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Non-isothermal hydrophobicity-dependent two-phase flow in the porous cathode gas diffusion layer of a polymer electrolyte fuel cell

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Abstract

In this paper, we extend a recent one-dimensional isothermal steady-state generalized Darcy model for two-phase flow in the porous cathode gas diffusion layer of a polymer electrolyte fuel cell, so as to include the effect of heat transfer. As for the isothermal case, we arrive at either a fixed- or free-boundary problem, depending on the main problem parameters: inlet temperature (\(T^\mathrm{in}\)), inlet water saturation (\(s^\mathrm{in}\)), inlet relative humidity (RH), porous medium hydrophobicity and cathode overpotential (\(\eta \)). The inclusion of heat transfer is found to limit the range of values of \(\eta ,T^\mathrm{in}\) and RH over which two-phase flow can occur, as compared to that predicted by the isothermal model. The ensuing non-isothermal two-phase flow model equations are then computed numerically, with particular care being required for the treatment of an integrably singular inter-phase mass transfer term.

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Acknowledgments

The authors acknowledge the support of the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), funded by the Science Foundation Ireland (SFI) Mathematics Initiative grant 06/MI/005 and SFI grant 12/IA/1683. The first author also acknowledges the award of a visiting researcher grant within the Government of Brazil’s “ Science without Borders” programme.

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Author notes

  1. M. Vynnycky

    Present address: Division of Casting of Metals, Department of Materials Science and Engineering, Royal Institute of Technology (KTH), Brinellvägen 23, 100 44, Stockholm, Sweden

  2. A. D. Gordon

    Present address: Altigi GmbH, Theodorstrasse 42-90, Haus 9, 22761, Hamburg, Germany

Authors and Affiliations

  1. Mathematics Applications Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, Limerick, Republic of Ireland

    M. Vynnycky & A. D. Gordon

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Correspondence to M. Vynnycky.

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Vynnycky, M., Gordon, A.D. Non-isothermal hydrophobicity-dependent two-phase flow in the porous cathode gas diffusion layer of a polymer electrolyte fuel cell. J Eng Math 92, 123–146 (2015). https://doi.org/10.1007/s10665-014-9748-8

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