A Simple Thermal Model of Pem Fuel Cell Stacks

A simple model is developed that determines the temperature distribution through a unit fuel cell with straight flow channels, in steady state operation. Using the large aspect ratio of the typical fuel cell geometry, the thermal model approximately decouples cross-plane thermal transport at each channel location. Using the fact that in-plane thermal conductivities are much larger than through-plane in typical bipolar plate construction, it is possible to further approximate the cross-plane thermal transport with a simple, one-dimensional model. We then consider the thermal coupling of several unit cells connected in series. In this way, we can simulate the effect of an anomalously hot cell in a stack environment. We take as inputs to the model the cell voltage and local current density, membrane resistance and condensation rates from a previously developed model. The thermal model outputs the average coolant temperature and the temperature distribution through the bipolar plates and membrane electrode assembly at each location down the channel. Although we are aware that there are significant coupling effects between the thermal distribution and performance, this is not taken into account in this study. INTRODUCTION A Polymer Electrolyte Membrane Fuel Cell is an electrochemical device in which the energy of the chemical reaction is converted directly into electricity. By combining hydrogen fuel with oxygen from air, electricity is formed without combustion of any form. Water and heat are the only by products when hydrogen is used as the fuel source. Further details of general fuel cell operation can be found in Larminie and Dicks (2003). Computational modeling of fuel cell operation has been seen as a way to perform design optimization more efficiently than by experimental testing in certain situations, just has been undertaken for other technologies, most notably in Aeronautics. Early models of unit cell performance were developed by Springer et al. (1991) and others. A modern version of this kind of low-dimensional averaged model was recently developed by our group (Berg et al., 2004). Recent three-dimensional computational models have been developed (Berning et al, 2001; Dutta et al. 2001; Mazumder and Cole, 2003; and Natarajan and Van Nguyen, 2003). These are 3-D finite volume computational tools that describe the coupled mass transport and electrochemistry in unit cells. The next few years hold the promise of robust, commercially available threedimensional and transient unit cell codes capable of describing many aspects of fuel cell operation. A few authors (Nguyen and White, 1993; Djilali and Lu, 2002) have concentrated specifically on computational models of heat transfer in fuel cells. However, there have been few attempts to model the effects of cell-to-cell coupling in a stack environment. In this paper, we develop simple models for the temperature distribution in a unit cell with straight flow channels, in steady state operation. These simple models are then extended to the stack environment. Some preliminary computations show how excess heat from a center hot cell spreads to neighboring cells. The results are of interest in design since temperature increases of even a few degrees at the membrane can lead to thermal runaway: higher temperatures leading to dryer membranes which have lower conductivity and so further increase temperature. However, the coupling of temperature profiles to performance in this way has not yet been done. A further limitation of this study is that at this time, experimental results to validate and fit the model are not yet available. THE SINGLE CELL MODEL Our approach is to begin with computational output from our unit cell code (Berg et al., 2004). This code assumes a linear coolant temperature profile between given inlet and outlet coolant temperatures. It also assumes the temperature is locally constant through the MEA. With these assumptions it computes performance (local current and water crossover) based on given operating conditions. This output can be used to predict a nonlinear temperature profile in the cell using the models described below. This can be considered as one step of an iterative procedure. The following data is used from the unit cell computational model: local current density ; cell voltage V ; cathode condensation rate ) (y i ) (y Γ ; and membrane area-specific resistivity . Here is the down-channel coordinate from cathode inlet ) (y R y ) 0 ( = y to outlet . The cell length is =0.67m. The other coordinates are through-MEA (membrane electrode assembly) and cross-channel ) ( c L y = c L z x . The condensation rate is computed using a difference approximation of