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

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 (Tⁱⁿ), inlet water saturation (sⁱⁿ), inlet relative humidity (RH), porous medium hydrophobicity and cathode overpotential (η). The inclusion of heat transfer is found to limit the range of values of η,Tⁱⁿ 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.