Magnetotomography and Electric Currents in a Fuel Cell

Abstract

Magnetotomography, applied to fuel cells, gives rise to several questions: first, how well can the electric current density in the fuel cell be reconstructed by measuring its external magnetic field? It is quite clear that the connection between magnetic field and current alone will lead to ambiguous results. Two further relations lead to unique reconstruction: the continuity equation and Ohm's law. Second, application of Ohm's law in the membrane electrode assembly (MEA) of a fuel cell – is it not a questionable procedure? We show that in the MEA Ohm's law is not needed, when applying a rather mild approximation, we call it the ‘thin MEA approximation'. The advantage of this is the linear relation between magnetic field and electric current density, not only in the neighbourhood of the operating point but over the whole range. Third, can a functional connection be derived between resolution of the current density and the precision requirements of the measurement devices? We present a procedure leading to a unique relation between the two. This procedure can be extended to finding the optimum measuring positions, thus essentially decreasing the number of measuring points, and thus the time scale of measurable dynamical disturbances, all this without a loss of fine resolution. We present explicit numerical results for two geometries, typical for DMFC and PEMFC fuel cells.