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Simulation of a Lithium-Ion Battery
Published in Yoshiaki Kato, Zenpachi Ogumi, José Manuel Perlado Martín, Lithium-Ion Batteries, 2019
Takumi Yanagawa, Hitoshi Sakagami, Kunioki Mima
where k is the reaction rate constant, cs is the lithium-ion concentration in the active particle, and cs,max is the maximum concentration of lithium ions allowed to be stored in the active particle. In the case of considering a more complex chemical reaction model than the Butler-Volmer model, you may modify Eq. 6.38 with the estimated flux given by the new complex model. The lithium-ion flux obtained by the above process is the amount of lithium ions intercalated into/de-intercalated from the active particle, namely () ∂∂t∫VcsdV=∫Sjsz+FdS,
Parabolic Equations: Time‐Dependent Diffusion Problems
Published in Saad A. Ragab, Hassan E. Fayed, Introduction to Finite Element Analysis for Engineers, 2018
Saad A. Ragab, Hassan E. Fayed
Pennes’ thermal model has many applications in bioheat. Torvi and Dale [47] used the 1D model to investigate skin thermal injuries of first‐, second‐, and third‐degree burns due to exposure to flash fire. Henriques’ thermal injury model [18], which is an Arrhenius‐type chemical reaction model, is used to determine the degree of damage. Torvi and Dale modeled the skin tissue by a three‐layer model of different thermophysical properties for each layer: the epidermis, dermis, and the subcutaneous region. Galerkin’s weighted‐residual (strong form) finite‐element method is used in space and Crank‐Nicholson is used for time integration. Johnson et al. [21] also investigated thermal injuries of a skin exposed to hot water. They modeled the skin by a four‐layer tissue: the epidermis, dermis, the subcutaneous layer, and muscle. They used a second‐order finite‐difference method in space and an explicit first‐order method in time.
Modeling Exposure
Published in Samuel C. Morris, Cancer Risk Assessment, 2020
The first order chemical reaction model is stated as: C=C0 exp[−kt]orC=C0 exp[−t/T]
Two-Dimensional Numerical Simulation of Detonation Transition with Multi-Step Reaction Model: Effects of Obstacle Height
Published in Combustion Science and Technology, 2019
Ayu Ago, Nobuyuki Tsuboi, Edyta Dzieminska, A. Koichi Hayashi
Observation of DDT is performed in short time and small space, and the reproducibility of DDT process so is low that observation by visualization is difficult. Therefore, the profound detailed of the mechanisms are not well understood. The problem remains in numerical analysis of DDT as well. Calculation cost increases due to the high resolution needed to correctly resolve phenomena such as combustion wave, local explosion, and shock wave interference. There is also another problem with satisfying the grid resolution sufficiently. In addition, most researchers use a one-step model as a chemical reaction model but not that many detailed reaction model called here a multi-step chemical reaction model. Comparing the detailed model with the simplified model, it is reported that analysis by a simplified model may quantitatively lead to erroneous results (Ivanov et al., 2011) because detailed chemical reaction model includes correct elementary reactions. There is also different view on the DDT mechanism, as the chemical reaction model used is different. The conclusion about the DDT mechanism by Gamezo et al, who investigated DDT using a single-step Arrhenius kinetics was that: “The accelerating flow generates strong shocks that reflect from obstacles and eventually create hot spots that produce detonations through Zeldovich’s gradient mechanism” (Gamezo et al., 2008). The opposite conclusion was drawn by Liberman et al. (2011, 2012). They showed that DDT is occurring by the mechanism of a positive feedback and mutual amplification of the reaction front and the shock wave in DDT simulation using multi-step reaction model.
Toward the long-term aging influence and novel reaction kinetics models of bitumen
Published in International Journal of Pavement Engineering, 2022
Shisong Ren, Xueyan Liu, Peng Lin, Ruxin Jing, Sandra Erkens
The two-steps consecutive reaction model is adopted to quantitatively describe the aging reaction kinetics of bitumen for the first time. During the aging of bitumen, the aromatic fraction would convert to the resin fraction, which further changes into the asphaltene components. There are different complex chemical reaction models with several-steps reactions, including the chain reaction, opposing reaction, parallel reaction as well as the consecutive reaction (Guo and Lua 2001, Tjahjono et al. 2009, Leroy et al. 2013). By definition, during the consecutive reaction model, there are at least two-steps reactions, in which the reactant in the next reaction is the product of the previous step.
Reactivity of CO/H2/CH4/Air Mixtures Derived from In-Cylinder Fuel Reformation Examined by a Micro Flow Reactor with a Controlled Temperature Profile
Published in Combustion Science and Technology, 2021
Yuki Murakami, Hisashi Nakamura, Takuya Tezuka, Go Asai, Kaoru Maruta
In the present study, the effects of composition changes in CO/H2/CH4 mixtures on the reactivity are evaluated based on weak flame responses in MFR. Specifically, the ratios of H2 and CH4 are varied widely at a constant fraction of CO. Details of the mixture conditions investigated in this study are discussed later. Experimental measurements are compared to computational predictions using several detailed chemical reaction models. A further chemical reaction analysis is then conducted to investigate chemical mechanism behind a trend observed in the experiments.