• Bulletin of the Korean Chemical Society
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• v.27 no.10
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• pp.1659-1663
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• 2006

A many-body master equation is constructed by incorporating stochastic terms responsible for chemical reactions into the many-body Smoluchowski equation. Two forms of Langevin-type of memory equations describing the time evolution of dynamical variables under the influence of time-independent perturbation with an arbitrary intensity are derived. One form is convenient in obtaining the dynamics approaching the steady-state attained by the perturbation and the other in describing the fluctuation dynamics at the steady-state and consequently in obtaining the linear response of the system at the steady-state to time-dependent perturbation. In both cases, the kinetics of statistical averages of variables is found to be obtained by analyzing the dynamics of time-correlation functions of the variables.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.3
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• pp.7-20
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• 2007

We examined the steady state solution for a strongly exothermic mixtures in some class A geometries subjected to different boundary conditions under Arrhenius, Bimolecular and Sensitised reactions. The solution of the governing nonlinear reaction diffusion equation was obtained using the variational method formulation executed in Mathematica package. The paper elucidates the influence of geometry, boundary conditions and types of reaction on the thermal ignition of the reactive mixture. Apart from validating known results in literature, the solution gave further insight into the influence of material properties and conditions on the occurrence of thermal ignition.

• Journal of the Korean Ceramic Society
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• v.18 no.2
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• pp.79-82
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• 1981

SiC powder was heated in air over the temperature range of 1100-135$0^{\circ}C$. $\beta$-cristobalite was formed to cover the surfaces of SiC particles by the reaction: $SiC(s)+20_2(g)=SiO_2(s)+CO_2(g)$. It is assumed that the diffusion of oxygen ion through the formed surface layer of $\beta$-cristobalite controls the oxidation of the SiC particles. The diffusion coefficient of oxygen ion through the $\beta$-cristobalite layer was obtained as the following equation: $D=3.84{\times}10^{-17}$exp(-14.7/RT)

• Nuclear Engineering and Technology
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• v.52 no.4
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• pp.819-826
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• 2020

The method of the Laplace transform has been used to obtain an analytical solution of the three-dimensional steady state advection diffusion equation for the airborne radionuclide release from any nuclear installation such as the power reactor in an area source. The present treatment takes into account the removal of the pollutants through the nuclear reaction. We assume that the pollutants are emitted as a constant rate from the area source. This physical consideration is achieved by assuming that the vertical eddy diffusivity coefficient should be a constant. The prevailing wind speed is a constant in 𝑥- direction and a linear function of the vertical height z. The present model calculations are compared with the other models and the available data of the atmospheric dispersion experiments that were carried out in the nuclear power plant of Angra dos Reis (Brazil). The results show that the present treatment performs well as the analytical dispersion model and there is a good agreement between the values computed by our model and the observed data.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.04a
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• pp.214-217
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• 2004

The cure kinetics of blends of epoxy(tetraglycidyl-4,4'-diaminodiphenylmethane ; TGDDM)/curing agent(diaminodiphenyl sulfone ; DDS) resin with amine terminated polyetherimide-CTBN-amine terminated polyetherimide triblock copolymer(ABA) were studied using differential scanning calorimetry under isothermal conditions to determine the reaction parameters such as activation energy and reaction constants. By increasing the amount of ABA in the blends, the final cure conversion was decreased. Lower values of the final cure conversions in the epoxy/ABA blends indicated that ABA hinders the cure reaction between the epoxy and curing agents. 1be value of the reaction order, m, for the initial autocatlytic reaction was not affected by blending ABA with epoxy resin, and the value was approximately 1.0. The value of n for the nth order component in the autocatalytic analysis was increased by increasing the amount of ABA in the blends, and the value increased from 2.0-3.4. A diffusion controlled reaction was observed as the cure conversion increased and the rate equation was successfully analyzed by incorporating the diffusion control term for the epoxy/DDS/ABA blends.

• Proceedings of the Korean Vacuum Society Conference
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• 2015.08a
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• pp.190.1-190.1
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• 2015

Graphite has excellent mechanical and physical properties. It is known to advanced materials and is used to materials for molds, thermal treatment of furnace, sinter of diamond and cemented carbide tool etc. SiC materials are coated on the surface and holes of graphite to protect particles emitted from porous graphite with 5%~20% porosity and make graphite hard surface. SiC materials have high durability and thermal stability. Thermal CVD method is widely used to manufacture SiC thin films but high cost of machine investment and production are required. SiC thin films manufactured by Si reaction liquid and vapore with carbon are effective because of low cost of machine and production. SiC thin films made by vapor silicon infiltration into porous graphite can be obtained for shorter time than liquid silicon. Si materials are evaporated to the graphite surface in about $10^{-2}$ torr and high temperature. Si materials are melted in $1410^{\circ}C$. Si vapor is infiltrated into the surface hole of porous graphite and $Si_xC_y$ compound is made. $Si_x$ component is proportional to the Si vapor concentration. Si diffusion coefficient is estimated from quadratic equation obtained by Fick's second law. The steady stae is assumed. Si concentration variation for the depth from graphite surface is fitted to quadratic equation. Diffusion coefficient of Si vapor is estimated at about $10^{-8}cm^2s^{-1}$.

• Korean Journal of Food Science and Technology
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• v.27 no.3
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• pp.387-393
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• 1995

Diffusion coefficients of moisture and solid, reaction rate constants of carotene destruction, and the fitness of drying models for moisture transfer were determined to study the characteristics of mass transfer during osmotic dehydration. Moisture loss and solid gain were increased with increase of temperature and concentration; temperature had higher osmotic effect than concentration. Diffusion coefficient showed similar trend with osmotic effect. Diffusion coefficients of solids were larger than those of moisture because the movement of solid was faster than that of moisture at the high temperature. Reaction rate constants were affected to the greater extent by concentration changes than by temperature changes. Arrhenius equation was applied to determine the effect of temperature on diffusion coefficients and reaction rate constants. Moisture diffusion required high activation energy in $20^{\circ}Brix$, while relatively low in $60^{\circ}Brix$. To predict the diffusion coefficients and reaction rate constants, a model was established by using the optimum functions of temperature and concentration. The model had high $R^2$ value when applied to diffusion coefficients, but low when applied to reaction rate constants. Quadratic drying model was most fittable to express moisture transfer during drying. In conclusion, moisture content of carrots could be predictable during the osmotic dehydration process, and thereby mass transfer characteristics could be determined by predicted moisture content and diffusion coefficient.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.441-447
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• 1999

A free boundary problem is derived from a singular limit system of a reaction diffusion equation whose reaction terms are bistable type. In this paper, we shall consider a free boundary problem with two layers satisfying the zero flux boundary condition and shall show that the Hopf bifurcation can not occur as a parameter varies.

• Journal of the Korean institute of surface engineering
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• v.27 no.5
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• pp.303-311
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• 1994

In this study, the factors, such as coating temperature T(K), reaction time t(sec) and mobile carbon content $C^*$ (wt%) of steels affecting, the growth rate of carbide layer were investigated in the reactive deposition and diffusion coating using the fluidized bed. From the results, the coating thickness d(cm) can be expressed by an equation. d=$C^*$$(KT)^{1/2}$, where K=K$\circ$exp(~Q/RT), KTEX>$\circ$ = 1.4$\times$$10^{-2}cm^{-2}$/sec, and Q=46Kcal/ mol. It was in a good aggrement with the experimental results, reguardless of the diffusion coating method and the carbide layer. Therefore, if the mobile carbon content of carbon steels and alloyed steels is known, the thickness under coating conditions can be predicted from the previous equation.

• Carbon letters
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• v.9 no.2
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• pp.121-126
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• 2008

High modulus pitch based carbon fibers (HM) were exposed to isothermal oxidation using tube furnace in carbon dioxide gas to study the oxidation kinetics under the temperature of $800-1100^{\circ}C$. The kinetic equation $f=1-{\exp}(-at^b)$ was introduced and the constant b was obtained in the range of 1.02~1.42. The oxidation kinetics were evaluated by the reaction-controlling regime (RCR) depending upon the apparent activation energies with the conversion increasing from 0.2 to 0.8. The activation energies decrease from 24.7 to 21.0 kcal/mole with the conversion increasing from 0.2 to 0.8, respectively. According to the RCR, the reaction was limited by more diffusion controlling regime for the HM fibers with the conversion increasing. Therefore, it seems that the oxidation which is under the diffusion controlling regime takes place continuously from the skin to the core of the fiber.