Stack thermal coupling

In Section 9.2 below, a summary of the nomenclature used in the chapter is given. In Section 9.3, a summary of fuel cell stack geometry, and a discussion of the dimensional reductions used in the model is given. In Section 9.4, the model of 1-D MEA transport is presented, followed by Section 9.5 on the model of channel flow for a unit cell and Section 9.6 on the electrical and thermal coupling in a stack environment. In Section 9.7, a summary of the stack model is given followed by its discretization. In Section 9.8, the iterative solution strategy for the discrete system is presented, followed by sample computational results in Section 9.9. The current state of stack modeling in this framework and future directions are summarized in the final section. 

K. Promislow and B. Wetton, A Simple, Mathematical Model of Thermal Coupling in Fuel Cell Stacks, accepted in the J. Power Sources, 150,129-135. February, (2005). 

Also in 2010, a systematic approach combining experimental measurements and postmortem stack analyses coupled with numerical analyses was described by Blum et al. [26]. The results revealed that even small thermal gradients lead to stress zones within the stack, in particular in the vicinity of the manifolds. Furthermore, the stack operating in a furnace would not explicitly reflect the stack behavior operating during a real process. 

Promislow, K. and Wetton, B. (2005) A simple, mathematical model of thermal coupling in fuel cell stacks. J. Power Sources, 150, 129-135. 

So far we have considered electric phenomena in an isothermal stack or thermal phenomena in a stack element with ideally conductive bipolar plates. In reality the electric and thermal phenomena in a stack are coupled. This coupling is due to the strong (exponential) temperature dependence of the electric conductivity of various stack layers and of the half-cell exchange current densities. 

The role of thermal fluctuations for membranes interacting via arbitrary potentials, which constitutes a problem of general interest, is however still unsolved. Earlier treatments G-7 coupled the fluctuations and the interaction potential and revealed that the fluctuation pressure has a different functional dependence on the intermembrane separation than that predicted by Helfrich for rigid-wall interactions. The calculations were refined later by using variational methods.3 8 The first of them employed a symmetric functional form for the distribution of the membrane positions as the solution of a diffusion equation in an infinite well.3 However, recent Monte Carlo simulations of stacks of lipid bilayers interacting via realistic potentials indicated that the distribution of the intermembrane distances is asymmetric 9 the root-mean-square fluctuations obtained from experiment were also shown to be in disagreement with this theory.10... 

At high temperature, TTF TCNQ is metallic, with a(T) oc T-2 3 since TTF TCNQ has a fairly high coefficient of thermal expansion, a more meaningful quantity to consider is the conductivity at constant volume phonon scattering processes are dominant. A CDW starts at about 160K on the TCNQ stacks at 54 K, CDW s on different TCNQ chains couple at 49 K a CDW starts on the TTF stacks, and by 38 K a full Peierls transition is seen. At TP the TTF molecules slip by only about 0.034 A along their long molecular axis. 

Unusual magnetic and electrical properties might also arise from quasi one-dimensional crystal structures of these compounds. The acceptor stacks /especially TCNQ/ may be either regular, i, e. with equally spaced molecules, or alternating when composed of diads, triads or tetrads. In the latter case some substances exhibit EPR spectrum characteristic of mobile, thermally activated triplet states /triplet excitons/, The spectrum may result from the excitation of two or more coupled TCNQ entities /6, 7/. The triplet character of the paramagnetic excitation is shown by the anisotropic two-lines EPR spectrum which results from a zero field splitting of the triplet levels being described by the spin Hamiltonian /8/j... 

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