A Compact Thermal Resistance Model for Determining Effective Thermal Conductivity in the Fibrous Gas Diffusion Layers of Fuel Cells

Accurate information on the temperature eld and associated heat transfer rates are particularly important in devising appropriate heat and water management strategies in proton exchange membrane (PEM) fuel cells. An important parameter in fuel cell performance analysis is the effective thermal conductivity of the gas diffusion layer (GDL). Estimation of the effective thermal conductivity is complicated because of the random nature of the GDL micro structure. In the present study, a compact analytical model for evaluating the effective thermal conductivity of brous GDLs is developed. The model accounts for the salient geometric features, effects of bipolar pressure variation, gas rarefaction effects, and spreading resistance. The model predictions are in good agreement with existing experimental data over a wide range of porosities. Parametric studies are performed using the proposed model to investigate the effect of bipolar plate pressure, aspect ratio, ber diameter, ber angle, and operating temperature. NOMENCLATURE A = area, m2 a;b = major and minor semi axes of elliptical contact area, m d = ber diameter, m E = Young's modulus, Pa E 0 = effective elastic modulus, Pa F = contact load, N F1 = integral function of (ρ0=ρ00), Eq. (8) GDL = gas diffusion layer K( ) = complete elliptic integral of the rst kind k = thermal conductivity,W=mK ke f f = effective thermal conductivity,W=mK PhD Candidate. Corresponding author. E-mail: [email protected]. †Assistant Professor and Mem. ASME ‡Professor ke f f0 = effective thermal conductivity of the reference basic cell,W=mK k = non-dimensional effective thermal conductivity, ke f f =ke f f0 l = distance between two adjacent bers in x-direction (Fig. 3), m PBP = bipolar pressure, Pa Pg = gas pressure, Pa PGDL = GDL pressure, Pa Pr = Prandtl number, [ ] Qgc = heat transfer rate through gas lled gap,W R = thermal resistance, K=W Rco = thermal constriction resistance, K=W Rsp = thermal spreading resistance, K=W T = temperature, K Vs = ber (solid) volume of basic cell, m3 Vtot = total volume of basic cell, m3 w = distance between two adjacent bers in the y-direction (Fig. 3), m Greek α = thermal accommodation parameter, [ ] β = uid property parameter, Eq. (17) δ(x) = local gap thickness, m ε = porosity, [ ] η = modulus of elliptic integral, [ ] γ = heat capacity ratio, [ ] Λ = mean free path of gas molecules, m λ = ratio of relative radii of curvature (ρ0=ρ00), [ ] μ = ratio of molecular weights of the gas and the solid (Mg=Ms), [ ] θ = angle between two bers, rad ρ0;ρ00 = major and minor relative radii of curvature, m ρ1;ρ 0 2 = principal radii of curvature, m 1 Copyright c 2008 by ASME ρe = equivalent radius of curvature of the contacting surfaces, m υ = Poisson's ratio, [ ] ξ = aspect ratio (w=l), [ ] Subscripts 0 = reference state 1 = bottom block of the basic cell 2 = top block of the basic cell ∞ = standard condition state c = contact plane g = gas gc = gas lled gap max = maximum value s = solid (carbon ber) t = upper boundary of the top block tot = total value