The Boltzmann Transport Equation (BTE) for phonons best describes the heat flow in solid nonmetallic thin films. The BTE, in its most general form, however, is difficult to solve analytically or even numerically using deterministic approaches. Past research has enabled its solution by neglecting important effects such as dispersion and interactions between the longitudinal and transverse polarizations of phonon propagation. In this article, a comprehensive Monte Carlo solution technique of the BTE is presented. The method accounts for dual polarizations of phonon propagation, and non-linear dispersion relationships. Scattering by various mechanisms is treated individually. Transition between the two polarization branches, and creation and destruction of phonons due to scattering is taken into account. The code has been verified and evaluated by close examination of its ability or failure to capture various regimes of phonon transport ranging from diffusive to the ballistic limit. Validation results show close agreement with experimental data for silicon thin films with and without doping. Simulation results show that above 100 K, transverse acoustic phonons are the primary carriers of energy in silicon.

In this part of the paper, we present a model to treat formation and transport of liquid water in proton exchange membrane ͑PEM͒ fuel cells ͑FCs͒ in three-dimensional ͑3-D͒ geometry. The performance of modern-day PEM FCs at high current density are largely dictated by the effective management of liquid water. In the first part of this paper, a rigorous model was presented to model PEM FCs using a computational fluid dynamic technique. It was found that under the assumption of no liquid water formation, the model consistently overpredicted measured polarization behavior. In the model presented here, the phase change process is modeled as an equilibrium process, while the transport of liquid water is governed by pressure, surface tension, gravity and electro-osmotic drag. Results show that the inclusion of liquid water transport greatly enhances the predictive capability of the model and is necessary to match experimental data at high current density.Despite several studies on water management in proton exchange membrane ͑PEM͒ fuel cells ͑FCs͒ within the past decade, effective water management has remained elusive. This is partly due to the fact that once liquid water is formed, it is transported within the membrane-electrode-assembly ͑MEA͒ by several co-existing and comparable forces, and therefore, it is extremely difficult to control its motion. The other complication results from the conflict that while liquid water is necessary to maintain high electrical conductivity of the membrane, excessive water can result in clogging of the electrodes. In particular, in a hydrogen-air PEM FC operating at high loads, water is generated at the cathode due to electrochemical reactions, and significant condensation and clogging can occur within the cathode if the liquid water is not managed properly. Thus, it is neither desirable to remove water completely, nor is it desirable to have it in excessive amounts, and this poses a design challenge. The best scenario is to have liquid water in optimum amounts in certain regions of the MEA only, and this is almost impossible to achieve. One can only hope to alleviate the problem by understanding how much water is produced, where it finally resides within the cell, and what effects it has on the performance of the cell. Part of the role of modeling and simulation is to answer these questions.Modeling of liquid water formation and transport has been a topic of intense debate and discussion in the past five years. While such modeling can be extremely useful in understanding some of the aforementioned issues, the models available today are by no means predictive in the truest sense of the word. In this paper, we carefully explore the various ''gray areas'' associated with liquid water formation and transport that make the modeling difficult, and point out their repercussions in the prediction of performance of the FC.Several examples of mathematical modeling of water transport in PEM FCs can be found in the literature. The earliest models 1-3 were semi-empirical in nature, and attempte...

This article presents a rigorous mathematical model to predict performance of proton exchange membrane ͑PEM͒ fuel cells ͑FCs͒ of arbitrary three-dimensional ͑3-D͒ geometry. Mathematical modeling of FCs is necessary in order to understand the precise effect of operating conditions and material properties on the performance of fuel cells. The model is based on solution of the conservation equations of mass, momentum, energy, species, and electric current in a fully integrated finite-volume solver. Simulations are performed in 2-D and 3-D geometries assuming that water stays in its vapor phase and that no liquid water is formed. Results are compared against experimental data under various operating conditions, and show that 3-D modeling is key to predicting performance of PEM FCs at high current densities.

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The Monte Carlo method has found prolific use in the solution of the Boltzmann transport equation for phonons for the prediction of nonequilibrium heat conduction in crystalline thin films. This paper contributes to the state-of-the-art by performing a systematic study of the role of the various phonon modes on thermal conductivity predictions, in particular, optical phonons. A procedure to calculate three-phonon scattering time-scales with the inclusion of optical phonons is described and implemented. The roles of various phonon modes are assessed. It is found that transverse acoustic (TA) phonons are the primary carriers of energy at low temperatures. At high temperatures (T>200 K), longitudinal acoustic (LA) phonons carry more energy than TA phonons. When optical phonons are included, there is a significant change in the amount of energy carried by various phonons modes, especially at room temperature, where optical modes are found to carry about 25% of the energy at steady state in silicon thin films. Most importantly, it is found that inclusion of optical phonons results in better match with experimental observations for silicon thin-film thermal conductivity. The inclusion of optical phonons is found to decrease the thermal conductivity at intermediate temperatures (50–200 K) and to increase it at high temperature (>200 K), especially when the film is thin. The effect of number of stochastic samples, the dimensionality of the computational domain (two-dimensional versus three-dimensional), and the lateral (in-plane) dimension of the film on the statistical accuracy and computational efficiency is systematically studied and elucidated for all temperatures.

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