roles in the optimization process and thus to reduce the free independent variables that have to be considered. This information may also be used for design improvement purposes.Originality/valueIn this paper, entropy generation analysis is used for a multi‐physics problem that involves various irreversible terms, with the double use of this physical quantity: as a guide to select the most relevant design geometrical quantities to be modified and as objective function to be minimized in the optimization process.