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Having the property to modify only the geometry of a polygonal structure, preserving its physical magnitudes, the Conformal Mapping is an exceptional tool to solve electromagnetism problems with known boundary conditions. This work aims to introduce a new developed mathematical operator, based on polynomial extrapolation. This operator has the capacity to accelerate an optimization method applied in conformal mappings, to determinate the equipotential lines, the field lines, the capacitance, and the permeance of some polygonal geometry electrical devices with an inner dielectric of permittivityε. The results obtained in this work are compared with other simulations performed by the software of finite elements method, Flux2D.

This paper presents a PEM fuel cell dynamic modeling, to be employed with electronic circuit simulator software -PSIM. Simulations of the proposed model for the fuelcell, supplying a step-up DC-DC converter are presented. Comparisons with existing models are also made. Practical results are presented in this paper for a Ballard 1.2kW Nexa Power Module for theoretical-experimental comparisons. Index Terms--Dynamic Model, Circuit simulator, Fuel cell. I. NOMENCLATURE E o cell's maximum theoretical voltage at open circuit(V) E N cell's reversible voltage no-load (V) T temperature in Kelvin (K) R universal gas constant (8314 JK/mol) F Faraday constant (96487 C) PH 2 hydrogen pressure (atm) PO 2 oxygen pressure (atm) CH 2 hydrogen concentration (mol/cm 3 ) CO 2 oxygen concentration (mol/cm 3 ) V Ω ohmic losses (A) R a equivalent activation resistance (Ω) R s membrane and electrodes resistance (Ω) R auxiliary resistance for the model (Ω) L auxiliary inductance for the model (H) C cell's equivalent capacitance (F) τ cell's time constant (s) i fuel cell's current (A) V activ activation losses (V) V conc concentration losses (V) V cell cell's output voltage (V) thickness of the membrane (m) α transference coefficient n reagent moles number n c number of cells in stack i L cell's maximum current (A).

SUMMARY The main purpose of this work is to present a methodology to calculate Carter's factor using the actual air‐gap geometry, that is, without simplifications of the slot geometry. The methodology is based on the finite element method, and its results are compared with some traditional procedures used for Carter's factor calculation and also with a domain transformation technique. It is shown that the finite element method and the domain transformation methodologies present similar results, which are different from the results obtained with traditional procedures. Copyright © 2011 John Wiley & Sons, Ltd.

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