TY - JOUR

T1 - Reviewing the mathematical validity of a fuel cell cathode model. Existence of weak bounded solution

AU - Al-arydah, Mo'tassem

AU - Carraro, Thomas

N1 - Funding Information:
TC was supported by the German Research Council (DFG) , Germany through project CA 633/2-1 . We acknowledge support by the state of Baden-Württemberg through bwHPC , Germany and the German Research Foundation (DFG) , Germany through grant INST 35/1134-1 FUGG .
Publisher Copyright:
© 2018 Elsevier Ltd

PY - 2019/3/15

Y1 - 2019/3/15

N2 - 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.

AB - 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.

KW - Fuel cell cathode

KW - System of PDEs

KW - Weak solution

UR - http://www.scopus.com/inward/record.url?scp=85054124733&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2018.08.001

DO - 10.1016/j.camwa.2018.08.001

M3 - Article

AN - SCOPUS:85054124733

SN - 0898-1221

VL - 77

SP - 1425

EP - 1436

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 6

ER -