• Korean Chemical Engineering Research
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• 제57권5호
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• pp.652-665
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• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• Journal of applied mathematics & informatics
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• 제41권4호
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• pp.893-906
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• 2023

In this article, we are devoted to study the problem of the existence, uniqueness and positivity of the global solutions of the 3 × 3 reaction-diffusion systems with the total mass of the components with time. We also suppose that the nonlinear reaction term has a critical growth with respect to the gradient. The technique that we used to prove the global existence is the method of the compact semigroup.

• Nuclear Engineering and Technology
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• 제53권3호
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• pp.833-841
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• 2021

During the postulated severe accident of nuclear reactor, eutectic reaction leads to low-temperature melting of fuel cladding and early failure of core structure. In order to model eutectic melting with the moving particle semi-implicit (MPS) method, the eutectic reaction model is developed to simulate the eutectic reaction phenomenon. The coupling of mass diffusion and phase diagram is applied to calculate the eutectic reaction with the uniform temperature. A heat transfer formula is proposed based on the phase diagram to handle the heat release or absorption during the process of eutectic reaction, and it can combine with mass diffusion and phase diagram to describe the eutectic reaction with temperature variation. The heat transfer formula is verified by the one-dimensional melting simulations and the predicted interface position agrees well with the theoretical solution. In order to verify the eutectic reaction models, the eutectic reaction of uranium and iron in two semi-infinite domains is simulated, and the profile of solid thickness decrease over time follows the parabolic law. The modified MPS method is applied to calculate Transient Reactor Test Facility (TREAT) experiment, the penetration rate in the simulations are agreeable with the experiment results. In addition, a hypothetical case based on the TREAT experiment is also conducted to validate the eutectic reaction with temperature variation, the results present continuity with the simulations of TREAT experiment. Thus the improved method is proved to be capable of simulating the eutectic reaction in the severe accident.

• Bulletin of the Korean Chemical Society
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• 제35권10호
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• pp.3089-3091
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• 2014

• Bulletin of the Korean Chemical Society
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• 제34권5호
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• pp.1454-1456
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• 2013

The fluctuations in concentrations of reactants dominate the long-time dynamics of the single (A + A ${\rightarrow}$ 0) and two species (A + B ${\rightarrow}$ 0) diffusion-influenced annihilation reactions. Although hierarchical Smoluchowski approaches can provide a systematic and flexible framework to deal with the fluctuation effects, their results are too complicated to be analytically solved. For the efficient numerical calculation of the complicated fluctuation effect terms, we show that the presented point particle approximation is not only practical but also quite accurate for most conditions in diffusion-influenced reaction systems.

• International Journal of Concrete Structures and Materials
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• 제6권3호
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• pp.155-163
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• 2012

In order to predict the neutralization of concrete which is the reaction of carbonation dioxide from the outside and cement hydration product, such as calcium hydroxide and C-S-H, it was studied the numerical analysis method considering change of the pore structure and relative humidity during the neutralization reaction. Diffusion-reaction neutralization model was developed to predict the neutralization depth of concrete with coating finishing material. In order to build numerical analysis models considering outdoor environment and finishing materials, the adaption of proposed model was shown the results of existing outdoor exposure test results and accelerated carbonation test.

• 한국세라믹학회지
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• 제24권5호
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• pp.484-490
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• 1987

Diffusion coupling experiment was done to study expansion of body and soild reaction in BaCO3-TiO2 system. Specimen of BaCO3 and TiO2 was formed with Pt-mark's method. Each specimen was fired at interval of 25℃ from 900℃ to 1000℃ for 2hrs. After that, specimen was fixed with resin and polished. Product layers of specimen were observed with SEM and EDS. The result were following; 1. Diffusion component is Ba2+, which diffuse toward TiO2. 2. Large crack between layer of BaCO3 and Ba2TiO4 was generated because of difference of thermal expansion coefficient. 3. Ba2TiO4 is formed to TiO2 body by the reaction of BaTiO3 and BaO and its structure is very porous. 4. BaTiO3 changes immediately to Ba2TiO4 by the reaction of BaO. But BaTiO3 which formed by the reaction of TiO2 and Ba2TiO4 exsists as layer because the diffusion distance of Ba2+ is far.

• Journal of Advanced Marine Engineering and Technology
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• 제30권1호
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• pp.140-149
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• 2006

Characteristics of a laminar diffusion flame placed near wall in microgravity have been numerically analyzed in a two-dimension. The fuel for the flame is $C_2H_4$. The flame is initiated by imposing a high temperature ignition source. The flow field, temperature field, and flame shape in microgravity diffusion flame are detailed. Especially, effects of surrounding air velocity and fuel injection velocity on the microgravity diffusion flame have been discussed accounting for standoff distance. And, the effect of curvature rate has been also studied. The results showed that velocities in a diffusion flame were overshoot because of volumetric expansion and distribution of temperature showed regularity by free-buoyancy This means that the diffusion flame in microgravity is very stable, while the flame in normal gravity is not regular and unstable due to buoyancy. Standoff distance decreases with increase in surrounding air velocity and with decrease in fuel injection velocity. With increasing curvature rate, the position of reaction rate moves away the wall.

• Journal of Welding and Joining
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• 제15권3호
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• pp.128-135
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• 1997

Reaction diffusion and formation of $Ni_3Al$phase with $L1_2$ structure have been studied in temperature range of 1432K to 1573K using the diffusion couple of (Ni-40, 5at%Al)/(Ni-14, 1at%Al) and (Ni-49, 2at%Al)/ (Nickel). The layer growth of Ni$_{3}$Al pyhase in the annealed diffusion couple was measured by optical microscope and electron probe microanalyzer (EPMA). The layer growth of $Ni_3Al$phase in diffusion zone obeyed the parabolic law without any indication of grain boundary effects. The layer growth of $Ni_3Al$phase in temperature range of 1423K to 1573K was mainly controlled by the volume diffusion mechanism. The rate of layer growth of $Ni_3Al$phase was found to be colsely related to the composition of intermetallic compound NiAl phase. The activation energy for layer growth of $Ni_3Al$phase was calculated to be 127kJ/mol.

• 한국연소학회지
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• 제7권3호
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• pp.9-15
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• 2002

Soot generation by combustion process has been investigated with objective of understanding of chemical reaction responsible for its formation in a coaxial laminar propane jet diffusion flame. For the direct photos, as the coflowing air flow rate is reduced, the area of soot luminous zone increases at first, then becomes smaller and smaller, and even disappears. The aspects of soot deposition can be acquired by using nine $15{\mu}m$ thin SiC fibers are positioned horizontally across the flame. Deposited soots on SiC fibers show the soot inception point and growth and soot oxidation zone in a typical propane diffusion. Soot is not generated anymore in a oxidizer deficient conditions of near-extinction and flame is fully occupied by transparent blue flame. It suggests that nonsooting pyroligneous blue reaction is being dominant in a oxidizer deficient ambience. In comparison with luminosities of SiC fibers and flame itself, indirect evidence is found that the process of soot nucleation and growth is endothermic reaction. It is remarkable that there exists two adjacent regions to have antithesis characteristics; one is exothermic reaction of blue flame and another endothermic reaction zone of soot formation.