Reviewing the mathematical validity of a fuel cell cathode model. Existence of weak bounded solution

Mo'tassem Al-arydah, Thomas Carraro

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider a system of nonlinear PDEs in a domain with a triple phase boundary, describing electrochemical processes in a mixed conduction, solid-oxide cathode of a fuel cell. It represents oxygen diffusion (with nonlinear diffusion coefficient) in the gas phase, oxygen ion diffusion in the bulk phase, electron diffusion in the electrolyte, surface exchange (nonlinear) on the interface of gas and the (mixed conduction) electrode material and finally charge transfer (nonlinear) at the interface between the electrolyte and the electrode material. We prove the validity of the model both mathematically and numerically. In fact, we prove the existence of a bounded weak solution using the Schauder fixed point theorem. We calculate the numerical solutions for given function and parameter values, and show that they correspond to theoretical results. In particular, we provide a numerical confirmation of the a priori bounds.

Original languageBritish English
Pages (from-to)1425-1436
Number of pages12
JournalComputers and Mathematics with Applications
Volume77
Issue number6
DOIs
StatePublished - 15 Mar 2019

Keywords

  • Fuel cell cathode
  • System of PDEs
  • Weak solution

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