A Simulation of the Solid Oxide Fuel Cell Electrochemical Light Off Phenomenon

During latter-stage, “start-up” heating of a solid oxide fuel cell (SOFC) stack to a desired operating temperature, heat may be generated in an accelerating manner during the establishment of electrochemical reactions. This is because a temperature rise in the stack causes an acceleration of electrochemical transport given the typical Arrhenius nature of the electrolyte conductivity. Considering a potentiostatic condition (i.e., prescribed cell potential), symbiosis thus occurs because greater current prevalently leads to greater by-product heat generation, and vice versa. This interplay of the increasing heat generation and electrochemistry is termed “light off”, and an initial model has been developed to characterize this important thermal cycling phenomenon. The results of the simulation begin elucidating the prospect of using cell potential as well as other electrochemical operating conditions (e.g., reactants utilization) as dynamic controls in managing light off transients and possibly mitigating thermal cycling issues.

Thermal Transport Network Model for High-Porosity Materials: Application to Nanoporous Aerogels

Nanoporous thin films have received attention in the microelectronics field for their application as next-generation low-k inner-layer dielectric (ILD) materials due dielectric constants approaching 1.4. In addition, emerging applications as thermal insulation for microsystems aim to exploit the materials’ unique thermal properties in sensor and component products. However, its thermal properties can vary greatly depending on fabrication processes and material morphology. In addition, a variety of transport phenomena are present and delineation among them is difficult. In this work, we examine heat transport in aerogel, one of the most common embodiments of nanoporous materials, to identify the main modes of energy transport. We employ a modified diffusion-limited cluster aggregation (DLCA) technique to simulate aerogel’s highly porous, amorphous solid structure. Network models then simulate heat transport through the structure to extract effective thermal conductivity. The models are verified by comparing calculated bulk data to published aerogel literature. Preliminary models yield thermal conductivity on the order of 0.010 W/m*K, which is consistent with published data for aerogel films. These values vary inversely with porosity of the aerogel following an inverse power law often used to fit aerogel experimental data. This methodology is most useful for examining the sensitivity of thermal conductivity to salient structural features such as porosity, pore size distribution, solid thermal properties, average branch width, and sub-continuum phenomena. The results of this study can be used as a predictive tool in optimizing aerogel fabrication process to yield morphologies that best-suit the requirements of the application.

Heat Transport Characteristics in Closed Loop Oscillating Heat Pipes

Heat transport rates of micro scale SEMOS (Self-Exciting Mode Oscillating) heat pipe with inner diameter of 1.5mm, 1.2mm and 0.9mm, were investigated by using R141b, ethanol and water as working fluids. The effects of inner diameter, liquid volume faction, and material properties of the working fluids are examined. It shows that the smaller the inner diameter, the higher the thermal transport density is. For removing high heat flux, the water is the most promising working fluid as it has the largest critical heat transfer rate and the widest operating range among the three kinds of working fluids. A one-dimensional numerical simulation is carried out to describe the heat transport characteristics and the two-phase flow behavior in the closed loop SEMOS heat pipe. The numerical prediction agrees with the experimental results fairly well, when the input heat through was not very high and the flow pattern was slug flow. This paper was also originally published as part of the Proceedings of the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems.

Constructal Theory of the Minimum Requirements for Forced Convection Cooling Solutions

The advances in microfluidics and microelectronics bring with them the need to provide new cooling solutions for many applications. A number of technologies are under development for forced convection cooling at the microscale. This short paper, through the new constructal theory of Bejan, presents the minimum velocity requirements of any such technology to be truly useful in a new design. Thus the theory presented in this paper, should form the first step in the design process of any new forced cooling technology for mini-micro scale applications. Furthermore, it is demonstrated that the use of the constructal theory provides a heightened level of understanding to the problem of forced convection, while simultaneously deriving the empirical correlations proposed in the literature over the past number of decades.

Radiative Heat Transfer During Growth of Carbon Nanotubes by Vertical Electric-Arc Process

A macroscopic finite elements model of heat transfer occurring during production of carbon nanotubes was developed. Radiation heat transfer was modeled using the Discrete Ordinates (DO) model and the Rosseland diffusion approximation. The arc is modeled as semitransparent, with the optical thickness ranging from zero to infinity. The results are compared to the limited data available. The optical thickens has a significant impact on the temperature field in (i) the arc and (ii) the anode surfaces exposed to the arc. The temperature of the cathode side-surface on which the small diameter carbon nanotube grew, is not sensitive to the optical thickness of the arc. The model indicates that the optical thickness of the arc should be high, aL ≥ 100.

Homogenization of a Conductive and Radiative Heat Transfer Problem, Simulation With CAST3M

We are interested in conductive and radiative transfer of energy in the core of gas cooled reactors. Two scales characterize the problem: macroscopic and microscopic. We want to consider the domain like an equivalent homogenous medium. So we use homogenization theory to compute the effective macroscopic properties which take into account the microscopic structure. We first present a full mathematical study of a simpler conduction problem with non linear boundary condition and its simulation with the CEA’s (French Atomic Energy Commissariat) computer code CAST3M. Then we present the homogenization of the real physical problem (including radiative boundary condition).

Use of Contact Resistance Algorithm to Implement Jump Boundary Conditions for the Radiation Diffusion Approximation

Thermal conduction codes can be used as solvers for the diffusion approximation for radiation heat transfer. Energy fluxes and temperature distributions that result from thermal radiation in an optically-thick participating medium can be estimated. Allowing dependence on temperatures from either side of the interface, a contact resistance algorithm can be used to implement “jump” (or slip) boundary conditions appropriate for the diffusion approximation in solving the radiation transfer equation. For steady, pure radiation (no conduction) systems analytical expressions exist to specify the temperature in the radiating medium at the wall as a function of the wall temperature, wall emissivity, and extinction coefficient. Radiation and conduction solutions for gray, absorbing/emitting and conducting media bound by diffuse surfaces for the simple case of the steady planar layer are considered. Reference solutions are developed by detailed zone-methods solving the coupled differential forms of both the radiation and conduction heat transfer equations. From the reference solutions, empirical relations are developed for surface resistance as functions of the local wall and adjacent media temperatures, the wall emissivity, the absorptivity, and the thermal conductivity of the medium. Performance of the approximate solution is compared to the reference solutions.

Numerical Optimization of the Thermoelectric Cooling Devices

The present study proposes the unified numerical approach to the problem of optimum design of the thermoelectric devices for cooling electronic components. The method is illustrated with several examples which are based on the standard mathematical model of a single-stage thermoelectric cooler with constant material properties. The model takes into account the thermal resistances from the hot and cold sides of the TEC. Values of the main physical parameters governing the TEC performance (Zeebeck coefficient, electrical resistance and thermal conductance) are derived from the manufacturer catalog data on the maximum achievable temperature difference, and the corresponding electric current and voltage. The independent variables for the optimization search are the number of the thermoelectric coolers, the electric current and the cold side temperature of the TEC. The additional independent variables in other cases are the number of thermoelectric couples and the height-to area ratio of the thermoelectric pellet. The objective for the optimization search is the maximum of the total cooling rate or maximum of COP. In the present study, the problems of optimum design of thermoelectric cooling devices are solved using the so-called Multistart Adaptive Random Search (MARS) method [16].

Evaporation and Nucleate Boiling of an Individual Droplet on Surfaces

A visual study was conducted to investigate the evaporation and nucleate boiling of a water droplet on heated copper, aluminum, or stainless surfaces with temperature ranging from 50°C to 112°C. Using a high-speed video imaging system, the dynamical process of the evaporation of a droplet was recoded to measure the transient variation of its diameter, height, and contact angle. When the contact temperature was lower than the saturation temperature, the evaporation was in film evaporation regime, and the evaporation could be divided into two stages. When the surface temperature was higher than the saturation temperature, the nucleate boiling was observed. The dynamical behavior of nucleation, bubble dynamics droplet were detail observed and discussed. The linear relationships of the average heat flux vs. temperature of the heated surfaces were found to hold for both the film evaporation regime and nucleate boiling regime. The different slopes indicated their heat transfer mechanism was distinct, the heat flux decreased in the nucleate boiling regime more rapidly than in the film evaporation due to the strong interaction between the bubbles.

Design and Calibration of a Novel High Temperature Heat Flux Gage

A new type of heat flux sensor (HTHFS) has been designed and constructed for applications at high temperature and high heat flux. It is constructed by connecting solid metal plates to form brass/steel thermocouple junctions in a series circuit. The thermal resistance layer of the HTHFS consists of the thermocouple materials themselves, thus improving temperature limits and lowering the temperature disruption of the sensor. The sensor can even withstand considerable erosion of the surface with little effect on the operation. A new type of convection calibration apparatus was designed and built specifically to supply a large convection heat flux. The heat flux was supplied simultaneously to both a test and standard gage by using two heated jets of air that impinged perpendicularly on the surface of each gage. The sensitivity for the HTHFS was measured to have an average value of 20 μV/(W/cm2). The uncertainty in this result was determined to be ±10% over the entire range tested. The sensitivity agrees with the theoretically calculated sensitivity for the materials and geometry used. Recommendations for future improvements in the construction and use of the sensors are discussed.