*(María García Camprubí, July 2011)*

This thesis presents a comprehensive mathematical model that describes the performance of a hydrogen-fed, self-supported solid-oxide fuel-cell, and the corresponding numerical method to solve the model. The latter has been implemented using an open-source CFD-toolbox, OpenFOAM. The validity of the resulting numerical tool has been shown by comparison of its results with experimental data taken from the literature, and its applicability has been illustrated in a further numerical analysis.

**Mathematical model**

A comprehensive multiphysics model has been developed, describing the operating principle of a single hydrogen-fed self supported solid-oxide fuel-cell. The model considers:

1 - Momentum conservation of gases in channels and porous media.

2 - Multicomponent mass transport through channels and porous media.

3 - Conjugate heat transfer within the fuel cell components considering every heat transfer mechanisms, ie convection, conduction and radiation.

4 - Electrochemical reaction.

5 - Charge transport.

**Numerical method**

The numerical solution of the mathematical model describing the operation of a solid-oxide cell is addressed by developing an in-house algorithm solvable in OpenFOAM (version: OpenFOAM-1.5-dev). OpenFOAM (Open Field Operation and Manipulation) is a free, open source CFD software package that uses ﬁnite volume numerics to solve systems of partial diﬀerential equations ascribed on any 3D unstructured mesh of polyhedral cells. The main features of this numerical method are:

1 - The numerical domain is split into ﬁve adjacent numerical subdomains, that facilitate the solution of the proper model in each of the SOFC layers; namely: (1) the fuel channel; (2) the anode; (3) the electrolyte; (4) the cathode; and (5) the air channel. This implies that the numerical solution is calculated in ﬁve separate numerical meshes.

2 - The spatial multidomain nature of this solution procedure requires of an algorithm to exchange information between adjacent subdomains. The subdomain coupling is done, in this work, either by mapping ﬁeld between adjacent subdomains or by using a coupled solver.

3 - The numerical algorithm can be run in parallel.

**Validation and application**

The validity of the numerical tool has been veriﬁed by comparing the numerical results with experimental data for a hydrogen-fed anode-supported solid oxide fuel cell, taken from the literature. The numerical tool has been further used to characterize in detail the mass-transfer process within the porous media, as well as to investigate the suitability of some common assumptions made in other SOFC modelling works.

**Open source code contribution**

Parts of this numerical algorithm, viz those subroutines embodying species mass-transfer within the channels and electrodes, have been included in an open-source mass-transfer library that has been published in the Computer Physics Communications Program Library (http://cpc.cs.qub.ac.uk/).

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