• International Journal of Computer Science & Network Security
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• v.22 no.6
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• pp.91-96
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• 2022

The photocatalytic degradation of salicylic acid takes place in several stages involving coupled phenomena, such as the transport of molecules and the chemical reaction. The systems of transport equations and the photocatalytic reaction are numerically solved using COMSOL Mutiphysics (CM) simulation software. CM will make it possible to couple the phenomena of flow, the transport of pollutants (salicylic acid) by convection and diffusion, and the chemical reaction to the catalytic area (bauxite or TiO2 doped by nanoparticles). The simulation of the conversion rate allows to correctly fit the experimental results. The temporal simulation shows that the reaction reaches equilibrium after a transitional stage lasting over one minute. The outcomes of the study highlight the importance of diffusion in the boundary layer and the usefulness of injecting micro-agitation into the microchannel flow. Under such conditions, salicylic acid degrades completely.

• Bulletin of the Korean Chemical Society
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• v.35 no.4
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• pp.1209-1211
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• 2014

• Journal of the Korean Ceramic Society
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• v.38 no.10
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• pp.881-885
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• 2001

Kinetics and mechanisms of intermediate phases formation in $Ba(Mg_{1/3}Ta_{2/3})O_3$, obtained by a solid state reaction were studied. $Ba{Ta_2}{O_6}$ and ${Ba_4}{Ta_2}{O_9}$ as intermediate products were first formed at $700^{\circ}C$. $Ba(Mg_{1/3}Ta_{2/3})O_3$ was appeared at $800^{\circ}C$. Several reactions take place on heating process. $Ba{Ta_2}{O_6}$ is found at the first stage of the reaction, and then $Ba{Ta_2}{O_6}$ or ${Ba_4}{Ta_2}{O_9}$ react with MgO to form $Ba(Mg_{1/3}Ta_{2/3})O_3$. The reaction of $Ba(Mg_{1/3}Ta_{2/3})O_3$ formation does not complete until fired at $1350^{\circ}C$ for 60 min. The kinetics of solid-state reaction between powdered reactants was controlled by diffusion mechanism, and can be explained by the Jander's model for three-dimensional diffusion.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.5
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• pp.1671-1678
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• 1996

In external chemical vapor deposition processes including VAD and OVD the distribution of flame-synthesized silica particles is determined by heat and mass transfer limitations to particle formation. Combustion gas flow velocities are such that the particle diffusion time scale is longer than that of gas flow convection in the zone of particle formation. The consequence of these effects is that the particles formed tend to remain along straight smooth flow stream lines. Silica particles are formed due to oxidation and hydrolysis. In the hydrolysis, the particles are formed in diffuse bands and particle formation thus requires the diffusion of SiCl$\_$4/ toward CH$\_$4//O$\_$2/ combustion zone to react with H$\_$2/O diffusing away from these same zones on the torch face. The conversion kinetics of hydrolysis is fast compared to diffusion and the rate of conversion is thus diffusion-limited. In the language of combustion, the hydrolysis occurs as a Burke-Schumann process. In selected conditions, reaction zone shape and temperature distributions predicted by the Burke-Schumann analysis are introduced and compared with experimental data available. The calculated centerline temperatures inside the reaction zone agree well with the data, but the calculated values outside the reaction zone are a little higher than the data since the analysis does not consider diffusion in the axial direction and mixing of the combustion products with ambient air. The temperatures along the radial direction agree with the data near the centerline, but gradually diverge from the data as the distance is away from the centerline. This is caused by the convection in the radial direction, which is not considered in the analysis. Spatial distribution of silica particles are affected by convection and diffusion, resulting in a Gaussian form in the radial direction.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.49-58
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• 2010

In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.517-529
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• 2009

In this paper, a singularly perturbed reaction-convection-diffusion problem with two parameters is considered. A parameter-uniform error bound for the numerical derivative is derived. The numerical method considered here is a standard finite difference scheme on piecewise-uniform Shishkin mesh, which is fitted to both boundary and initial layers. Numerical results are provided to illustrate the theoretical results.

• 한국연소학회:학술대회논문집
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• 1998.10a
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• pp.155-164
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• 1998

Numerical analysis was performed with multicomponent transport properties and detailed reaction mechanisms for axisymetric 2-D CH4 jet diffusion, partial premixed, premixed flame. Calculations were carried out twice with C2-Full Mechanism including prompt NO reaction in addition to the above C2-Thermal NO Mechanism. The role of thermal NO mechanism and prompt NO mechanism on each flame's NO production is investigated by using the numerical result. The NOx production of each flame were evaluated Quantitatively in terms of the NOx emission index

• Bulletin of the Korean Chemical Society
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• v.12 no.6
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• pp.692-698
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• 1991

The reaction path Smoluchowski equation approach developed in a recent work to calculate the rate constant for a diffusive multidimensional barrier crossing process is extended to incorporate the configuration-dependent diffusion matrix. The resulting formalism is then applied to the investigation of stilbene photoisomerization dynamics. Adapting a model two-dimensional potential and a model diffusion matrix proposed by Agmon and Kosloff [J. Phys. Chem.,91 (1987) 1988], we derive an eigenvalue equlation for the relaxation rate constant of the stilbene photoisomerization. This eigenvalue equation is solved numerically by using the finite element method. The advantages and limitations of the present method are discussed.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.753-767
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• 2024

In this paper, we developed the existence and uniqueness results by monotone method for non-linear fractional reaction-diffusion equation together with initial and boundary conditions. In this text the Hilfer fractional derivative is used to denote the time fractional derivative. The employment of monotone method generates two sequences of minimal and maximal solutions which converges to lower and upper solutions respectively.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.125-141
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• 2003

This paper treats the conditions for the existence and stability properties of stationary solutions of reaction-diffusion equations of Gierer-Meinhardt type, subject to Neumann boundary data. The domains in which diffusion takes place are of three types: a regular hexagon, a rectangle and an isosceles rectangular triangle. Considering one of the relevant features of the domains as a bifurcation parameter it will be shown that at a certain critical value a diffusion driven instability occurs and Turing bifurcation takes place: a pattern emerges.