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Abstract: In this paper, a three-dimensional (3D), nonisothermal, multiphysics, two-phase steady state transport model and its efficient numerical methods are systematically studied for a full proton exchange membrane fuel cell (PEMFC) in the sense of efficiency and accuracy. The conservation equations of mass, momentum, species, charge and energy are fully addressed in view of nonisothermality and multiphase characteristics. In addition, from an accurate numerical discretization’s point of view, we present some new formulations for species equations by investigating the interactions among the species. In a framework of the combined finite element-upwind finite volume method, some efficient numerical methods are developed in terms of Kirchhoff transformation for the sake of a fast and convergent numerical simulation. The 3D simulations demonstrate that the convergent solutions can be attained within 80 nonlinear iterations, in contrast to the oscillating and nonconvergent iterations conducted by commercial flow solvers or in-house code with standard finite element/volume methods. Numerical convergence tests are carried out to verify the efficiency and accuracy of our numerical algorithms and techniques. [Copyright &y& Elsevier]