Fuel Cell Exergy Losses of Activation Energy and Cathode Polarizaztion

Abstract

This article investigates thermochemical irreversibilities of activation energy and concentration polarization in fuel cells. The predictive formulation uses the Butler-Volmer equation for the activation overpotential and it includes both Knudsen and self-diffusion for the concentration polarization. Entropy production of activation energy occurs due to a portion of cell voltage lost in driving the chemical reaction to transfer electrons to/from the electrode. In this article, exergy losses associated with these activation and concentration irreversibilities are formulated based on the Second Law. Unlike past studies of entropy production in solid oxide fuel cells, this article extends past methods to half-cell reactions and thermochemical irreversiblities in a proton-exchange membrane fuel cell. Voltage losses are derived based on entropy production within the fuel cell, in contrast to past methods involving polarization curves. The entropy-based method provides a useful alternative to past conventional methods, because it can encompass both electrochemical irreversibilities (such as electrode polarization) and thermofluid irreversibilities (such as fuel channel friction). NomenclatureFaraday's constant, 96,785 C/mol G = Gibbs free energy, J i = current density, A/m 2 J = flux, mol/s K = equilibrium constant l = thickness, m M = molar masṡ m = mass flow rate, kg/s N = number of moles per mole H 2 n d = electro-osmotic drag coefficient n e = moles of electrons per half-cell reaction P = pressure, Pȧ P s = entropy production rate, W/mol K Q = heat transfer rate, W R = universal gas constant, 8.314 J/mol K s = molar entropy, J/mol K T = temperature, K v = specific volume, m 3 /kġ W = power, W X dest = exergy destruction rate, W/mol β = transfer coefficient γ = stoichiometric ratio η = polarization, V ρ = density, kg/m 3 a, c = anode, cathode eff = effective fc = fuel cell H 2 = hydrogen H 2 O = water vapor m = membrane/electrolyte O 2 = oxygen P, R = products, reactants 0 = exchange Superscripts I = inlet conditions rev = reversible