• Journal of applied mathematics & informatics
• /
• v.40 no.1_2
• /
• pp.25-45
• /
• 2022

In this study, the non-standard finite difference method for the numerical solution of singularly perturbed parabolic reaction-diffusion subject to Robin boundary conditions has presented. To discretize temporal and spatial variables, we use the implicit Euler and non-standard finite difference method on a uniform mesh, respectively. We proved that the proposed scheme shows uniform convergence in time with first-order and in space with second-order irrespective of the perturbation parameter. We compute three numerical examples to confirm the theoretical findings.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2008.04a
• /
• pp.501-504
• /
• 2008

A concrete carbonation model has been constructed that takes account of the diffusion of carbon dioxide through a coating and reaction with calcium hydroxide, and this model has been validated by an accelerated carbonation experiment. (1) By using values for the coatings calculated on the basis of a diffusion.permeation theory as input data for the analysis of diffusion.reaction carbonation in an unsteady state, the effect of the coatings in reducing carbonation can be represented with high accuracy. (2) Through a sensitivity analysis of the diffusion.reaction carbonation model and the experimental results, we found that the diffusion coefficient of calcium hydroxide shows a high interrelationship at 1e-12($m^2/s$). The reaction rate constant for carbonation shows a high interrelationship at 5e-5($m^3/mol/s$).

• Nuclear Engineering and Technology
• /
• v.47 no.5
• /
• pp.588-595
• /
• 2015

This study presents an effective method for additional recovery of residual actinides in liquid electrodes after the electrowinning process of pyroprocessing. The major distinctive feature of this method is a reactor with multiple reaction cells separated by partition walls in order to improve the recovery yield, thereby using the interelement difference in diffusion coefficients within the liquid electrode and controlling the selectivity and purity of element recovery. Through an example of numerical simulation of the diffusion scenarios of individual elements, we verified that the proposed method could effectively separate the actinides (U and Pu) and rare-earth elements contained in liquid cadmium. We performed a five-step consecutive recovery process using a simplified conceptual reaction cell and recovered 58% of the initial amount of actinides (U + Pu) in high purity (${\geq}99%$).

• Journal of the Korean Society of Safety
• /
• v.8 no.2
• /
• pp.3-9
• /
• 1993

For comparison, we used Ca and Mg as reducers to produce TiFe hydrogen stroage alloy from Fe and TiO$_2$by the Reduction-Diffusion process. The results obtained were as follow. \circled1 Ca was found to be effective both for reduction and diffusion processes. Moreover, Ca oxide was easily removed in an NH$_4$Cl solution after the reaction. \circled2 In the case of using Ca as a reducer, the Reduction-Diffusion process is considered to take place in the foiling three steps. First, TiO$_2$is reduced to Ti by Ca over 100$0^{\circ}C$. Second, the atomic Ti drifts in the Ca melt and meets Fe particles. Finally, the atomic Ti diffuses in to the Fe particles. \circled3 In the case of using Mg as a reducer, We found that the reduction reaction of TiO$_2$went well. But the reduced Ti scarcely diffused into Fe particles. This was probably because no Mg melt was formed due to the high vapor pressure of Mg.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.21 no.9
• /
• pp.1174-1184
• /
• 1997

Extinction characteristics of pure hydrogen-oxygen diffusion flames, at high pressures in the neighborhood of the critical pressure of oxygen, is numerically studied by employing counterflow diffusion flame as a model flame let in turbulent flames in rocket engines. The numerical results show that extinction strain rate increases almost linearly with pressure up to 100 atm, which can be explained by comparison of the chain-branching-reaction rate with the recombination-reaction rate. Since contributions of the chain-branching reactions, two-body reactions, are found to be much greater than those of the recombination reactions, three-body reactions, extinction is controlled by two-body reactions, thereby resulting in the linearity of extinction strain rate to pressure. Therefore, it is found that the chemical kinetic behaviors don't change up to 100 atm. Consideration of the pressure fall-off reactions shows a slight increase in extinction strain rate, but does not modify its linearity to pressure. The reduced kinetic mechanisms, which were verified at low pressures, are found to be still valid at high pressures and show good qualitative agreement in prediction of extinction strain rates. Effect of real gas is negligible on chemical kinetic behaviors of the flames.

• Korean Journal of Materials Research
• /
• v.28 no.7
• /
• pp.428-434
• /
• 2018

Hydrogen evolution on a steel surface and subsequent hydrogen diffusion into the steel matrix are evaluated using an electrochemical permeation test with no applied cathodic current on the hydrogen charging side. In particular, cyclic operation in the permeation test is also conducted to clarify the corrosion-induced hydrogen evolution behavior. In contrast to the conventional perception that the cathodic reduction reaction on the steel in neutral aqueous environments is an oxygen reduction reaction, this study demonstrates that atomic hydrogen may be generated on the steel surface by the corrosion reaction, even in a neutral environment. Although a much lower permeation current density and significant slower diffusion kinetics of hydrogen are observed compared to the results measured in acidic environments, they contribute to the increase in the embrittlement index. This study suggests that the research on hydrogen embrittlement in ultra-strong steels should be approached from the viewpoint of corrosion reactions on the steel surface and subsequent hydrogen evolution/diffusion behavior.

• Proceedings of the International Microelectronics And Packaging Society Conference
• /
• 2001.11a
• /
• pp.134-137
• /
• 2001

The cure kinetics of a cycloalipatic epoxy / anhydride / Co(II) system for a no-flow underfill encapsulant, has been studied by using a differential scanning calorimetry(DSC) under isothermal and dynamic conditions over the temperature range of $160^{\circ}C ~220^{\circ}C$. The kinetic analysis was carried out by fitting dynamic/isothermal heating experimental data to the kinetic expressions to determine the reaction parameters, such as order of reaction and reaction constants. Diffusion-controlled reaction has been observed as the cure conversion increases and successfully analyzed by incorporating the diffusion control term into the rate equation. The prediction of reaction rates by the model equation corresponded well to experimental data at all temperature.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2001.11b
• /
• pp.332-336
• /
• 2001

In this study, the reaction at UBM(Under Bump Metallurgy) and solder interface was investigated. The UBM employed in conventional optical packages, Au/Pt/Ti layer, were found to dissolve into molten Au-Sn eutectic solder during reflow soldering. Therefore, the reaction with different diffusion barrier layer such as Fe, Co, Ni were investigated to replace the conventional Pt layer. The reaction behavior was investigated by reflowing the solder on the pad of the metals defined by Cr layer for 1, 2, 3, 4, and 5 minutes at $330^{\circ}C$. Among the metals, Co was found to be most suitable for the diffusion barrier layer as the wettability with the solder was reasonable and the reaction rate of intermetallic formation at the interface is relatively slow.

• Journal of Powder Materials
• /
• v.4 no.3
• /
• pp.196-204
• /
• 1997

Joining of AIN ceramics to W and Cu by active-metal brazing method was tried with use of (Ag-Cu)-Ti alloy as insert-metal. Joints were produced under various conditions of temperature, holding time and Ti-content in (Ag-Cu) alloy Reaction and microstructural development in bonded interface were investigated through observation and analysis by SEM/EDS, EPMA and XRD. Joint strengths were measured by shear test. Bonded interface consists of two layers: an insert-metal layer of eutectic Ag- and Cu-rich phases and a reaction layer of TiN. Thickness of reaction layer increases with bonding temperature, holding time and Ti-content of insert-metal. It was confirmed that the growth of reaction layer is a diffusion-controlled process. Activation energy for this process was 260 KJ/mol which is lower than that for N diffusion in TiN. Maximum shear strength of 108 MPa and 72 MPa were obtained for AIN/W and AIN/Cu joints, respectively. Relationship between processing variables, joint strength and thickness of reaction layer was also explained.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2001.11a
• /
• pp.332-336
• /
• 2001

In this study, the reaction at UBM(Under Bump Metallurgy) and solder interface was investigated. The UBM employed in conventional optical packages, Au/Pt/Ti layer, were found to dissolve into molten Au-Sn eutectic solder during reflow soldering. Therefore, the reaction with different diffusion barrier layer such as Fe, Co, Ni were investigated to replace the conventional R layer. The reaction behavior was investigated by reflowing the solder on the pad of the metals defined by Cr layer for 1, 2, 3, 4, and 5 minutes at 330$^{\circ}C$. Among the metals, Co was found to be most suitable for the diffusion barrier layer as the wettability with the solder was reasonable and the reaction rate of intermetallic formation at the interface is relatively slow.