ASME 2008 Summer Heat transfer Conference August 10-14, 2008, Jacksonville, FL., USA HT2008-56158 A COMPACT THERMAL RESISTANCE MODEL FOR DETERMINING EFFECTIVE THERMAL CONDUCTIVITY IN THE FIBROUS GAS DIFFUSION LAYERS OF FUEL CELLS E. Sadeghi  , M. Bahrami  , and N. Djilali  Department of Mechanical Engineering, University of Victoria Victoria, BC , V8W 2Y2, Canada ABSTRACT Accurate information on the temperature eld and associ- ated heat transfer rates are particularly important in devising ap- propriate heat and water management strategies in proton ex- change membrane (PEM) fuel cells. An important parameter in fuel cell performance analysis is the effective thermal conductiv- ity of the gas diffusion layer (GDL). Estimation of the effective thermal conductivity is complicated because of the random na- ture of the GDL micro structure. In the present study, a compact analytical model for evaluating the effective thermal conductiv- ity 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 pre- dictions 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, m 2 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 F 1 = integral function of (ρ 0 =ρ 00 ), Eq. (8) GDL = gas diffusion layer K() = complete elliptic integral of the rst kind k = thermal conductivity, W =mK k eff = effective thermal conductivity, W =mK  PhD Candidate. Corresponding author. E-mail: ehsans@uvic.ca.  Assistant Professor and Mem. ASME  Professor k eff 0 = effective thermal conductivity of the reference basic cell, W =mK k  = non-dimensional effective thermal conductivity, k eff =k eff 0 l = distance between two adjacent bers in x-direction (Fig. 3), m P BP = bipolar pressure, Pa P g = gas pressure, Pa P GDL = GDL pressure, Pa Pr = Prandtl number, [] Q gc = heat transfer rate through gas lled gap, W R = thermal resistance, K=W R co = thermal constriction resistance, K=W R sp = thermal spreading resistance, K=W T = temperature, K V s = ber (solid) volume of basic cell, m 3 V tot = total volume of basic cell, m 3 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 (ρ 0 =ρ 00 ), []  = ratio of molecular weights of the gas and the solid (M g =M s ), [] θ = angle between two bers, rad ρ 0 ; ρ 00 = major and minor relative radii of curvature, m ρ 0 1 ; ρ 0 2 = principal radii of curvature, m 1 Copyright c  2008 by ASME