Mathematical Modeling of Direct Liquid Fuel Cells - Multidimensional Analytical Solutions and Experimental Validation

Abstract

This thesis focuses on deriving approximate analytical solutions that preserve geometric resolution for direct liquid fuel cell (DLFC) models by addressing the several nonlinearities inherent in multidimensional mechanistic DLFC models via mathematical techniques such as algebra, spatial smoothing, integration, homogenization, transformation, Taylor series expansions, scaling arguments, separation of variables, and the method of eigenfunction expansion. The results are three- and two-dimensional approximate analytical solutions that are able to predict the local transports within the cell for different types of flow distributers (porous and plain) and fuels (methanol and ethanol). We then verified the solutions with their respective full set of numerically solved equations as well as validated with experiments for which good agreements are found. We further demonstrate experimental validation for a two phase DLFC model that are based on a statistically efficient design of experiments. The derived multidimensional approximate analytical solutions are fast, reliable, and are able predict the mechanistic behaviour of the cell, thus lending themselves well to optimization, real-time control, and stack studies.