Mathematical Model for Design of Battery Electrodes: I . Potential Distribution

1982 ◽  
Vol 129 (4) ◽  
pp. 688-695 ◽  
Author(s):  
Won G. Sunu ◽  
Brian W. Burrows
Keyword(s):  
Mathematical Model ◽  
Potential Distribution

Numerical Study on Electric Characteristics and Thermal Stresses of Solid Oxide Fuel Cells

2012 ◽  
Author(s):  
Pengfei Fan ◽  
Xiongwen Zhang ◽  
Guojun Li
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Thermal Stress ◽  
Fuel Cell ◽  
Solid Oxide Fuel Cells ◽  
Temperature Profile ◽  
Potential Distribution ◽  
Electrical Potential ◽  
Solid Oxide ◽  
Oxide Fuel

A generalized, three-dimensional (3D) mathematical model of solid oxide fuel cells (SOFCs) for various geometries is constructed in this paper. A finite-volume method is applied to calculate the electric characteristics, which is based on the fundamental conservation law of mass, energy and electrical charge. The electrical potential distribution, the current density distribution, the concentrations distribution of the chemical species and the temperature profile are calculated by solving the governing equations of a single-unit model with double channels of co-flow and counter-flow pattern using the commercial computational fluid dynamic software Fluent. The internal steam reforming and the water shift reactions are taken into account in the mathematical model. The Knudsen diffusion is considered for computation of the gases diffusion in the porous electrodes and the concentration overpotential. The Butler-Volmer equation and the function of the reaction gases composition for the exchange density are used in the model to analyze the activation overpotential. Numerical simulations are performed for a planar geometry solid oxide fuel cell and the detailed features of the temperature, the electrical potential distribution and the gases composition are illustrated. The simulation results agree well with the Benchmark results for planar configuration. With the simulated temperature profile in the planar SOFC, the finite-element method is employed to calculate the thermal stress distribution in the planar solid oxide fuel cell. A 3D finite-element model consists of positive electrode-electrolyte-negative electrode (PEN) and interconnects assembly is constructed by using commercial finite-element code Abaqus. The effects of temperature profile, electrodes and electrolyte thickness, and coefficients of thermal expansion (CTE) mismatch between components are characterized. The calculated results indicate that the maximum stress appears on the electrode and electrolyte interface. The value and distribution of the thermal stress are the functions of the applied materials CTE, applied temperature profiles and the thicknesses of electrode and electrolyte. The calculated results can be applied as the guide for the SOFC materials selection and the SOFC structure design.

scholarly journals On the weak solutions of the forward problem in EEG

2003 ◽  
Vol 2003 (12) ◽  
pp. 647-656 ◽  
Author(s):  
M. I. Troparevsky ◽  
D. Rubio
Keyword(s):  
Mathematical Model ◽  
Weak Solutions ◽  
Electric Potential ◽  
Potential Distribution ◽  
Forward Problem ◽  
Eeg Signals ◽  
The Brain

The process underlying the generation of the EEG signals can be described as a set of current sources within the brain. The potential distribution produced by these sources can be measured on the scalp and inside the brain by means of an EEG recorder. There is a well-known mathematical model that relates the electric potential in the head with the intracerebral sources. In this work, we study and prove some properties of the solutions of the model for known sources. In particular, we study the error in the potential, introduced by considering an approximated shape of the head.

Calculation of potential and concentration gradients in trickle-bed electrodes producing hydrogen peroxide

1986 ◽  
Vol 51 (9) ◽  
pp. 1883-1898 ◽  
Author(s):  
Otomar Špalek
Keyword(s):  
Mathematical Model ◽  
Hydrogen Peroxide ◽  
Current Density ◽  
Potential Distribution ◽  
Current Flow ◽  
Anode Chamber ◽  
Current Yield ◽  
Concentration Gradients ◽  
Electrolyte Flow ◽  
Trickle Bed

A mathematical model for describing the trickle-bed electrode has been developed and used to calculate the potential distribution along the current flow and the hydrogen peroxide concentration profile along the electrolyte flow (normal to the direction of current). Polarization curves and dependences of the current yield of hydrogen peroxide and the peroxide losses due to the processes occurring (reduction, decomposition, and transport into the anode chamber) on the current density have also been calculated. A comparison is made between calculated and measured dependences of the current yield of hydrogen peroxide on the current density.

The effects of surface absorbed monolayer microdiffraction patterns

1988 ◽  
Vol 46 ◽  
pp. 680-681
Author(s):  
M. Pan ◽  
J.M. Cowley
Keyword(s):  
Surface Potential ◽  
Electron Probe ◽  
Potential Distribution ◽  
Crystal Surface ◽  
Normal Direction ◽  
Surface Image ◽  
Extended Surface ◽  
Gas Molecules ◽  
Surface Nature ◽  
Electron Microdiffraction

Electron microdiffraction patterns, obtained when a small electron probe with diameter of 10-15 Å is directed to run parallel to and outside a flat crystal surface, are sensitive to the surface nature of the crystals. Dynamical diffraction calculations have shown that most of the experimental observations for a flat (100) face of a MgO crystal, such as the streaking of the central spot in the surface normal direction and (100)-type forbidden reflections etc., could be explained satisfactorily by assuming a modified image potential field outside the crystal surface. However the origin of this extended surface potential remains uncertain. A theoretical analysis by Howie et al suggests that the surface image potential should have a form different from above-mentioned image potential and also be smaller by several orders of magnitude. Nevertheless the surface potential distribution may in practice be modified in various ways, such as by the adsorption of a monolayer of gas molecules.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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